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- /**
- * Cesium - https://github.com/AnalyticalGraphicsInc/cesium
- *
- * Copyright 2011-2017 Cesium Contributors
- *
- * Licensed under the Apache License, Version 2.0 (the "License");
- * you may not use this file except in compliance with the License.
- * You may obtain a copy of the License at
- *
- * http://www.apache.org/licenses/LICENSE-2.0
- *
- * Unless required by applicable law or agreed to in writing, software
- * distributed under the License is distributed on an "AS IS" BASIS,
- * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
- * See the License for the specific language governing permissions and
- * limitations under the License.
- *
- * Columbus View (Pat. Pend.)
- *
- * Portions licensed separately.
- * See https://github.com/AnalyticalGraphicsInc/cesium/blob/master/LICENSE.md for full licensing details.
- */
- define(['exports', './when-8d13db60', './Check-70bec281', './Math-61ede240', './Cartographic-fe4be337', './Cartesian2-85064f09', './Cartesian4-5af5bb24', './RuntimeError-ba10bc3e'], function (exports, when, Check, _Math, Cartographic, Cartesian2, Cartesian4, RuntimeError) { 'use strict';
- /**
- * A simple map projection where longitude and latitude are linearly mapped to X and Y by multiplying
- * them by the {@link Ellipsoid#maximumRadius}. This projection
- * is commonly known as geographic, equirectangular, equidistant cylindrical, or plate carrée. It
- * is also known as EPSG:4326.
- *
- * @alias GeographicProjection
- * @constructor
- *
- * @param {Ellipsoid} [ellipsoid=Ellipsoid.WGS84] The ellipsoid.
- *
- * @see WebMercatorProjection
- */
- function GeographicProjection(ellipsoid) {
- this._ellipsoid = when.defaultValue(ellipsoid, Cartesian2.Ellipsoid.WGS84);
- this._semimajorAxis = this._ellipsoid.maximumRadius;
- this._oneOverSemimajorAxis = 1.0 / this._semimajorAxis;
- }
- Object.defineProperties(GeographicProjection.prototype, {
- /**
- * Gets the {@link Ellipsoid}.
- *
- * @memberof GeographicProjection.prototype
- *
- * @type {Ellipsoid}
- * @readonly
- */
- ellipsoid : {
- get : function() {
- return this._ellipsoid;
- }
- }
- });
- /**
- * Projects a set of {@link Cartographic} coordinates, in radians, to map coordinates, in meters.
- * X and Y are the longitude and latitude, respectively, multiplied by the maximum radius of the
- * ellipsoid. Z is the unmodified height.
- *
- * @param {Cartographic} cartographic The coordinates to project.
- * @param {Cartesian3} [result] An instance into which to copy the result. If this parameter is
- * undefined, a new instance is created and returned.
- * @returns {Cartesian3} The projected coordinates. If the result parameter is not undefined, the
- * coordinates are copied there and that instance is returned. Otherwise, a new instance is
- * created and returned.
- */
- GeographicProjection.prototype.project = function(cartographic, result) {
- // Actually this is the special case of equidistant cylindrical called the plate carree
- var semimajorAxis = this._semimajorAxis;
- var x = cartographic.longitude * semimajorAxis;
- var y = cartographic.latitude * semimajorAxis;
- var z = cartographic.height;
- if (!when.defined(result)) {
- return new Cartographic.Cartesian3(x, y, z);
- }
- result.x = x;
- result.y = y;
- result.z = z;
- return result;
- };
- /**
- * Unprojects a set of projected {@link Cartesian3} coordinates, in meters, to {@link Cartographic}
- * coordinates, in radians. Longitude and Latitude are the X and Y coordinates, respectively,
- * divided by the maximum radius of the ellipsoid. Height is the unmodified Z coordinate.
- *
- * @param {Cartesian3} cartesian The Cartesian position to unproject with height (z) in meters.
- * @param {Cartographic} [result] An instance into which to copy the result. If this parameter is
- * undefined, a new instance is created and returned.
- * @returns {Cartographic} The unprojected coordinates. If the result parameter is not undefined, the
- * coordinates are copied there and that instance is returned. Otherwise, a new instance is
- * created and returned.
- */
- GeographicProjection.prototype.unproject = function(cartesian, result) {
- //>>includeStart('debug', pragmas.debug);
- if (!when.defined(cartesian)) {
- throw new Check.DeveloperError('cartesian is required');
- }
- //>>includeEnd('debug');
- var oneOverEarthSemimajorAxis = this._oneOverSemimajorAxis;
- var longitude = cartesian.x * oneOverEarthSemimajorAxis;
- var latitude = cartesian.y * oneOverEarthSemimajorAxis;
- var height = cartesian.z;
- if (!when.defined(result)) {
- return new Cartographic.Cartographic(longitude, latitude, height);
- }
- result.longitude = longitude;
- result.latitude = latitude;
- result.height = height;
- return result;
- };
- /**
- * This enumerated type is used in determining where, relative to the frustum, an
- * object is located. The object can either be fully contained within the frustum (INSIDE),
- * partially inside the frustum and partially outside (INTERSECTING), or somwhere entirely
- * outside of the frustum's 6 planes (OUTSIDE).
- *
- * @exports Intersect
- */
- var Intersect = {
- /**
- * Represents that an object is not contained within the frustum.
- *
- * @type {Number}
- * @constant
- */
- OUTSIDE : -1,
- /**
- * Represents that an object intersects one of the frustum's planes.
- *
- * @type {Number}
- * @constant
- */
- INTERSECTING : 0,
- /**
- * Represents that an object is fully within the frustum.
- *
- * @type {Number}
- * @constant
- */
- INSIDE : 1
- };
- var Intersect$1 = Object.freeze(Intersect);
- /**
- * Represents the closed interval [start, stop].
- * @alias Interval
- * @constructor
- *
- * @param {Number} [start=0.0] The beginning of the interval.
- * @param {Number} [stop=0.0] The end of the interval.
- */
- function Interval(start, stop) {
- /**
- * The beginning of the interval.
- * @type {Number}
- * @default 0.0
- */
- this.start = when.defaultValue(start, 0.0);
- /**
- * The end of the interval.
- * @type {Number}
- * @default 0.0
- */
- this.stop = when.defaultValue(stop, 0.0);
- }
- /**
- * A 3x3 matrix, indexable as a column-major order array.
- * Constructor parameters are in row-major order for code readability.
- * @alias Matrix3
- * @constructor
- *
- * @param {Number} [column0Row0=0.0] The value for column 0, row 0.
- * @param {Number} [column1Row0=0.0] The value for column 1, row 0.
- * @param {Number} [column2Row0=0.0] The value for column 2, row 0.
- * @param {Number} [column0Row1=0.0] The value for column 0, row 1.
- * @param {Number} [column1Row1=0.0] The value for column 1, row 1.
- * @param {Number} [column2Row1=0.0] The value for column 2, row 1.
- * @param {Number} [column0Row2=0.0] The value for column 0, row 2.
- * @param {Number} [column1Row2=0.0] The value for column 1, row 2.
- * @param {Number} [column2Row2=0.0] The value for column 2, row 2.
- *
- * @see Matrix3.fromColumnMajorArray
- * @see Matrix3.fromRowMajorArray
- * @see Matrix3.fromQuaternion
- * @see Matrix3.fromScale
- * @see Matrix3.fromUniformScale
- * @see Matrix2
- * @see Matrix4
- */
- function Matrix3(column0Row0, column1Row0, column2Row0,
- column0Row1, column1Row1, column2Row1,
- column0Row2, column1Row2, column2Row2) {
- this[0] = when.defaultValue(column0Row0, 0.0);
- this[1] = when.defaultValue(column0Row1, 0.0);
- this[2] = when.defaultValue(column0Row2, 0.0);
- this[3] = when.defaultValue(column1Row0, 0.0);
- this[4] = when.defaultValue(column1Row1, 0.0);
- this[5] = when.defaultValue(column1Row2, 0.0);
- this[6] = when.defaultValue(column2Row0, 0.0);
- this[7] = when.defaultValue(column2Row1, 0.0);
- this[8] = when.defaultValue(column2Row2, 0.0);
- }
- /**
- * The number of elements used to pack the object into an array.
- * @type {Number}
- */
- Matrix3.packedLength = 9;
- /**
- * Stores the provided instance into the provided array.
- *
- * @param {Matrix3} value The value to pack.
- * @param {Number[]} array The array to pack into.
- * @param {Number} [startingIndex=0] The index into the array at which to start packing the elements.
- *
- * @returns {Number[]} The array that was packed into
- */
- Matrix3.pack = function(value, array, startingIndex) {
- //>>includeStart('debug', pragmas.debug);
- Check.Check.typeOf.object('value', value);
- Check.Check.defined('array', array);
- //>>includeEnd('debug');
- startingIndex = when.defaultValue(startingIndex, 0);
- array[startingIndex++] = value[0];
- array[startingIndex++] = value[1];
- array[startingIndex++] = value[2];
- array[startingIndex++] = value[3];
- array[startingIndex++] = value[4];
- array[startingIndex++] = value[5];
- array[startingIndex++] = value[6];
- array[startingIndex++] = value[7];
- array[startingIndex++] = value[8];
- return array;
- };
- /**
- * Retrieves an instance from a packed array.
- *
- * @param {Number[]} array The packed array.
- * @param {Number} [startingIndex=0] The starting index of the element to be unpacked.
- * @param {Matrix3} [result] The object into which to store the result.
- * @returns {Matrix3} The modified result parameter or a new Matrix3 instance if one was not provided.
- */
- Matrix3.unpack = function(array, startingIndex, result) {
- //>>includeStart('debug', pragmas.debug);
- Check.Check.defined('array', array);
- //>>includeEnd('debug');
- startingIndex = when.defaultValue(startingIndex, 0);
- if (!when.defined(result)) {
- result = new Matrix3();
- }
- result[0] = array[startingIndex++];
- result[1] = array[startingIndex++];
- result[2] = array[startingIndex++];
- result[3] = array[startingIndex++];
- result[4] = array[startingIndex++];
- result[5] = array[startingIndex++];
- result[6] = array[startingIndex++];
- result[7] = array[startingIndex++];
- result[8] = array[startingIndex++];
- return result;
- };
- /**
- * Duplicates a Matrix3 instance.
- *
- * @param {Matrix3} matrix The matrix to duplicate.
- * @param {Matrix3} [result] The object onto which to store the result.
- * @returns {Matrix3} The modified result parameter or a new Matrix3 instance if one was not provided. (Returns undefined if matrix is undefined)
- */
- Matrix3.clone = function(matrix, result) {
- if (!when.defined(matrix)) {
- return undefined;
- }
- if (!when.defined(result)) {
- return new Matrix3(matrix[0], matrix[3], matrix[6],
- matrix[1], matrix[4], matrix[7],
- matrix[2], matrix[5], matrix[8]);
- }
- result[0] = matrix[0];
- result[1] = matrix[1];
- result[2] = matrix[2];
- result[3] = matrix[3];
- result[4] = matrix[4];
- result[5] = matrix[5];
- result[6] = matrix[6];
- result[7] = matrix[7];
- result[8] = matrix[8];
- return result;
- };
- /**
- * Creates a Matrix3 from 9 consecutive elements in an array.
- *
- * @param {Number[]} array The array whose 9 consecutive elements correspond to the positions of the matrix. Assumes column-major order.
- * @param {Number} [startingIndex=0] The offset into the array of the first element, which corresponds to first column first row position in the matrix.
- * @param {Matrix3} [result] The object onto which to store the result.
- * @returns {Matrix3} The modified result parameter or a new Matrix3 instance if one was not provided.
- *
- * @example
- * // Create the Matrix3:
- * // [1.0, 2.0, 3.0]
- * // [1.0, 2.0, 3.0]
- * // [1.0, 2.0, 3.0]
- *
- * var v = [1.0, 1.0, 1.0, 2.0, 2.0, 2.0, 3.0, 3.0, 3.0];
- * var m = Cesium.Matrix3.fromArray(v);
- *
- * // Create same Matrix3 with using an offset into an array
- * var v2 = [0.0, 0.0, 1.0, 1.0, 1.0, 2.0, 2.0, 2.0, 3.0, 3.0, 3.0];
- * var m2 = Cesium.Matrix3.fromArray(v2, 2);
- */
- Matrix3.fromArray = function(array, startingIndex, result) {
- //>>includeStart('debug', pragmas.debug);
- Check.Check.defined('array', array);
- //>>includeEnd('debug');
- startingIndex = when.defaultValue(startingIndex, 0);
- if (!when.defined(result)) {
- result = new Matrix3();
- }
- result[0] = array[startingIndex];
- result[1] = array[startingIndex + 1];
- result[2] = array[startingIndex + 2];
- result[3] = array[startingIndex + 3];
- result[4] = array[startingIndex + 4];
- result[5] = array[startingIndex + 5];
- result[6] = array[startingIndex + 6];
- result[7] = array[startingIndex + 7];
- result[8] = array[startingIndex + 8];
- return result;
- };
- /**
- * Creates a Matrix3 instance from a column-major order array.
- *
- * @param {Number[]} values The column-major order array.
- * @param {Matrix3} [result] The object in which the result will be stored, if undefined a new instance will be created.
- * @returns {Matrix3} The modified result parameter, or a new Matrix3 instance if one was not provided.
- */
- Matrix3.fromColumnMajorArray = function(values, result) {
- //>>includeStart('debug', pragmas.debug);
- Check.Check.defined('values', values);
- //>>includeEnd('debug');
- return Matrix3.clone(values, result);
- };
- /**
- * Creates a Matrix3 instance from a row-major order array.
- * The resulting matrix will be in column-major order.
- *
- * @param {Number[]} values The row-major order array.
- * @param {Matrix3} [result] The object in which the result will be stored, if undefined a new instance will be created.
- * @returns {Matrix3} The modified result parameter, or a new Matrix3 instance if one was not provided.
- */
- Matrix3.fromRowMajorArray = function(values, result) {
- //>>includeStart('debug', pragmas.debug);
- Check.Check.defined('values', values);
- //>>includeEnd('debug');
- if (!when.defined(result)) {
- return new Matrix3(values[0], values[1], values[2],
- values[3], values[4], values[5],
- values[6], values[7], values[8]);
- }
- result[0] = values[0];
- result[1] = values[3];
- result[2] = values[6];
- result[3] = values[1];
- result[4] = values[4];
- result[5] = values[7];
- result[6] = values[2];
- result[7] = values[5];
- result[8] = values[8];
- return result;
- };
- /**
- * Computes a 3x3 rotation matrix from the provided quaternion.
- *
- * @param {Quaternion} quaternion the quaternion to use.
- * @param {Matrix3} [result] The object in which the result will be stored, if undefined a new instance will be created.
- * @returns {Matrix3} The 3x3 rotation matrix from this quaternion.
- */
- Matrix3.fromQuaternion = function(quaternion, result) {
- //>>includeStart('debug', pragmas.debug);
- Check.Check.typeOf.object('quaternion', quaternion);
- //>>includeEnd('debug');
- var x2 = quaternion.x * quaternion.x;
- var xy = quaternion.x * quaternion.y;
- var xz = quaternion.x * quaternion.z;
- var xw = quaternion.x * quaternion.w;
- var y2 = quaternion.y * quaternion.y;
- var yz = quaternion.y * quaternion.z;
- var yw = quaternion.y * quaternion.w;
- var z2 = quaternion.z * quaternion.z;
- var zw = quaternion.z * quaternion.w;
- var w2 = quaternion.w * quaternion.w;
- var m00 = x2 - y2 - z2 + w2;
- var m01 = 2.0 * (xy - zw);
- var m02 = 2.0 * (xz + yw);
- var m10 = 2.0 * (xy + zw);
- var m11 = -x2 + y2 - z2 + w2;
- var m12 = 2.0 * (yz - xw);
- var m20 = 2.0 * (xz - yw);
- var m21 = 2.0 * (yz + xw);
- var m22 = -x2 - y2 + z2 + w2;
- if (!when.defined(result)) {
- return new Matrix3(m00, m01, m02,
- m10, m11, m12,
- m20, m21, m22);
- }
- result[0] = m00;
- result[1] = m10;
- result[2] = m20;
- result[3] = m01;
- result[4] = m11;
- result[5] = m21;
- result[6] = m02;
- result[7] = m12;
- result[8] = m22;
- return result;
- };
- /**
- * Computes a 3x3 rotation matrix from the provided headingPitchRoll. (see http://en.wikipedia.org/wiki/Conversion_between_quaternions_and_Euler_angles )
- *
- * @param {HeadingPitchRoll} headingPitchRoll the headingPitchRoll to use.
- * @param {Matrix3} [result] The object in which the result will be stored, if undefined a new instance will be created.
- * @returns {Matrix3} The 3x3 rotation matrix from this headingPitchRoll.
- */
- Matrix3.fromHeadingPitchRoll = function(headingPitchRoll, result) {
- //>>includeStart('debug', pragmas.debug);
- Check.Check.typeOf.object('headingPitchRoll', headingPitchRoll);
- //>>includeEnd('debug');
- var cosTheta = Math.cos(-headingPitchRoll.pitch);
- var cosPsi = Math.cos(-headingPitchRoll.heading);
- var cosPhi = Math.cos(headingPitchRoll.roll);
- var sinTheta = Math.sin(-headingPitchRoll.pitch);
- var sinPsi = Math.sin(-headingPitchRoll.heading);
- var sinPhi = Math.sin(headingPitchRoll.roll);
- var m00 = cosTheta * cosPsi;
- var m01 = -cosPhi * sinPsi + sinPhi * sinTheta * cosPsi;
- var m02 = sinPhi * sinPsi + cosPhi * sinTheta * cosPsi;
- var m10 = cosTheta * sinPsi;
- var m11 = cosPhi * cosPsi + sinPhi * sinTheta * sinPsi;
- var m12 = -sinPhi * cosPsi + cosPhi * sinTheta * sinPsi;
- var m20 = -sinTheta;
- var m21 = sinPhi * cosTheta;
- var m22 = cosPhi * cosTheta;
- if (!when.defined(result)) {
- return new Matrix3(m00, m01, m02,
- m10, m11, m12,
- m20, m21, m22);
- }
- result[0] = m00;
- result[1] = m10;
- result[2] = m20;
- result[3] = m01;
- result[4] = m11;
- result[5] = m21;
- result[6] = m02;
- result[7] = m12;
- result[8] = m22;
- return result;
- };
- /**
- * Computes a Matrix3 instance representing a non-uniform scale.
- *
- * @param {Cartesian3} scale The x, y, and z scale factors.
- * @param {Matrix3} [result] The object in which the result will be stored, if undefined a new instance will be created.
- * @returns {Matrix3} The modified result parameter, or a new Matrix3 instance if one was not provided.
- *
- * @example
- * // Creates
- * // [7.0, 0.0, 0.0]
- * // [0.0, 8.0, 0.0]
- * // [0.0, 0.0, 9.0]
- * var m = Cesium.Matrix3.fromScale(new Cesium.Cartesian3(7.0, 8.0, 9.0));
- */
- Matrix3.fromScale = function(scale, result) {
- //>>includeStart('debug', pragmas.debug);
- Check.Check.typeOf.object('scale', scale);
- //>>includeEnd('debug');
- if (!when.defined(result)) {
- return new Matrix3(
- scale.x, 0.0, 0.0,
- 0.0, scale.y, 0.0,
- 0.0, 0.0, scale.z);
- }
- result[0] = scale.x;
- result[1] = 0.0;
- result[2] = 0.0;
- result[3] = 0.0;
- result[4] = scale.y;
- result[5] = 0.0;
- result[6] = 0.0;
- result[7] = 0.0;
- result[8] = scale.z;
- return result;
- };
- /**
- * Computes a Matrix3 instance representing a uniform scale.
- *
- * @param {Number} scale The uniform scale factor.
- * @param {Matrix3} [result] The object in which the result will be stored, if undefined a new instance will be created.
- * @returns {Matrix3} The modified result parameter, or a new Matrix3 instance if one was not provided.
- *
- * @example
- * // Creates
- * // [2.0, 0.0, 0.0]
- * // [0.0, 2.0, 0.0]
- * // [0.0, 0.0, 2.0]
- * var m = Cesium.Matrix3.fromUniformScale(2.0);
- */
- Matrix3.fromUniformScale = function(scale, result) {
- //>>includeStart('debug', pragmas.debug);
- Check.Check.typeOf.number('scale', scale);
- //>>includeEnd('debug');
- if (!when.defined(result)) {
- return new Matrix3(
- scale, 0.0, 0.0,
- 0.0, scale, 0.0,
- 0.0, 0.0, scale);
- }
- result[0] = scale;
- result[1] = 0.0;
- result[2] = 0.0;
- result[3] = 0.0;
- result[4] = scale;
- result[5] = 0.0;
- result[6] = 0.0;
- result[7] = 0.0;
- result[8] = scale;
- return result;
- };
- /**
- * Computes a Matrix3 instance representing the cross product equivalent matrix of a Cartesian3 vector.
- *
- * @param {Cartesian3} vector the vector on the left hand side of the cross product operation.
- * @param {Matrix3} [result] The object in which the result will be stored, if undefined a new instance will be created.
- * @returns {Matrix3} The modified result parameter, or a new Matrix3 instance if one was not provided.
- *
- * @example
- * // Creates
- * // [0.0, -9.0, 8.0]
- * // [9.0, 0.0, -7.0]
- * // [-8.0, 7.0, 0.0]
- * var m = Cesium.Matrix3.fromCrossProduct(new Cesium.Cartesian3(7.0, 8.0, 9.0));
- */
- Matrix3.fromCrossProduct = function(vector, result) {
- //>>includeStart('debug', pragmas.debug);
- Check.Check.typeOf.object('vector', vector);
- //>>includeEnd('debug');
- if (!when.defined(result)) {
- return new Matrix3(
- 0.0, -vector.z, vector.y,
- vector.z, 0.0, -vector.x,
- -vector.y, vector.x, 0.0);
- }
- result[0] = 0.0;
- result[1] = vector.z;
- result[2] = -vector.y;
- result[3] = -vector.z;
- result[4] = 0.0;
- result[5] = vector.x;
- result[6] = vector.y;
- result[7] = -vector.x;
- result[8] = 0.0;
- return result;
- };
- /**
- * Creates a rotation matrix around the x-axis.
- *
- * @param {Number} angle The angle, in radians, of the rotation. Positive angles are counterclockwise.
- * @param {Matrix3} [result] The object in which the result will be stored, if undefined a new instance will be created.
- * @returns {Matrix3} The modified result parameter, or a new Matrix3 instance if one was not provided.
- *
- * @example
- * // Rotate a point 45 degrees counterclockwise around the x-axis.
- * var p = new Cesium.Cartesian3(5, 6, 7);
- * var m = Cesium.Matrix3.fromRotationX(Cesium.Math.toRadians(45.0));
- * var rotated = Cesium.Matrix3.multiplyByVector(m, p, new Cesium.Cartesian3());
- */
- Matrix3.fromRotationX = function(angle, result) {
- //>>includeStart('debug', pragmas.debug);
- Check.Check.typeOf.number('angle', angle);
- //>>includeEnd('debug');
- var cosAngle = Math.cos(angle);
- var sinAngle = Math.sin(angle);
- if (!when.defined(result)) {
- return new Matrix3(
- 1.0, 0.0, 0.0,
- 0.0, cosAngle, -sinAngle,
- 0.0, sinAngle, cosAngle);
- }
- result[0] = 1.0;
- result[1] = 0.0;
- result[2] = 0.0;
- result[3] = 0.0;
- result[4] = cosAngle;
- result[5] = sinAngle;
- result[6] = 0.0;
- result[7] = -sinAngle;
- result[8] = cosAngle;
- return result;
- };
- /**
- * Creates a rotation matrix around the y-axis.
- *
- * @param {Number} angle The angle, in radians, of the rotation. Positive angles are counterclockwise.
- * @param {Matrix3} [result] The object in which the result will be stored, if undefined a new instance will be created.
- * @returns {Matrix3} The modified result parameter, or a new Matrix3 instance if one was not provided.
- *
- * @example
- * // Rotate a point 45 degrees counterclockwise around the y-axis.
- * var p = new Cesium.Cartesian3(5, 6, 7);
- * var m = Cesium.Matrix3.fromRotationY(Cesium.Math.toRadians(45.0));
- * var rotated = Cesium.Matrix3.multiplyByVector(m, p, new Cesium.Cartesian3());
- */
- Matrix3.fromRotationY = function(angle, result) {
- //>>includeStart('debug', pragmas.debug);
- Check.Check.typeOf.number('angle', angle);
- //>>includeEnd('debug');
- var cosAngle = Math.cos(angle);
- var sinAngle = Math.sin(angle);
- if (!when.defined(result)) {
- return new Matrix3(
- cosAngle, 0.0, sinAngle,
- 0.0, 1.0, 0.0,
- -sinAngle, 0.0, cosAngle);
- }
- result[0] = cosAngle;
- result[1] = 0.0;
- result[2] = -sinAngle;
- result[3] = 0.0;
- result[4] = 1.0;
- result[5] = 0.0;
- result[6] = sinAngle;
- result[7] = 0.0;
- result[8] = cosAngle;
- return result;
- };
- /**
- * Creates a rotation matrix around the z-axis.
- *
- * @param {Number} angle The angle, in radians, of the rotation. Positive angles are counterclockwise.
- * @param {Matrix3} [result] The object in which the result will be stored, if undefined a new instance will be created.
- * @returns {Matrix3} The modified result parameter, or a new Matrix3 instance if one was not provided.
- *
- * @example
- * // Rotate a point 45 degrees counterclockwise around the z-axis.
- * var p = new Cesium.Cartesian3(5, 6, 7);
- * var m = Cesium.Matrix3.fromRotationZ(Cesium.Math.toRadians(45.0));
- * var rotated = Cesium.Matrix3.multiplyByVector(m, p, new Cesium.Cartesian3());
- */
- Matrix3.fromRotationZ = function(angle, result) {
- //>>includeStart('debug', pragmas.debug);
- Check.Check.typeOf.number('angle', angle);
- //>>includeEnd('debug');
- var cosAngle = Math.cos(angle);
- var sinAngle = Math.sin(angle);
- if (!when.defined(result)) {
- return new Matrix3(
- cosAngle, -sinAngle, 0.0,
- sinAngle, cosAngle, 0.0,
- 0.0, 0.0, 1.0);
- }
- result[0] = cosAngle;
- result[1] = sinAngle;
- result[2] = 0.0;
- result[3] = -sinAngle;
- result[4] = cosAngle;
- result[5] = 0.0;
- result[6] = 0.0;
- result[7] = 0.0;
- result[8] = 1.0;
- return result;
- };
- /**
- * Creates an Array from the provided Matrix3 instance.
- * The array will be in column-major order.
- *
- * @param {Matrix3} matrix The matrix to use..
- * @param {Number[]} [result] The Array onto which to store the result.
- * @returns {Number[]} The modified Array parameter or a new Array instance if one was not provided.
- */
- Matrix3.toArray = function(matrix, result) {
- //>>includeStart('debug', pragmas.debug);
- Check.Check.typeOf.object('matrix', matrix);
- //>>includeEnd('debug');
- if (!when.defined(result)) {
- return [matrix[0], matrix[1], matrix[2], matrix[3], matrix[4], matrix[5], matrix[6], matrix[7], matrix[8]];
- }
- result[0] = matrix[0];
- result[1] = matrix[1];
- result[2] = matrix[2];
- result[3] = matrix[3];
- result[4] = matrix[4];
- result[5] = matrix[5];
- result[6] = matrix[6];
- result[7] = matrix[7];
- result[8] = matrix[8];
- return result;
- };
- /**
- * Computes the array index of the element at the provided row and column.
- *
- * @param {Number} row The zero-based index of the row.
- * @param {Number} column The zero-based index of the column.
- * @returns {Number} The index of the element at the provided row and column.
- *
- * @exception {DeveloperError} row must be 0, 1, or 2.
- * @exception {DeveloperError} column must be 0, 1, or 2.
- *
- * @example
- * var myMatrix = new Cesium.Matrix3();
- * var column1Row0Index = Cesium.Matrix3.getElementIndex(1, 0);
- * var column1Row0 = myMatrix[column1Row0Index]
- * myMatrix[column1Row0Index] = 10.0;
- */
- Matrix3.getElementIndex = function(column, row) {
- //>>includeStart('debug', pragmas.debug);
- Check.Check.typeOf.number.greaterThanOrEquals('row', row, 0);
- Check.Check.typeOf.number.lessThanOrEquals('row', row, 2);
- Check.Check.typeOf.number.greaterThanOrEquals('column', column, 0);
- Check.Check.typeOf.number.lessThanOrEquals('column', column, 2);
- //>>includeEnd('debug');
- return column * 3 + row;
- };
- /**
- * Retrieves a copy of the matrix column at the provided index as a Cartesian3 instance.
- *
- * @param {Matrix3} matrix The matrix to use.
- * @param {Number} index The zero-based index of the column to retrieve.
- * @param {Cartesian3} result The object onto which to store the result.
- * @returns {Cartesian3} The modified result parameter.
- *
- * @exception {DeveloperError} index must be 0, 1, or 2.
- */
- Matrix3.getColumn = function(matrix, index, result) {
- //>>includeStart('debug', pragmas.debug);
- Check.Check.typeOf.object('matrix', matrix);
- Check.Check.typeOf.number.greaterThanOrEquals('index', index, 0);
- Check.Check.typeOf.number.lessThanOrEquals('index', index, 2);
- Check.Check.typeOf.object('result', result);
- //>>includeEnd('debug');
- var startIndex = index * 3;
- var x = matrix[startIndex];
- var y = matrix[startIndex + 1];
- var z = matrix[startIndex + 2];
- result.x = x;
- result.y = y;
- result.z = z;
- return result;
- };
- /**
- * Computes a new matrix that replaces the specified column in the provided matrix with the provided Cartesian3 instance.
- *
- * @param {Matrix3} matrix The matrix to use.
- * @param {Number} index The zero-based index of the column to set.
- * @param {Cartesian3} cartesian The Cartesian whose values will be assigned to the specified column.
- * @param {Matrix3} result The object onto which to store the result.
- * @returns {Matrix3} The modified result parameter.
- *
- * @exception {DeveloperError} index must be 0, 1, or 2.
- */
- Matrix3.setColumn = function(matrix, index, cartesian, result) {
- //>>includeStart('debug', pragmas.debug);
- Check.Check.typeOf.object('matrix', matrix);
- Check.Check.typeOf.number.greaterThanOrEquals('index', index, 0);
- Check.Check.typeOf.number.lessThanOrEquals('index', index, 2);
- Check.Check.typeOf.object('cartesian', cartesian);
- Check.Check.typeOf.object('result', result);
- //>>includeEnd('debug');
- result = Matrix3.clone(matrix, result);
- var startIndex = index * 3;
- result[startIndex] = cartesian.x;
- result[startIndex + 1] = cartesian.y;
- result[startIndex + 2] = cartesian.z;
- return result;
- };
- /**
- * Retrieves a copy of the matrix row at the provided index as a Cartesian3 instance.
- *
- * @param {Matrix3} matrix The matrix to use.
- * @param {Number} index The zero-based index of the row to retrieve.
- * @param {Cartesian3} result The object onto which to store the result.
- * @returns {Cartesian3} The modified result parameter.
- *
- * @exception {DeveloperError} index must be 0, 1, or 2.
- */
- Matrix3.getRow = function(matrix, index, result) {
- //>>includeStart('debug', pragmas.debug);
- Check.Check.typeOf.object('matrix', matrix);
- Check.Check.typeOf.number.greaterThanOrEquals('index', index, 0);
- Check.Check.typeOf.number.lessThanOrEquals('index', index, 2);
- Check.Check.typeOf.object('result', result);
- //>>includeEnd('debug');
- var x = matrix[index];
- var y = matrix[index + 3];
- var z = matrix[index + 6];
- result.x = x;
- result.y = y;
- result.z = z;
- return result;
- };
- /**
- * Computes a new matrix that replaces the specified row in the provided matrix with the provided Cartesian3 instance.
- *
- * @param {Matrix3} matrix The matrix to use.
- * @param {Number} index The zero-based index of the row to set.
- * @param {Cartesian3} cartesian The Cartesian whose values will be assigned to the specified row.
- * @param {Matrix3} result The object onto which to store the result.
- * @returns {Matrix3} The modified result parameter.
- *
- * @exception {DeveloperError} index must be 0, 1, or 2.
- */
- Matrix3.setRow = function(matrix, index, cartesian, result) {
- //>>includeStart('debug', pragmas.debug);
- Check.Check.typeOf.object('matrix', matrix);
- Check.Check.typeOf.number.greaterThanOrEquals('index', index, 0);
- Check.Check.typeOf.number.lessThanOrEquals('index', index, 2);
- Check.Check.typeOf.object('cartesian', cartesian);
- Check.Check.typeOf.object('result', result);
- //>>includeEnd('debug');
- result = Matrix3.clone(matrix, result);
- result[index] = cartesian.x;
- result[index + 3] = cartesian.y;
- result[index + 6] = cartesian.z;
- return result;
- };
- var scratchColumn = new Cartographic.Cartesian3();
- /**
- * Extracts the non-uniform scale assuming the matrix is an affine transformation.
- *
- * @param {Matrix3} matrix The matrix.
- * @param {Cartesian3} result The object onto which to store the result.
- * @returns {Cartesian3} The modified result parameter.
- */
- Matrix3.getScale = function(matrix, result) {
- //>>includeStart('debug', pragmas.debug);
- Check.Check.typeOf.object('matrix', matrix);
- Check.Check.typeOf.object('result', result);
- //>>includeEnd('debug');
- result.x = Cartographic.Cartesian3.magnitude(Cartographic.Cartesian3.fromElements(matrix[0], matrix[1], matrix[2], scratchColumn));
- result.y = Cartographic.Cartesian3.magnitude(Cartographic.Cartesian3.fromElements(matrix[3], matrix[4], matrix[5], scratchColumn));
- result.z = Cartographic.Cartesian3.magnitude(Cartographic.Cartesian3.fromElements(matrix[6], matrix[7], matrix[8], scratchColumn));
- return result;
- };
- var scratchScale = new Cartographic.Cartesian3();
- /**
- * Computes the maximum scale assuming the matrix is an affine transformation.
- * The maximum scale is the maximum length of the column vectors.
- *
- * @param {Matrix3} matrix The matrix.
- * @returns {Number} The maximum scale.
- */
- Matrix3.getMaximumScale = function(matrix) {
- Matrix3.getScale(matrix, scratchScale);
- return Cartographic.Cartesian3.maximumComponent(scratchScale);
- };
- /**
- * Computes the product of two matrices.
- *
- * @param {Matrix3} left The first matrix.
- * @param {Matrix3} right The second matrix.
- * @param {Matrix3} result The object onto which to store the result.
- * @returns {Matrix3} The modified result parameter.
- */
- Matrix3.multiply = function(left, right, result) {
- //>>includeStart('debug', pragmas.debug);
- Check.Check.typeOf.object('left', left);
- Check.Check.typeOf.object('right', right);
- Check.Check.typeOf.object('result', result);
- //>>includeEnd('debug');
- var column0Row0 = left[0] * right[0] + left[3] * right[1] + left[6] * right[2];
- var column0Row1 = left[1] * right[0] + left[4] * right[1] + left[7] * right[2];
- var column0Row2 = left[2] * right[0] + left[5] * right[1] + left[8] * right[2];
- var column1Row0 = left[0] * right[3] + left[3] * right[4] + left[6] * right[5];
- var column1Row1 = left[1] * right[3] + left[4] * right[4] + left[7] * right[5];
- var column1Row2 = left[2] * right[3] + left[5] * right[4] + left[8] * right[5];
- var column2Row0 = left[0] * right[6] + left[3] * right[7] + left[6] * right[8];
- var column2Row1 = left[1] * right[6] + left[4] * right[7] + left[7] * right[8];
- var column2Row2 = left[2] * right[6] + left[5] * right[7] + left[8] * right[8];
- result[0] = column0Row0;
- result[1] = column0Row1;
- result[2] = column0Row2;
- result[3] = column1Row0;
- result[4] = column1Row1;
- result[5] = column1Row2;
- result[6] = column2Row0;
- result[7] = column2Row1;
- result[8] = column2Row2;
- return result;
- };
- /**
- * Computes the sum of two matrices.
- *
- * @param {Matrix3} left The first matrix.
- * @param {Matrix3} right The second matrix.
- * @param {Matrix3} result The object onto which to store the result.
- * @returns {Matrix3} The modified result parameter.
- */
- Matrix3.add = function(left, right, result) {
- //>>includeStart('debug', pragmas.debug);
- Check.Check.typeOf.object('left', left);
- Check.Check.typeOf.object('right', right);
- Check.Check.typeOf.object('result', result);
- //>>includeEnd('debug');
- result[0] = left[0] + right[0];
- result[1] = left[1] + right[1];
- result[2] = left[2] + right[2];
- result[3] = left[3] + right[3];
- result[4] = left[4] + right[4];
- result[5] = left[5] + right[5];
- result[6] = left[6] + right[6];
- result[7] = left[7] + right[7];
- result[8] = left[8] + right[8];
- return result;
- };
- /**
- * Computes the difference of two matrices.
- *
- * @param {Matrix3} left The first matrix.
- * @param {Matrix3} right The second matrix.
- * @param {Matrix3} result The object onto which to store the result.
- * @returns {Matrix3} The modified result parameter.
- */
- Matrix3.subtract = function(left, right, result) {
- //>>includeStart('debug', pragmas.debug);
- Check.Check.typeOf.object('left', left);
- Check.Check.typeOf.object('right', right);
- Check.Check.typeOf.object('result', result);
- //>>includeEnd('debug');
- result[0] = left[0] - right[0];
- result[1] = left[1] - right[1];
- result[2] = left[2] - right[2];
- result[3] = left[3] - right[3];
- result[4] = left[4] - right[4];
- result[5] = left[5] - right[5];
- result[6] = left[6] - right[6];
- result[7] = left[7] - right[7];
- result[8] = left[8] - right[8];
- return result;
- };
- /**
- * Computes the product of a matrix and a column vector.
- *
- * @param {Matrix3} matrix The matrix.
- * @param {Cartesian3} cartesian The column.
- * @param {Cartesian3} result The object onto which to store the result.
- * @returns {Cartesian3} The modified result parameter.
- */
- Matrix3.multiplyByVector = function(matrix, cartesian, result) {
- //>>includeStart('debug', pragmas.debug);
- Check.Check.typeOf.object('matrix', matrix);
- Check.Check.typeOf.object('cartesian', cartesian);
- Check.Check.typeOf.object('result', result);
- //>>includeEnd('debug');
- var vX = cartesian.x;
- var vY = cartesian.y;
- var vZ = cartesian.z;
- var x = matrix[0] * vX + matrix[3] * vY + matrix[6] * vZ;
- var y = matrix[1] * vX + matrix[4] * vY + matrix[7] * vZ;
- var z = matrix[2] * vX + matrix[5] * vY + matrix[8] * vZ;
- result.x = x;
- result.y = y;
- result.z = z;
- return result;
- };
- /**
- * Computes the product of a matrix and a scalar.
- *
- * @param {Matrix3} matrix The matrix.
- * @param {Number} scalar The number to multiply by.
- * @param {Matrix3} result The object onto which to store the result.
- * @returns {Matrix3} The modified result parameter.
- */
- Matrix3.multiplyByScalar = function(matrix, scalar, result) {
- //>>includeStart('debug', pragmas.debug);
- Check.Check.typeOf.object('matrix', matrix);
- Check.Check.typeOf.number('scalar', scalar);
- Check.Check.typeOf.object('result', result);
- //>>includeEnd('debug');
- result[0] = matrix[0] * scalar;
- result[1] = matrix[1] * scalar;
- result[2] = matrix[2] * scalar;
- result[3] = matrix[3] * scalar;
- result[4] = matrix[4] * scalar;
- result[5] = matrix[5] * scalar;
- result[6] = matrix[6] * scalar;
- result[7] = matrix[7] * scalar;
- result[8] = matrix[8] * scalar;
- return result;
- };
- /**
- * Computes the product of a matrix times a (non-uniform) scale, as if the scale were a scale matrix.
- *
- * @param {Matrix3} matrix The matrix on the left-hand side.
- * @param {Cartesian3} scale The non-uniform scale on the right-hand side.
- * @param {Matrix3} result The object onto which to store the result.
- * @returns {Matrix3} The modified result parameter.
- *
- *
- * @example
- * // Instead of Cesium.Matrix3.multiply(m, Cesium.Matrix3.fromScale(scale), m);
- * Cesium.Matrix3.multiplyByScale(m, scale, m);
- *
- * @see Matrix3.fromScale
- * @see Matrix3.multiplyByUniformScale
- */
- Matrix3.multiplyByScale = function(matrix, scale, result) {
- //>>includeStart('debug', pragmas.debug);
- Check.Check.typeOf.object('matrix', matrix);
- Check.Check.typeOf.object('scale', scale);
- Check.Check.typeOf.object('result', result);
- //>>includeEnd('debug');
- result[0] = matrix[0] * scale.x;
- result[1] = matrix[1] * scale.x;
- result[2] = matrix[2] * scale.x;
- result[3] = matrix[3] * scale.y;
- result[4] = matrix[4] * scale.y;
- result[5] = matrix[5] * scale.y;
- result[6] = matrix[6] * scale.z;
- result[7] = matrix[7] * scale.z;
- result[8] = matrix[8] * scale.z;
- return result;
- };
- /**
- * Creates a negated copy of the provided matrix.
- *
- * @param {Matrix3} matrix The matrix to negate.
- * @param {Matrix3} result The object onto which to store the result.
- * @returns {Matrix3} The modified result parameter.
- */
- Matrix3.negate = function(matrix, result) {
- //>>includeStart('debug', pragmas.debug);
- Check.Check.typeOf.object('matrix', matrix);
- Check.Check.typeOf.object('result', result);
- //>>includeEnd('debug');
- result[0] = -matrix[0];
- result[1] = -matrix[1];
- result[2] = -matrix[2];
- result[3] = -matrix[3];
- result[4] = -matrix[4];
- result[5] = -matrix[5];
- result[6] = -matrix[6];
- result[7] = -matrix[7];
- result[8] = -matrix[8];
- return result;
- };
- /**
- * Computes the transpose of the provided matrix.
- *
- * @param {Matrix3} matrix The matrix to transpose.
- * @param {Matrix3} result The object onto which to store the result.
- * @returns {Matrix3} The modified result parameter.
- */
- Matrix3.transpose = function(matrix, result) {
- //>>includeStart('debug', pragmas.debug);
- Check.Check.typeOf.object('matrix', matrix);
- Check.Check.typeOf.object('result', result);
- //>>includeEnd('debug');
- var column0Row0 = matrix[0];
- var column0Row1 = matrix[3];
- var column0Row2 = matrix[6];
- var column1Row0 = matrix[1];
- var column1Row1 = matrix[4];
- var column1Row2 = matrix[7];
- var column2Row0 = matrix[2];
- var column2Row1 = matrix[5];
- var column2Row2 = matrix[8];
- result[0] = column0Row0;
- result[1] = column0Row1;
- result[2] = column0Row2;
- result[3] = column1Row0;
- result[4] = column1Row1;
- result[5] = column1Row2;
- result[6] = column2Row0;
- result[7] = column2Row1;
- result[8] = column2Row2;
- return result;
- };
- var UNIT = new Cartographic.Cartesian3(1, 1, 1);
- /**
- * Extracts the rotation assuming the matrix is an affine transformation.
- *
- * @param {Matrix3} matrix The matrix.
- * @param {Matrix3} result The object onto which to store the result.
- * @returns {Matrix3} The modified result parameter
- */
- Matrix3.getRotation = function(matrix, result) {
- //>>includeStart('debug', pragmas.debug);
- Check.Check.typeOf.object('matrix', matrix);
- Check.Check.typeOf.object('result', result);
- //>>includeEnd('debug');
- var inverseScale = Cartographic.Cartesian3.divideComponents(UNIT, Matrix3.getScale(matrix, scratchScale), scratchScale);
- result = Matrix3.multiplyByScale(matrix, inverseScale, result);
- return result;
- };
- function computeFrobeniusNorm(matrix) {
- var norm = 0.0;
- for (var i = 0; i < 9; ++i) {
- var temp = matrix[i];
- norm += temp * temp;
- }
- return Math.sqrt(norm);
- }
- var rowVal = [1, 0, 0];
- var colVal = [2, 2, 1];
- function offDiagonalFrobeniusNorm(matrix) {
- // Computes the "off-diagonal" Frobenius norm.
- // Assumes matrix is symmetric.
- var norm = 0.0;
- for (var i = 0; i < 3; ++i) {
- var temp = matrix[Matrix3.getElementIndex(colVal[i], rowVal[i])];
- norm += 2.0 * temp * temp;
- }
- return Math.sqrt(norm);
- }
- function shurDecomposition(matrix, result) {
- // This routine was created based upon Matrix Computations, 3rd ed., by Golub and Van Loan,
- // section 8.4.2 The 2by2 Symmetric Schur Decomposition.
- //
- // The routine takes a matrix, which is assumed to be symmetric, and
- // finds the largest off-diagonal term, and then creates
- // a matrix (result) which can be used to help reduce it
- var tolerance = _Math.CesiumMath.EPSILON15;
- var maxDiagonal = 0.0;
- var rotAxis = 1;
- // find pivot (rotAxis) based on max diagonal of matrix
- for (var i = 0; i < 3; ++i) {
- var temp = Math.abs(matrix[Matrix3.getElementIndex(colVal[i], rowVal[i])]);
- if (temp > maxDiagonal) {
- rotAxis = i;
- maxDiagonal = temp;
- }
- }
- var c = 1.0;
- var s = 0.0;
- var p = rowVal[rotAxis];
- var q = colVal[rotAxis];
- if (Math.abs(matrix[Matrix3.getElementIndex(q, p)]) > tolerance) {
- var qq = matrix[Matrix3.getElementIndex(q, q)];
- var pp = matrix[Matrix3.getElementIndex(p, p)];
- var qp = matrix[Matrix3.getElementIndex(q, p)];
- var tau = (qq - pp) / 2.0 / qp;
- var t;
- if (tau < 0.0) {
- t = -1.0 / (-tau + Math.sqrt(1.0 + tau * tau));
- } else {
- t = 1.0 / (tau + Math.sqrt(1.0 + tau * tau));
- }
- c = 1.0 / Math.sqrt(1.0 + t * t);
- s = t * c;
- }
- result = Matrix3.clone(Matrix3.IDENTITY, result);
- result[Matrix3.getElementIndex(p, p)] = result[Matrix3.getElementIndex(q, q)] = c;
- result[Matrix3.getElementIndex(q, p)] = s;
- result[Matrix3.getElementIndex(p, q)] = -s;
- return result;
- }
- var jMatrix = new Matrix3();
- var jMatrixTranspose = new Matrix3();
- /**
- * Computes the eigenvectors and eigenvalues of a symmetric matrix.
- * <p>
- * Returns a diagonal matrix and unitary matrix such that:
- * <code>matrix = unitary matrix * diagonal matrix * transpose(unitary matrix)</code>
- * </p>
- * <p>
- * The values along the diagonal of the diagonal matrix are the eigenvalues. The columns
- * of the unitary matrix are the corresponding eigenvectors.
- * </p>
- *
- * @param {Matrix3} matrix The matrix to decompose into diagonal and unitary matrix. Expected to be symmetric.
- * @param {Object} [result] An object with unitary and diagonal properties which are matrices onto which to store the result.
- * @returns {Object} An object with unitary and diagonal properties which are the unitary and diagonal matrices, respectively.
- *
- * @example
- * var a = //... symetric matrix
- * var result = {
- * unitary : new Cesium.Matrix3(),
- * diagonal : new Cesium.Matrix3()
- * };
- * Cesium.Matrix3.computeEigenDecomposition(a, result);
- *
- * var unitaryTranspose = Cesium.Matrix3.transpose(result.unitary, new Cesium.Matrix3());
- * var b = Cesium.Matrix3.multiply(result.unitary, result.diagonal, new Cesium.Matrix3());
- * Cesium.Matrix3.multiply(b, unitaryTranspose, b); // b is now equal to a
- *
- * var lambda = Cesium.Matrix3.getColumn(result.diagonal, 0, new Cesium.Cartesian3()).x; // first eigenvalue
- * var v = Cesium.Matrix3.getColumn(result.unitary, 0, new Cesium.Cartesian3()); // first eigenvector
- * var c = Cesium.Cartesian3.multiplyByScalar(v, lambda, new Cesium.Cartesian3()); // equal to Cesium.Matrix3.multiplyByVector(a, v)
- */
- Matrix3.computeEigenDecomposition = function(matrix, result) {
- //>>includeStart('debug', pragmas.debug);
- Check.Check.typeOf.object('matrix', matrix);
- //>>includeEnd('debug');
- // This routine was created based upon Matrix Computations, 3rd ed., by Golub and Van Loan,
- // section 8.4.3 The Classical Jacobi Algorithm
- var tolerance = _Math.CesiumMath.EPSILON20;
- var maxSweeps = 10;
- var count = 0;
- var sweep = 0;
- if (!when.defined(result)) {
- result = {};
- }
- var unitaryMatrix = result.unitary = Matrix3.clone(Matrix3.IDENTITY, result.unitary);
- var diagMatrix = result.diagonal = Matrix3.clone(matrix, result.diagonal);
- var epsilon = tolerance * computeFrobeniusNorm(diagMatrix);
- while (sweep < maxSweeps && offDiagonalFrobeniusNorm(diagMatrix) > epsilon) {
- shurDecomposition(diagMatrix, jMatrix);
- Matrix3.transpose(jMatrix, jMatrixTranspose);
- Matrix3.multiply(diagMatrix, jMatrix, diagMatrix);
- Matrix3.multiply(jMatrixTranspose, diagMatrix, diagMatrix);
- Matrix3.multiply(unitaryMatrix, jMatrix, unitaryMatrix);
- if (++count > 2) {
- ++sweep;
- count = 0;
- }
- }
- return result;
- };
- /**
- * Computes a matrix, which contains the absolute (unsigned) values of the provided matrix's elements.
- *
- * @param {Matrix3} matrix The matrix with signed elements.
- * @param {Matrix3} result The object onto which to store the result.
- * @returns {Matrix3} The modified result parameter.
- */
- Matrix3.abs = function(matrix, result) {
- //>>includeStart('debug', pragmas.debug);
- Check.Check.typeOf.object('matrix', matrix);
- Check.Check.typeOf.object('result', result);
- //>>includeEnd('debug');
- result[0] = Math.abs(matrix[0]);
- result[1] = Math.abs(matrix[1]);
- result[2] = Math.abs(matrix[2]);
- result[3] = Math.abs(matrix[3]);
- result[4] = Math.abs(matrix[4]);
- result[5] = Math.abs(matrix[5]);
- result[6] = Math.abs(matrix[6]);
- result[7] = Math.abs(matrix[7]);
- result[8] = Math.abs(matrix[8]);
- return result;
- };
- /**
- * Computes the determinant of the provided matrix.
- *
- * @param {Matrix3} matrix The matrix to use.
- * @returns {Number} The value of the determinant of the matrix.
- */
- Matrix3.determinant = function(matrix) {
- //>>includeStart('debug', pragmas.debug);
- Check.Check.typeOf.object('matrix', matrix);
- //>>includeEnd('debug');
- var m11 = matrix[0];
- var m21 = matrix[3];
- var m31 = matrix[6];
- var m12 = matrix[1];
- var m22 = matrix[4];
- var m32 = matrix[7];
- var m13 = matrix[2];
- var m23 = matrix[5];
- var m33 = matrix[8];
- return m11 * (m22 * m33 - m23 * m32) + m12 * (m23 * m31 - m21 * m33) + m13 * (m21 * m32 - m22 * m31);
- };
- /**
- * Computes the inverse of the provided matrix.
- *
- * @param {Matrix3} matrix The matrix to invert.
- * @param {Matrix3} result The object onto which to store the result.
- * @returns {Matrix3} The modified result parameter.
- *
- * @exception {DeveloperError} matrix is not invertible.
- */
- Matrix3.inverse = function(matrix, result) {
- //>>includeStart('debug', pragmas.debug);
- Check.Check.typeOf.object('matrix', matrix);
- Check.Check.typeOf.object('result', result);
- //>>includeEnd('debug');
- var m11 = matrix[0];
- var m21 = matrix[1];
- var m31 = matrix[2];
- var m12 = matrix[3];
- var m22 = matrix[4];
- var m32 = matrix[5];
- var m13 = matrix[6];
- var m23 = matrix[7];
- var m33 = matrix[8];
- var determinant = Matrix3.determinant(matrix);
- //>>includeStart('debug', pragmas.debug);
- if (Math.abs(determinant) <= _Math.CesiumMath.EPSILON15) {
- throw new Check.DeveloperError('matrix is not invertible');
- }
- //>>includeEnd('debug');
- result[0] = m22 * m33 - m23 * m32;
- result[1] = m23 * m31 - m21 * m33;
- result[2] = m21 * m32 - m22 * m31;
- result[3] = m13 * m32 - m12 * m33;
- result[4] = m11 * m33 - m13 * m31;
- result[5] = m12 * m31 - m11 * m32;
- result[6] = m12 * m23 - m13 * m22;
- result[7] = m13 * m21 - m11 * m23;
- result[8] = m11 * m22 - m12 * m21;
- var scale = 1.0 / determinant;
- return Matrix3.multiplyByScalar(result, scale, result);
- };
- /**
- * Compares the provided matrices componentwise and returns
- * <code>true</code> if they are equal, <code>false</code> otherwise.
- *
- * @param {Matrix3} [left] The first matrix.
- * @param {Matrix3} [right] The second matrix.
- * @returns {Boolean} <code>true</code> if left and right are equal, <code>false</code> otherwise.
- */
- Matrix3.equals = function(left, right) {
- return (left === right) ||
- (when.defined(left) &&
- when.defined(right) &&
- left[0] === right[0] &&
- left[1] === right[1] &&
- left[2] === right[2] &&
- left[3] === right[3] &&
- left[4] === right[4] &&
- left[5] === right[5] &&
- left[6] === right[6] &&
- left[7] === right[7] &&
- left[8] === right[8]);
- };
- /**
- * Compares the provided matrices componentwise and returns
- * <code>true</code> if they are within the provided epsilon,
- * <code>false</code> otherwise.
- *
- * @param {Matrix3} [left] The first matrix.
- * @param {Matrix3} [right] The second matrix.
- * @param {Number} epsilon The epsilon to use for equality testing.
- * @returns {Boolean} <code>true</code> if left and right are within the provided epsilon, <code>false</code> otherwise.
- */
- Matrix3.equalsEpsilon = function(left, right, epsilon) {
- //>>includeStart('debug', pragmas.debug);
- Check.Check.typeOf.number('epsilon', epsilon);
- //>>includeEnd('debug');
- return (left === right) ||
- (when.defined(left) &&
- when.defined(right) &&
- Math.abs(left[0] - right[0]) <= epsilon &&
- Math.abs(left[1] - right[1]) <= epsilon &&
- Math.abs(left[2] - right[2]) <= epsilon &&
- Math.abs(left[3] - right[3]) <= epsilon &&
- Math.abs(left[4] - right[4]) <= epsilon &&
- Math.abs(left[5] - right[5]) <= epsilon &&
- Math.abs(left[6] - right[6]) <= epsilon &&
- Math.abs(left[7] - right[7]) <= epsilon &&
- Math.abs(left[8] - right[8]) <= epsilon);
- };
- /**
- * An immutable Matrix3 instance initialized to the identity matrix.
- *
- * @type {Matrix3}
- * @constant
- */
- Matrix3.IDENTITY = Object.freeze(new Matrix3(1.0, 0.0, 0.0,
- 0.0, 1.0, 0.0,
- 0.0, 0.0, 1.0));
- /**
- * An immutable Matrix3 instance initialized to the zero matrix.
- *
- * @type {Matrix3}
- * @constant
- */
- Matrix3.ZERO = Object.freeze(new Matrix3(0.0, 0.0, 0.0,
- 0.0, 0.0, 0.0,
- 0.0, 0.0, 0.0));
- /**
- * The index into Matrix3 for column 0, row 0.
- *
- * @type {Number}
- * @constant
- */
- Matrix3.COLUMN0ROW0 = 0;
- /**
- * The index into Matrix3 for column 0, row 1.
- *
- * @type {Number}
- * @constant
- */
- Matrix3.COLUMN0ROW1 = 1;
- /**
- * The index into Matrix3 for column 0, row 2.
- *
- * @type {Number}
- * @constant
- */
- Matrix3.COLUMN0ROW2 = 2;
- /**
- * The index into Matrix3 for column 1, row 0.
- *
- * @type {Number}
- * @constant
- */
- Matrix3.COLUMN1ROW0 = 3;
- /**
- * The index into Matrix3 for column 1, row 1.
- *
- * @type {Number}
- * @constant
- */
- Matrix3.COLUMN1ROW1 = 4;
- /**
- * The index into Matrix3 for column 1, row 2.
- *
- * @type {Number}
- * @constant
- */
- Matrix3.COLUMN1ROW2 = 5;
- /**
- * The index into Matrix3 for column 2, row 0.
- *
- * @type {Number}
- * @constant
- */
- Matrix3.COLUMN2ROW0 = 6;
- /**
- * The index into Matrix3 for column 2, row 1.
- *
- * @type {Number}
- * @constant
- */
- Matrix3.COLUMN2ROW1 = 7;
- /**
- * The index into Matrix3 for column 2, row 2.
- *
- * @type {Number}
- * @constant
- */
- Matrix3.COLUMN2ROW2 = 8;
- Object.defineProperties(Matrix3.prototype, {
- /**
- * Gets the number of items in the collection.
- * @memberof Matrix3.prototype
- *
- * @type {Number}
- */
- length : {
- get : function() {
- return Matrix3.packedLength;
- }
- }
- });
- /**
- * Duplicates the provided Matrix3 instance.
- *
- * @param {Matrix3} [result] The object onto which to store the result.
- * @returns {Matrix3} The modified result parameter or a new Matrix3 instance if one was not provided.
- */
- Matrix3.prototype.clone = function(result) {
- return Matrix3.clone(this, result);
- };
- /**
- * Compares this matrix to the provided matrix componentwise and returns
- * <code>true</code> if they are equal, <code>false</code> otherwise.
- *
- * @param {Matrix3} [right] The right hand side matrix.
- * @returns {Boolean} <code>true</code> if they are equal, <code>false</code> otherwise.
- */
- Matrix3.prototype.equals = function(right) {
- return Matrix3.equals(this, right);
- };
- /**
- * @private
- */
- Matrix3.equalsArray = function(matrix, array, offset) {
- return matrix[0] === array[offset] &&
- matrix[1] === array[offset + 1] &&
- matrix[2] === array[offset + 2] &&
- matrix[3] === array[offset + 3] &&
- matrix[4] === array[offset + 4] &&
- matrix[5] === array[offset + 5] &&
- matrix[6] === array[offset + 6] &&
- matrix[7] === array[offset + 7] &&
- matrix[8] === array[offset + 8];
- };
- /**
- * Compares this matrix to the provided matrix componentwise and returns
- * <code>true</code> if they are within the provided epsilon,
- * <code>false</code> otherwise.
- *
- * @param {Matrix3} [right] The right hand side matrix.
- * @param {Number} epsilon The epsilon to use for equality testing.
- * @returns {Boolean} <code>true</code> if they are within the provided epsilon, <code>false</code> otherwise.
- */
- Matrix3.prototype.equalsEpsilon = function(right, epsilon) {
- return Matrix3.equalsEpsilon(this, right, epsilon);
- };
- /**
- * Creates a string representing this Matrix with each row being
- * on a separate line and in the format '(column0, column1, column2)'.
- *
- * @returns {String} A string representing the provided Matrix with each row being on a separate line and in the format '(column0, column1, column2)'.
- */
- Matrix3.prototype.toString = function() {
- return '(' + this[0] + ', ' + this[3] + ', ' + this[6] + ')\n' +
- '(' + this[1] + ', ' + this[4] + ', ' + this[7] + ')\n' +
- '(' + this[2] + ', ' + this[5] + ', ' + this[8] + ')';
- };
- /**
- * A 4x4 matrix, indexable as a column-major order array.
- * Constructor parameters are in row-major order for code readability.
- * @alias Matrix4
- * @constructor
- *
- * @param {Number} [column0Row0=0.0] The value for column 0, row 0.
- * @param {Number} [column1Row0=0.0] The value for column 1, row 0.
- * @param {Number} [column2Row0=0.0] The value for column 2, row 0.
- * @param {Number} [column3Row0=0.0] The value for column 3, row 0.
- * @param {Number} [column0Row1=0.0] The value for column 0, row 1.
- * @param {Number} [column1Row1=0.0] The value for column 1, row 1.
- * @param {Number} [column2Row1=0.0] The value for column 2, row 1.
- * @param {Number} [column3Row1=0.0] The value for column 3, row 1.
- * @param {Number} [column0Row2=0.0] The value for column 0, row 2.
- * @param {Number} [column1Row2=0.0] The value for column 1, row 2.
- * @param {Number} [column2Row2=0.0] The value for column 2, row 2.
- * @param {Number} [column3Row2=0.0] The value for column 3, row 2.
- * @param {Number} [column0Row3=0.0] The value for column 0, row 3.
- * @param {Number} [column1Row3=0.0] The value for column 1, row 3.
- * @param {Number} [column2Row3=0.0] The value for column 2, row 3.
- * @param {Number} [column3Row3=0.0] The value for column 3, row 3.
- *
- * @see Matrix4.fromColumnMajorArray
- * @see Matrix4.fromRowMajorArray
- * @see Matrix4.fromRotationTranslation
- * @see Matrix4.fromTranslationRotationScale
- * @see Matrix4.fromTranslationQuaternionRotationScale
- * @see Matrix4.fromTranslation
- * @see Matrix4.fromScale
- * @see Matrix4.fromUniformScale
- * @see Matrix4.fromCamera
- * @see Matrix4.computePerspectiveFieldOfView
- * @see Matrix4.computeOrthographicOffCenter
- * @see Matrix4.computePerspectiveOffCenter
- * @see Matrix4.computeInfinitePerspectiveOffCenter
- * @see Matrix4.computeViewportTransformation
- * @see Matrix4.computeView
- * @see Matrix2
- * @see Matrix3
- * @see Packable
- */
- function Matrix4(column0Row0, column1Row0, column2Row0, column3Row0,
- column0Row1, column1Row1, column2Row1, column3Row1,
- column0Row2, column1Row2, column2Row2, column3Row2,
- column0Row3, column1Row3, column2Row3, column3Row3) {
- this[0] = when.defaultValue(column0Row0, 0.0);
- this[1] = when.defaultValue(column0Row1, 0.0);
- this[2] = when.defaultValue(column0Row2, 0.0);
- this[3] = when.defaultValue(column0Row3, 0.0);
- this[4] = when.defaultValue(column1Row0, 0.0);
- this[5] = when.defaultValue(column1Row1, 0.0);
- this[6] = when.defaultValue(column1Row2, 0.0);
- this[7] = when.defaultValue(column1Row3, 0.0);
- this[8] = when.defaultValue(column2Row0, 0.0);
- this[9] = when.defaultValue(column2Row1, 0.0);
- this[10] = when.defaultValue(column2Row2, 0.0);
- this[11] = when.defaultValue(column2Row3, 0.0);
- this[12] = when.defaultValue(column3Row0, 0.0);
- this[13] = when.defaultValue(column3Row1, 0.0);
- this[14] = when.defaultValue(column3Row2, 0.0);
- this[15] = when.defaultValue(column3Row3, 0.0);
- }
- /**
- * The number of elements used to pack the object into an array.
- * @type {Number}
- */
- Matrix4.packedLength = 16;
- /**
- * Stores the provided instance into the provided array.
- *
- * @param {Matrix4} value The value to pack.
- * @param {Number[]} array The array to pack into.
- * @param {Number} [startingIndex=0] The index into the array at which to start packing the elements.
- *
- * @returns {Number[]} The array that was packed into
- */
- Matrix4.pack = function(value, array, startingIndex) {
- //>>includeStart('debug', pragmas.debug);
- Check.Check.typeOf.object('value', value);
- Check.Check.defined('array', array);
- //>>includeEnd('debug');
- startingIndex = when.defaultValue(startingIndex, 0);
- array[startingIndex++] = value[0];
- array[startingIndex++] = value[1];
- array[startingIndex++] = value[2];
- array[startingIndex++] = value[3];
- array[startingIndex++] = value[4];
- array[startingIndex++] = value[5];
- array[startingIndex++] = value[6];
- array[startingIndex++] = value[7];
- array[startingIndex++] = value[8];
- array[startingIndex++] = value[9];
- array[startingIndex++] = value[10];
- array[startingIndex++] = value[11];
- array[startingIndex++] = value[12];
- array[startingIndex++] = value[13];
- array[startingIndex++] = value[14];
- array[startingIndex] = value[15];
- return array;
- };
- /**
- * Retrieves an instance from a packed array.
- *
- * @param {Number[]} array The packed array.
- * @param {Number} [startingIndex=0] The starting index of the element to be unpacked.
- * @param {Matrix4} [result] The object into which to store the result.
- * @returns {Matrix4} The modified result parameter or a new Matrix4 instance if one was not provided.
- */
- Matrix4.unpack = function(array, startingIndex, result) {
- //>>includeStart('debug', pragmas.debug);
- Check.Check.defined('array', array);
- //>>includeEnd('debug');
- startingIndex = when.defaultValue(startingIndex, 0);
- if (!when.defined(result)) {
- result = new Matrix4();
- }
- result[0] = array[startingIndex++];
- result[1] = array[startingIndex++];
- result[2] = array[startingIndex++];
- result[3] = array[startingIndex++];
- result[4] = array[startingIndex++];
- result[5] = array[startingIndex++];
- result[6] = array[startingIndex++];
- result[7] = array[startingIndex++];
- result[8] = array[startingIndex++];
- result[9] = array[startingIndex++];
- result[10] = array[startingIndex++];
- result[11] = array[startingIndex++];
- result[12] = array[startingIndex++];
- result[13] = array[startingIndex++];
- result[14] = array[startingIndex++];
- result[15] = array[startingIndex];
- return result;
- };
- /**
- * Duplicates a Matrix4 instance.
- *
- * @param {Matrix4} matrix The matrix to duplicate.
- * @param {Matrix4} [result] The object onto which to store the result.
- * @returns {Matrix4} The modified result parameter or a new Matrix4 instance if one was not provided. (Returns undefined if matrix is undefined)
- */
- Matrix4.clone = function(matrix, result) {
- if (!when.defined(matrix)) {
- return undefined;
- }
- if (!when.defined(result)) {
- return new Matrix4(matrix[0], matrix[4], matrix[8], matrix[12],
- matrix[1], matrix[5], matrix[9], matrix[13],
- matrix[2], matrix[6], matrix[10], matrix[14],
- matrix[3], matrix[7], matrix[11], matrix[15]);
- }
- result[0] = matrix[0];
- result[1] = matrix[1];
- result[2] = matrix[2];
- result[3] = matrix[3];
- result[4] = matrix[4];
- result[5] = matrix[5];
- result[6] = matrix[6];
- result[7] = matrix[7];
- result[8] = matrix[8];
- result[9] = matrix[9];
- result[10] = matrix[10];
- result[11] = matrix[11];
- result[12] = matrix[12];
- result[13] = matrix[13];
- result[14] = matrix[14];
- result[15] = matrix[15];
- return result;
- };
- /**
- * Creates a Matrix4 from 16 consecutive elements in an array.
- * @function
- *
- * @param {Number[]} array The array whose 16 consecutive elements correspond to the positions of the matrix. Assumes column-major order.
- * @param {Number} [startingIndex=0] The offset into the array of the first element, which corresponds to first column first row position in the matrix.
- * @param {Matrix4} [result] The object onto which to store the result.
- * @returns {Matrix4} The modified result parameter or a new Matrix4 instance if one was not provided.
- *
- * @example
- * // Create the Matrix4:
- * // [1.0, 2.0, 3.0, 4.0]
- * // [1.0, 2.0, 3.0, 4.0]
- * // [1.0, 2.0, 3.0, 4.0]
- * // [1.0, 2.0, 3.0, 4.0]
- *
- * var v = [1.0, 1.0, 1.0, 1.0, 2.0, 2.0, 2.0, 2.0, 3.0, 3.0, 3.0, 3.0, 4.0, 4.0, 4.0, 4.0];
- * var m = Cesium.Matrix4.fromArray(v);
- *
- * // Create same Matrix4 with using an offset into an array
- * var v2 = [0.0, 0.0, 1.0, 1.0, 1.0, 1.0, 2.0, 2.0, 2.0, 2.0, 3.0, 3.0, 3.0, 3.0, 4.0, 4.0, 4.0, 4.0];
- * var m2 = Cesium.Matrix4.fromArray(v2, 2);
- */
- Matrix4.fromArray = Matrix4.unpack;
- /**
- * Computes a Matrix4 instance from a column-major order array.
- *
- * @param {Number[]} values The column-major order array.
- * @param {Matrix4} [result] The object in which the result will be stored, if undefined a new instance will be created.
- * @returns {Matrix4} The modified result parameter, or a new Matrix4 instance if one was not provided.
- */
- Matrix4.fromColumnMajorArray = function(values, result) {
- //>>includeStart('debug', pragmas.debug);
- Check.Check.defined('values', values);
- //>>includeEnd('debug');
- return Matrix4.clone(values, result);
- };
- /**
- * Computes a Matrix4 instance from a row-major order array.
- * The resulting matrix will be in column-major order.
- *
- * @param {Number[]} values The row-major order array.
- * @param {Matrix4} [result] The object in which the result will be stored, if undefined a new instance will be created.
- * @returns {Matrix4} The modified result parameter, or a new Matrix4 instance if one was not provided.
- */
- Matrix4.fromRowMajorArray = function(values, result) {
- //>>includeStart('debug', pragmas.debug);
- Check.Check.defined('values', values);
- //>>includeEnd('debug');
- if (!when.defined(result)) {
- return new Matrix4(values[0], values[1], values[2], values[3],
- values[4], values[5], values[6], values[7],
- values[8], values[9], values[10], values[11],
- values[12], values[13], values[14], values[15]);
- }
- result[0] = values[0];
- result[1] = values[4];
- result[2] = values[8];
- result[3] = values[12];
- result[4] = values[1];
- result[5] = values[5];
- result[6] = values[9];
- result[7] = values[13];
- result[8] = values[2];
- result[9] = values[6];
- result[10] = values[10];
- result[11] = values[14];
- result[12] = values[3];
- result[13] = values[7];
- result[14] = values[11];
- result[15] = values[15];
- return result;
- };
- /**
- * Computes a Matrix4 instance from a Matrix3 representing the rotation
- * and a Cartesian3 representing the translation.
- *
- * @param {Matrix3} rotation The upper left portion of the matrix representing the rotation.
- * @param {Cartesian3} [translation=Cartesian3.ZERO] The upper right portion of the matrix representing the translation.
- * @param {Matrix4} [result] The object in which the result will be stored, if undefined a new instance will be created.
- * @returns {Matrix4} The modified result parameter, or a new Matrix4 instance if one was not provided.
- */
- Matrix4.fromRotationTranslation = function(rotation, translation, result) {
- //>>includeStart('debug', pragmas.debug);
- Check.Check.typeOf.object('rotation', rotation);
- //>>includeEnd('debug');
- translation = when.defaultValue(translation, Cartographic.Cartesian3.ZERO);
- if (!when.defined(result)) {
- return new Matrix4(rotation[0], rotation[3], rotation[6], translation.x,
- rotation[1], rotation[4], rotation[7], translation.y,
- rotation[2], rotation[5], rotation[8], translation.z,
- 0.0, 0.0, 0.0, 1.0);
- }
- result[0] = rotation[0];
- result[1] = rotation[1];
- result[2] = rotation[2];
- result[3] = 0.0;
- result[4] = rotation[3];
- result[5] = rotation[4];
- result[6] = rotation[5];
- result[7] = 0.0;
- result[8] = rotation[6];
- result[9] = rotation[7];
- result[10] = rotation[8];
- result[11] = 0.0;
- result[12] = translation.x;
- result[13] = translation.y;
- result[14] = translation.z;
- result[15] = 1.0;
- return result;
- };
- /**
- * Computes a Matrix4 instance from a translation, rotation, and scale (TRS)
- * representation with the rotation represented as a quaternion.
- *
- * @param {Cartesian3} translation The translation transformation.
- * @param {Quaternion} rotation The rotation transformation.
- * @param {Cartesian3} scale The non-uniform scale transformation.
- * @param {Matrix4} [result] The object in which the result will be stored, if undefined a new instance will be created.
- * @returns {Matrix4} The modified result parameter, or a new Matrix4 instance if one was not provided.
- *
- * @example
- * var result = Cesium.Matrix4.fromTranslationQuaternionRotationScale(
- * new Cesium.Cartesian3(1.0, 2.0, 3.0), // translation
- * Cesium.Quaternion.IDENTITY, // rotation
- * new Cesium.Cartesian3(7.0, 8.0, 9.0), // scale
- * result);
- */
- Matrix4.fromTranslationQuaternionRotationScale = function(translation, rotation, scale, result) {
- //>>includeStart('debug', pragmas.debug);
- Check.Check.typeOf.object('translation', translation);
- Check.Check.typeOf.object('rotation', rotation);
- Check.Check.typeOf.object('scale', scale);
- //>>includeEnd('debug');
- if (!when.defined(result)) {
- result = new Matrix4();
- }
- var scaleX = scale.x;
- var scaleY = scale.y;
- var scaleZ = scale.z;
- var x2 = rotation.x * rotation.x;
- var xy = rotation.x * rotation.y;
- var xz = rotation.x * rotation.z;
- var xw = rotation.x * rotation.w;
- var y2 = rotation.y * rotation.y;
- var yz = rotation.y * rotation.z;
- var yw = rotation.y * rotation.w;
- var z2 = rotation.z * rotation.z;
- var zw = rotation.z * rotation.w;
- var w2 = rotation.w * rotation.w;
- var m00 = x2 - y2 - z2 + w2;
- var m01 = 2.0 * (xy - zw);
- var m02 = 2.0 * (xz + yw);
- var m10 = 2.0 * (xy + zw);
- var m11 = -x2 + y2 - z2 + w2;
- var m12 = 2.0 * (yz - xw);
- var m20 = 2.0 * (xz - yw);
- var m21 = 2.0 * (yz + xw);
- var m22 = -x2 - y2 + z2 + w2;
- result[0] = m00 * scaleX;
- result[1] = m10 * scaleX;
- result[2] = m20 * scaleX;
- result[3] = 0.0;
- result[4] = m01 * scaleY;
- result[5] = m11 * scaleY;
- result[6] = m21 * scaleY;
- result[7] = 0.0;
- result[8] = m02 * scaleZ;
- result[9] = m12 * scaleZ;
- result[10] = m22 * scaleZ;
- result[11] = 0.0;
- result[12] = translation.x;
- result[13] = translation.y;
- result[14] = translation.z;
- result[15] = 1.0;
- return result;
- };
- /**
- * Creates a Matrix4 instance from a {@link TranslationRotationScale} instance.
- *
- * @param {TranslationRotationScale} translationRotationScale The instance.
- * @param {Matrix4} [result] The object in which the result will be stored, if undefined a new instance will be created.
- * @returns {Matrix4} The modified result parameter, or a new Matrix4 instance if one was not provided.
- */
- Matrix4.fromTranslationRotationScale = function(translationRotationScale, result) {
- //>>includeStart('debug', pragmas.debug);
- Check.Check.typeOf.object('translationRotationScale', translationRotationScale);
- //>>includeEnd('debug');
- return Matrix4.fromTranslationQuaternionRotationScale(translationRotationScale.translation, translationRotationScale.rotation, translationRotationScale.scale, result);
- };
- /**
- * Creates a Matrix4 instance from a Cartesian3 representing the translation.
- *
- * @param {Cartesian3} translation The upper right portion of the matrix representing the translation.
- * @param {Matrix4} [result] The object in which the result will be stored, if undefined a new instance will be created.
- * @returns {Matrix4} The modified result parameter, or a new Matrix4 instance if one was not provided.
- *
- * @see Matrix4.multiplyByTranslation
- */
- Matrix4.fromTranslation = function(translation, result) {
- //>>includeStart('debug', pragmas.debug);
- Check.Check.typeOf.object('translation', translation);
- //>>includeEnd('debug');
- return Matrix4.fromRotationTranslation(Matrix3.IDENTITY, translation, result);
- };
- /**
- * Computes a Matrix4 instance representing a non-uniform scale.
- *
- * @param {Cartesian3} scale The x, y, and z scale factors.
- * @param {Matrix4} [result] The object in which the result will be stored, if undefined a new instance will be created.
- * @returns {Matrix4} The modified result parameter, or a new Matrix4 instance if one was not provided.
- *
- * @example
- * // Creates
- * // [7.0, 0.0, 0.0, 0.0]
- * // [0.0, 8.0, 0.0, 0.0]
- * // [0.0, 0.0, 9.0, 0.0]
- * // [0.0, 0.0, 0.0, 1.0]
- * var m = Cesium.Matrix4.fromScale(new Cesium.Cartesian3(7.0, 8.0, 9.0));
- */
- Matrix4.fromScale = function(scale, result) {
- //>>includeStart('debug', pragmas.debug);
- Check.Check.typeOf.object('scale', scale);
- //>>includeEnd('debug');
- if (!when.defined(result)) {
- return new Matrix4(
- scale.x, 0.0, 0.0, 0.0,
- 0.0, scale.y, 0.0, 0.0,
- 0.0, 0.0, scale.z, 0.0,
- 0.0, 0.0, 0.0, 1.0);
- }
- result[0] = scale.x;
- result[1] = 0.0;
- result[2] = 0.0;
- result[3] = 0.0;
- result[4] = 0.0;
- result[5] = scale.y;
- result[6] = 0.0;
- result[7] = 0.0;
- result[8] = 0.0;
- result[9] = 0.0;
- result[10] = scale.z;
- result[11] = 0.0;
- result[12] = 0.0;
- result[13] = 0.0;
- result[14] = 0.0;
- result[15] = 1.0;
- return result;
- };
- /**
- * Computes a Matrix4 instance representing a uniform scale.
- *
- * @param {Number} scale The uniform scale factor.
- * @param {Matrix4} [result] The object in which the result will be stored, if undefined a new instance will be created.
- * @returns {Matrix4} The modified result parameter, or a new Matrix4 instance if one was not provided.
- *
- * @example
- * // Creates
- * // [2.0, 0.0, 0.0, 0.0]
- * // [0.0, 2.0, 0.0, 0.0]
- * // [0.0, 0.0, 2.0, 0.0]
- * // [0.0, 0.0, 0.0, 1.0]
- * var m = Cesium.Matrix4.fromUniformScale(2.0);
- */
- Matrix4.fromUniformScale = function(scale, result) {
- //>>includeStart('debug', pragmas.debug);
- Check.Check.typeOf.number('scale', scale);
- //>>includeEnd('debug');
- if (!when.defined(result)) {
- return new Matrix4(scale, 0.0, 0.0, 0.0,
- 0.0, scale, 0.0, 0.0,
- 0.0, 0.0, scale, 0.0,
- 0.0, 0.0, 0.0, 1.0);
- }
- result[0] = scale;
- result[1] = 0.0;
- result[2] = 0.0;
- result[3] = 0.0;
- result[4] = 0.0;
- result[5] = scale;
- result[6] = 0.0;
- result[7] = 0.0;
- result[8] = 0.0;
- result[9] = 0.0;
- result[10] = scale;
- result[11] = 0.0;
- result[12] = 0.0;
- result[13] = 0.0;
- result[14] = 0.0;
- result[15] = 1.0;
- return result;
- };
- var fromCameraF = new Cartographic.Cartesian3();
- var fromCameraR = new Cartographic.Cartesian3();
- var fromCameraU = new Cartographic.Cartesian3();
- /**
- * Computes a Matrix4 instance from a Camera.
- *
- * @param {Camera} camera The camera to use.
- * @param {Matrix4} [result] The object in which the result will be stored, if undefined a new instance will be created.
- * @returns {Matrix4} The modified result parameter, or a new Matrix4 instance if one was not provided.
- */
- Matrix4.fromCamera = function(camera, result) {
- //>>includeStart('debug', pragmas.debug);
- Check.Check.typeOf.object('camera', camera);
- //>>includeEnd('debug');
- var position = camera.position;
- var direction = camera.direction;
- var up = camera.up;
- //>>includeStart('debug', pragmas.debug);
- Check.Check.typeOf.object('camera.position', position);
- Check.Check.typeOf.object('camera.direction', direction);
- Check.Check.typeOf.object('camera.up', up);
- //>>includeEnd('debug');
- Cartographic.Cartesian3.normalize(direction, fromCameraF);
- Cartographic.Cartesian3.normalize(Cartographic.Cartesian3.cross(fromCameraF, up, fromCameraR), fromCameraR);
- Cartographic.Cartesian3.normalize(Cartographic.Cartesian3.cross(fromCameraR, fromCameraF, fromCameraU), fromCameraU);
- var sX = fromCameraR.x;
- var sY = fromCameraR.y;
- var sZ = fromCameraR.z;
- var fX = fromCameraF.x;
- var fY = fromCameraF.y;
- var fZ = fromCameraF.z;
- var uX = fromCameraU.x;
- var uY = fromCameraU.y;
- var uZ = fromCameraU.z;
- var positionX = position.x;
- var positionY = position.y;
- var positionZ = position.z;
- var t0 = sX * -positionX + sY * -positionY+ sZ * -positionZ;
- var t1 = uX * -positionX + uY * -positionY+ uZ * -positionZ;
- var t2 = fX * positionX + fY * positionY + fZ * positionZ;
- // The code below this comment is an optimized
- // version of the commented lines.
- // Rather that create two matrices and then multiply,
- // we just bake in the multiplcation as part of creation.
- // var rotation = new Matrix4(
- // sX, sY, sZ, 0.0,
- // uX, uY, uZ, 0.0,
- // -fX, -fY, -fZ, 0.0,
- // 0.0, 0.0, 0.0, 1.0);
- // var translation = new Matrix4(
- // 1.0, 0.0, 0.0, -position.x,
- // 0.0, 1.0, 0.0, -position.y,
- // 0.0, 0.0, 1.0, -position.z,
- // 0.0, 0.0, 0.0, 1.0);
- // return rotation.multiply(translation);
- if (!when.defined(result)) {
- return new Matrix4(
- sX, sY, sZ, t0,
- uX, uY, uZ, t1,
- -fX, -fY, -fZ, t2,
- 0.0, 0.0, 0.0, 1.0);
- }
- result[0] = sX;
- result[1] = uX;
- result[2] = -fX;
- result[3] = 0.0;
- result[4] = sY;
- result[5] = uY;
- result[6] = -fY;
- result[7] = 0.0;
- result[8] = sZ;
- result[9] = uZ;
- result[10] = -fZ;
- result[11] = 0.0;
- result[12] = t0;
- result[13] = t1;
- result[14] = t2;
- result[15] = 1.0;
- return result;
- };
- /**
- * Computes a Matrix4 instance representing a perspective transformation matrix.
- *
- * @param {Number} fovY The field of view along the Y axis in radians.
- * @param {Number} aspectRatio The aspect ratio.
- * @param {Number} near The distance to the near plane in meters.
- * @param {Number} far The distance to the far plane in meters.
- * @param {Matrix4} result The object in which the result will be stored.
- * @returns {Matrix4} The modified result parameter.
- *
- * @exception {DeveloperError} fovY must be in (0, PI].
- * @exception {DeveloperError} aspectRatio must be greater than zero.
- * @exception {DeveloperError} near must be greater than zero.
- * @exception {DeveloperError} far must be greater than zero.
- */
- Matrix4.computePerspectiveFieldOfView = function(fovY, aspectRatio, near, far, result) {
- //>>includeStart('debug', pragmas.debug);
- Check.Check.typeOf.number.greaterThan('fovY', fovY, 0.0);
- Check.Check.typeOf.number.lessThan('fovY', fovY, Math.PI);
- Check.Check.typeOf.number.greaterThan('near', near, 0.0);
- Check.Check.typeOf.number.greaterThan('far', far, 0.0);
- Check.Check.typeOf.object('result', result);
- //>>includeEnd('debug');
- var bottom = Math.tan(fovY * 0.5);
- var column1Row1 = 1.0 / bottom;
- var column0Row0 = column1Row1 / aspectRatio;
- var column2Row2 = (far + near) / (near - far);
- var column3Row2 = (2.0 * far * near) / (near - far);
- result[0] = column0Row0;
- result[1] = 0.0;
- result[2] = 0.0;
- result[3] = 0.0;
- result[4] = 0.0;
- result[5] = column1Row1;
- result[6] = 0.0;
- result[7] = 0.0;
- result[8] = 0.0;
- result[9] = 0.0;
- result[10] = column2Row2;
- result[11] = -1.0;
- result[12] = 0.0;
- result[13] = 0.0;
- result[14] = column3Row2;
- result[15] = 0.0;
- return result;
- };
- /**
- * Computes a Matrix4 instance representing an orthographic transformation matrix.
- *
- * @param {Number} left The number of meters to the left of the camera that will be in view.
- * @param {Number} right The number of meters to the right of the camera that will be in view.
- * @param {Number} bottom The number of meters below of the camera that will be in view.
- * @param {Number} top The number of meters above of the camera that will be in view.
- * @param {Number} near The distance to the near plane in meters.
- * @param {Number} far The distance to the far plane in meters.
- * @param {Matrix4} result The object in which the result will be stored.
- * @returns {Matrix4} The modified result parameter.
- */
- Matrix4.computeOrthographicOffCenter = function(left, right, bottom, top, near, far, result) {
- //>>includeStart('debug', pragmas.debug);
- Check.Check.typeOf.number('left', left);
- Check.Check.typeOf.number('right', right);
- Check.Check.typeOf.number('bottom', bottom);
- Check.Check.typeOf.number('top', top);
- Check.Check.typeOf.number('near', near);
- Check.Check.typeOf.number('far', far);
- Check.Check.typeOf.object('result', result);
- //>>includeEnd('debug');
- var a = 1.0 / (right - left);
- var b = 1.0 / (top - bottom);
- var c = 1.0 / (far - near);
- var tx = -(right + left) * a;
- var ty = -(top + bottom) * b;
- var tz = -(far + near) * c;
- a *= 2.0;
- b *= 2.0;
- c *= -2.0;
- result[0] = a;
- result[1] = 0.0;
- result[2] = 0.0;
- result[3] = 0.0;
- result[4] = 0.0;
- result[5] = b;
- result[6] = 0.0;
- result[7] = 0.0;
- result[8] = 0.0;
- result[9] = 0.0;
- result[10] = c;
- result[11] = 0.0;
- result[12] = tx;
- result[13] = ty;
- result[14] = tz;
- result[15] = 1.0;
- return result;
- };
- /**
- * Computes a Matrix4 instance representing an off center perspective transformation.
- *
- * @param {Number} left The number of meters to the left of the camera that will be in view.
- * @param {Number} right The number of meters to the right of the camera that will be in view.
- * @param {Number} bottom The number of meters below of the camera that will be in view.
- * @param {Number} top The number of meters above of the camera that will be in view.
- * @param {Number} near The distance to the near plane in meters.
- * @param {Number} far The distance to the far plane in meters.
- * @param {Matrix4} result The object in which the result will be stored.
- * @returns {Matrix4} The modified result parameter.
- */
- Matrix4.computePerspectiveOffCenter = function(left, right, bottom, top, near, far, result) {
- //>>includeStart('debug', pragmas.debug);
- Check.Check.typeOf.number('left', left);
- Check.Check.typeOf.number('right', right);
- Check.Check.typeOf.number('bottom', bottom);
- Check.Check.typeOf.number('top', top);
- Check.Check.typeOf.number('near', near);
- Check.Check.typeOf.number('far', far);
- Check.Check.typeOf.object('result', result);
- //>>includeEnd('debug');
- var column0Row0 = 2.0 * near / (right - left);
- var column1Row1 = 2.0 * near / (top - bottom);
- var column2Row0 = (right + left) / (right - left);
- var column2Row1 = (top + bottom) / (top - bottom);
- var column2Row2 = -(far + near) / (far - near);
- var column2Row3 = -1.0;
- var column3Row2 = -2.0 * far * near / (far - near);
- result[0] = column0Row0;
- result[1] = 0.0;
- result[2] = 0.0;
- result[3] = 0.0;
- result[4] = 0.0;
- result[5] = column1Row1;
- result[6] = 0.0;
- result[7] = 0.0;
- result[8] = column2Row0;
- result[9] = column2Row1;
- result[10] = column2Row2;
- result[11] = column2Row3;
- result[12] = 0.0;
- result[13] = 0.0;
- result[14] = column3Row2;
- result[15] = 0.0;
- return result;
- };
- /**
- * Computes a Matrix4 instance representing an infinite off center perspective transformation.
- *
- * @param {Number} left The number of meters to the left of the camera that will be in view.
- * @param {Number} right The number of meters to the right of the camera that will be in view.
- * @param {Number} bottom The number of meters below of the camera that will be in view.
- * @param {Number} top The number of meters above of the camera that will be in view.
- * @param {Number} near The distance to the near plane in meters.
- * @param {Matrix4} result The object in which the result will be stored.
- * @returns {Matrix4} The modified result parameter.
- */
- Matrix4.computeInfinitePerspectiveOffCenter = function(left, right, bottom, top, near, result) {
- //>>includeStart('debug', pragmas.debug);
- Check.Check.typeOf.number('left', left);
- Check.Check.typeOf.number('right', right);
- Check.Check.typeOf.number('bottom', bottom);
- Check.Check.typeOf.number('top', top);
- Check.Check.typeOf.number('near', near);
- Check.Check.typeOf.object('result', result);
- //>>includeEnd('debug');
- var column0Row0 = 2.0 * near / (right - left);
- var column1Row1 = 2.0 * near / (top - bottom);
- var column2Row0 = (right + left) / (right - left);
- var column2Row1 = (top + bottom) / (top - bottom);
- var column2Row2 = -1.0;
- var column2Row3 = -1.0;
- var column3Row2 = -2.0 * near;
- result[0] = column0Row0;
- result[1] = 0.0;
- result[2] = 0.0;
- result[3] = 0.0;
- result[4] = 0.0;
- result[5] = column1Row1;
- result[6] = 0.0;
- result[7] = 0.0;
- result[8] = column2Row0;
- result[9] = column2Row1;
- result[10] = column2Row2;
- result[11] = column2Row3;
- result[12] = 0.0;
- result[13] = 0.0;
- result[14] = column3Row2;
- result[15] = 0.0;
- return result;
- };
- /**
- * Computes a Matrix4 instance that transforms from normalized device coordinates to window coordinates.
- *
- * @param {Object}[viewport = { x : 0.0, y : 0.0, width : 0.0, height : 0.0 }] The viewport's corners as shown in Example 1.
- * @param {Number}[nearDepthRange=0.0] The near plane distance in window coordinates.
- * @param {Number}[farDepthRange=1.0] The far plane distance in window coordinates.
- * @param {Matrix4} result The object in which the result will be stored.
- * @returns {Matrix4} The modified result parameter.
- *
- * @example
- * // Create viewport transformation using an explicit viewport and depth range.
- * var m = Cesium.Matrix4.computeViewportTransformation({
- * x : 0.0,
- * y : 0.0,
- * width : 1024.0,
- * height : 768.0
- * }, 0.0, 1.0, new Cesium.Matrix4());
- */
- Matrix4.computeViewportTransformation = function(viewport, nearDepthRange, farDepthRange, result) {
- //>>includeStart('debug', pragmas.debug);
- Check.Check.typeOf.object('result', result);
- //>>includeEnd('debug');
- viewport = when.defaultValue(viewport, when.defaultValue.EMPTY_OBJECT);
- var x = when.defaultValue(viewport.x, 0.0);
- var y = when.defaultValue(viewport.y, 0.0);
- var width = when.defaultValue(viewport.width, 0.0);
- var height = when.defaultValue(viewport.height, 0.0);
- nearDepthRange = when.defaultValue(nearDepthRange, 0.0);
- farDepthRange = when.defaultValue(farDepthRange, 1.0);
- var halfWidth = width * 0.5;
- var halfHeight = height * 0.5;
- var halfDepth = (farDepthRange - nearDepthRange) * 0.5;
- var column0Row0 = halfWidth;
- var column1Row1 = halfHeight;
- var column2Row2 = halfDepth;
- var column3Row0 = x + halfWidth;
- var column3Row1 = y + halfHeight;
- var column3Row2 = nearDepthRange + halfDepth;
- var column3Row3 = 1.0;
- result[0] = column0Row0;
- result[1] = 0.0;
- result[2] = 0.0;
- result[3] = 0.0;
- result[4] = 0.0;
- result[5] = column1Row1;
- result[6] = 0.0;
- result[7] = 0.0;
- result[8] = 0.0;
- result[9] = 0.0;
- result[10] = column2Row2;
- result[11] = 0.0;
- result[12] = column3Row0;
- result[13] = column3Row1;
- result[14] = column3Row2;
- result[15] = column3Row3;
- return result;
- };
- /**
- * Computes a Matrix4 instance that transforms from world space to view space.
- *
- * @param {Cartesian3} position The position of the camera.
- * @param {Cartesian3} direction The forward direction.
- * @param {Cartesian3} up The up direction.
- * @param {Cartesian3} right The right direction.
- * @param {Matrix4} result The object in which the result will be stored.
- * @returns {Matrix4} The modified result parameter.
- */
- Matrix4.computeView = function(position, direction, up, right, result) {
- //>>includeStart('debug', pragmas.debug);
- Check.Check.typeOf.object('position', position);
- Check.Check.typeOf.object('direction', direction);
- Check.Check.typeOf.object('up', up);
- Check.Check.typeOf.object('right', right);
- Check.Check.typeOf.object('result', result);
- //>>includeEnd('debug');
- result[0] = right.x;
- result[1] = up.x;
- result[2] = -direction.x;
- result[3] = 0.0;
- result[4] = right.y;
- result[5] = up.y;
- result[6] = -direction.y;
- result[7] = 0.0;
- result[8] = right.z;
- result[9] = up.z;
- result[10] = -direction.z;
- result[11] = 0.0;
- result[12] = -Cartographic.Cartesian3.dot(right, position);
- result[13] = -Cartographic.Cartesian3.dot(up, position);
- result[14] = Cartographic.Cartesian3.dot(direction, position);
- result[15] = 1.0;
- return result;
- };
- /**
- * Computes an Array from the provided Matrix4 instance.
- * The array will be in column-major order.
- *
- * @param {Matrix4} matrix The matrix to use..
- * @param {Number[]} [result] The Array onto which to store the result.
- * @returns {Number[]} The modified Array parameter or a new Array instance if one was not provided.
- *
- * @example
- * //create an array from an instance of Matrix4
- * // m = [10.0, 14.0, 18.0, 22.0]
- * // [11.0, 15.0, 19.0, 23.0]
- * // [12.0, 16.0, 20.0, 24.0]
- * // [13.0, 17.0, 21.0, 25.0]
- * var a = Cesium.Matrix4.toArray(m);
- *
- * // m remains the same
- * //creates a = [10.0, 11.0, 12.0, 13.0, 14.0, 15.0, 16.0, 17.0, 18.0, 19.0, 20.0, 21.0, 22.0, 23.0, 24.0, 25.0]
- */
- Matrix4.toArray = function(matrix, result) {
- //>>includeStart('debug', pragmas.debug);
- Check.Check.typeOf.object('matrix', matrix);
- //>>includeEnd('debug');
- if (!when.defined(result)) {
- return [matrix[0], matrix[1], matrix[2], matrix[3],
- matrix[4], matrix[5], matrix[6], matrix[7],
- matrix[8], matrix[9], matrix[10], matrix[11],
- matrix[12], matrix[13], matrix[14], matrix[15]];
- }
- result[0] = matrix[0];
- result[1] = matrix[1];
- result[2] = matrix[2];
- result[3] = matrix[3];
- result[4] = matrix[4];
- result[5] = matrix[5];
- result[6] = matrix[6];
- result[7] = matrix[7];
- result[8] = matrix[8];
- result[9] = matrix[9];
- result[10] = matrix[10];
- result[11] = matrix[11];
- result[12] = matrix[12];
- result[13] = matrix[13];
- result[14] = matrix[14];
- result[15] = matrix[15];
- return result;
- };
- /**
- * Computes the array index of the element at the provided row and column.
- *
- * @param {Number} row The zero-based index of the row.
- * @param {Number} column The zero-based index of the column.
- * @returns {Number} The index of the element at the provided row and column.
- *
- * @exception {DeveloperError} row must be 0, 1, 2, or 3.
- * @exception {DeveloperError} column must be 0, 1, 2, or 3.
- *
- * @example
- * var myMatrix = new Cesium.Matrix4();
- * var column1Row0Index = Cesium.Matrix4.getElementIndex(1, 0);
- * var column1Row0 = myMatrix[column1Row0Index];
- * myMatrix[column1Row0Index] = 10.0;
- */
- Matrix4.getElementIndex = function(column, row) {
- //>>includeStart('debug', pragmas.debug);
- Check.Check.typeOf.number.greaterThanOrEquals('row', row, 0);
- Check.Check.typeOf.number.lessThanOrEquals('row', row, 3);
- Check.Check.typeOf.number.greaterThanOrEquals('column', column, 0);
- Check.Check.typeOf.number.lessThanOrEquals('column', column, 3);
- //>>includeEnd('debug');
- return column * 4 + row;
- };
- /**
- * Retrieves a copy of the matrix column at the provided index as a Cartesian4 instance.
- *
- * @param {Matrix4} matrix The matrix to use.
- * @param {Number} index The zero-based index of the column to retrieve.
- * @param {Cartesian4} result The object onto which to store the result.
- * @returns {Cartesian4} The modified result parameter.
- *
- * @exception {DeveloperError} index must be 0, 1, 2, or 3.
- *
- * @example
- * //returns a Cartesian4 instance with values from the specified column
- * // m = [10.0, 11.0, 12.0, 13.0]
- * // [14.0, 15.0, 16.0, 17.0]
- * // [18.0, 19.0, 20.0, 21.0]
- * // [22.0, 23.0, 24.0, 25.0]
- *
- * //Example 1: Creates an instance of Cartesian
- * var a = Cesium.Matrix4.getColumn(m, 2, new Cesium.Cartesian4());
- *
- * @example
- * //Example 2: Sets values for Cartesian instance
- * var a = new Cesium.Cartesian4();
- * Cesium.Matrix4.getColumn(m, 2, a);
- *
- * // a.x = 12.0; a.y = 16.0; a.z = 20.0; a.w = 24.0;
- */
- Matrix4.getColumn = function(matrix, index, result) {
- //>>includeStart('debug', pragmas.debug);
- Check.Check.typeOf.object('matrix', matrix);
- Check.Check.typeOf.number.greaterThanOrEquals('index', index, 0);
- Check.Check.typeOf.number.lessThanOrEquals('index', index, 3);
- Check.Check.typeOf.object('result', result);
- //>>includeEnd('debug');
- var startIndex = index * 4;
- var x = matrix[startIndex];
- var y = matrix[startIndex + 1];
- var z = matrix[startIndex + 2];
- var w = matrix[startIndex + 3];
- result.x = x;
- result.y = y;
- result.z = z;
- result.w = w;
- return result;
- };
- /**
- * Computes a new matrix that replaces the specified column in the provided matrix with the provided Cartesian4 instance.
- *
- * @param {Matrix4} matrix The matrix to use.
- * @param {Number} index The zero-based index of the column to set.
- * @param {Cartesian4} cartesian The Cartesian whose values will be assigned to the specified column.
- * @param {Matrix4} result The object onto which to store the result.
- * @returns {Matrix4} The modified result parameter.
- *
- * @exception {DeveloperError} index must be 0, 1, 2, or 3.
- *
- * @example
- * //creates a new Matrix4 instance with new column values from the Cartesian4 instance
- * // m = [10.0, 11.0, 12.0, 13.0]
- * // [14.0, 15.0, 16.0, 17.0]
- * // [18.0, 19.0, 20.0, 21.0]
- * // [22.0, 23.0, 24.0, 25.0]
- *
- * var a = Cesium.Matrix4.setColumn(m, 2, new Cesium.Cartesian4(99.0, 98.0, 97.0, 96.0), new Cesium.Matrix4());
- *
- * // m remains the same
- * // a = [10.0, 11.0, 99.0, 13.0]
- * // [14.0, 15.0, 98.0, 17.0]
- * // [18.0, 19.0, 97.0, 21.0]
- * // [22.0, 23.0, 96.0, 25.0]
- */
- Matrix4.setColumn = function(matrix, index, cartesian, result) {
- //>>includeStart('debug', pragmas.debug);
- Check.Check.typeOf.object('matrix', matrix);
- Check.Check.typeOf.number.greaterThanOrEquals('index', index, 0);
- Check.Check.typeOf.number.lessThanOrEquals('index', index, 3);
- Check.Check.typeOf.object('cartesian', cartesian);
- Check.Check.typeOf.object('result', result);
- //>>includeEnd('debug');
- result = Matrix4.clone(matrix, result);
- var startIndex = index * 4;
- result[startIndex] = cartesian.x;
- result[startIndex + 1] = cartesian.y;
- result[startIndex + 2] = cartesian.z;
- result[startIndex + 3] = cartesian.w;
- return result;
- };
- /**
- * Computes a new matrix that replaces the translation in the rightmost column of the provided
- * matrix with the provided translation. This assumes the matrix is an affine transformation
- *
- * @param {Matrix4} matrix The matrix to use.
- * @param {Cartesian3} translation The translation that replaces the translation of the provided matrix.
- * @param {Matrix4} result The object onto which to store the result.
- * @returns {Matrix4} The modified result parameter.
- */
- Matrix4.setTranslation = function(matrix, translation, result) {
- //>>includeStart('debug', pragmas.debug);
- Check.Check.typeOf.object('matrix', matrix);
- Check.Check.typeOf.object('translation', translation);
- Check.Check.typeOf.object('result', result);
- //>>includeEnd('debug');
- result[0] = matrix[0];
- result[1] = matrix[1];
- result[2] = matrix[2];
- result[3] = matrix[3];
- result[4] = matrix[4];
- result[5] = matrix[5];
- result[6] = matrix[6];
- result[7] = matrix[7];
- result[8] = matrix[8];
- result[9] = matrix[9];
- result[10] = matrix[10];
- result[11] = matrix[11];
- result[12] = translation.x;
- result[13] = translation.y;
- result[14] = translation.z;
- result[15] = matrix[15];
- return result;
- };
- var scaleScratch = new Cartographic.Cartesian3();
- /**
- * Computes a new matrix that replaces the scale with the provided scale. This assumes the matrix is an affine transformation
- *
- * @param {Matrix4} matrix The matrix to use.
- * @param {Cartesian3} scale The scale that replaces the scale of the provided matrix.
- * @param {Matrix4} result The object onto which to store the result.
- * @returns {Matrix4} The modified result parameter.
- */
- Matrix4.setScale = function(matrix, scale, result) {
- //>>includeStart('debug', pragmas.debug);
- Check.Check.typeOf.object('matrix', matrix);
- Check.Check.typeOf.object('scale', scale);
- Check.Check.typeOf.object('result', result);
- //>>includeEnd('debug');
- var existingScale = Matrix4.getScale(matrix, scaleScratch);
- var newScale = Cartographic.Cartesian3.divideComponents(scale, existingScale, scaleScratch);
- return Matrix4.multiplyByScale(matrix, newScale, result);
- };
- /**
- * Retrieves a copy of the matrix row at the provided index as a Cartesian4 instance.
- *
- * @param {Matrix4} matrix The matrix to use.
- * @param {Number} index The zero-based index of the row to retrieve.
- * @param {Cartesian4} result The object onto which to store the result.
- * @returns {Cartesian4} The modified result parameter.
- *
- * @exception {DeveloperError} index must be 0, 1, 2, or 3.
- *
- * @example
- * //returns a Cartesian4 instance with values from the specified column
- * // m = [10.0, 11.0, 12.0, 13.0]
- * // [14.0, 15.0, 16.0, 17.0]
- * // [18.0, 19.0, 20.0, 21.0]
- * // [22.0, 23.0, 24.0, 25.0]
- *
- * //Example 1: Returns an instance of Cartesian
- * var a = Cesium.Matrix4.getRow(m, 2, new Cesium.Cartesian4());
- *
- * @example
- * //Example 2: Sets values for a Cartesian instance
- * var a = new Cesium.Cartesian4();
- * Cesium.Matrix4.getRow(m, 2, a);
- *
- * // a.x = 18.0; a.y = 19.0; a.z = 20.0; a.w = 21.0;
- */
- Matrix4.getRow = function(matrix, index, result) {
- //>>includeStart('debug', pragmas.debug);
- Check.Check.typeOf.object('matrix', matrix);
- Check.Check.typeOf.number.greaterThanOrEquals('index', index, 0);
- Check.Check.typeOf.number.lessThanOrEquals('index', index, 3);
- Check.Check.typeOf.object('result', result);
- //>>includeEnd('debug');
- var x = matrix[index];
- var y = matrix[index + 4];
- var z = matrix[index + 8];
- var w = matrix[index + 12];
- result.x = x;
- result.y = y;
- result.z = z;
- result.w = w;
- return result;
- };
- /**
- * Computes a new matrix that replaces the specified row in the provided matrix with the provided Cartesian4 instance.
- *
- * @param {Matrix4} matrix The matrix to use.
- * @param {Number} index The zero-based index of the row to set.
- * @param {Cartesian4} cartesian The Cartesian whose values will be assigned to the specified row.
- * @param {Matrix4} result The object onto which to store the result.
- * @returns {Matrix4} The modified result parameter.
- *
- * @exception {DeveloperError} index must be 0, 1, 2, or 3.
- *
- * @example
- * //create a new Matrix4 instance with new row values from the Cartesian4 instance
- * // m = [10.0, 11.0, 12.0, 13.0]
- * // [14.0, 15.0, 16.0, 17.0]
- * // [18.0, 19.0, 20.0, 21.0]
- * // [22.0, 23.0, 24.0, 25.0]
- *
- * var a = Cesium.Matrix4.setRow(m, 2, new Cesium.Cartesian4(99.0, 98.0, 97.0, 96.0), new Cesium.Matrix4());
- *
- * // m remains the same
- * // a = [10.0, 11.0, 12.0, 13.0]
- * // [14.0, 15.0, 16.0, 17.0]
- * // [99.0, 98.0, 97.0, 96.0]
- * // [22.0, 23.0, 24.0, 25.0]
- */
- Matrix4.setRow = function(matrix, index, cartesian, result) {
- //>>includeStart('debug', pragmas.debug);
- Check.Check.typeOf.object('matrix', matrix);
- Check.Check.typeOf.number.greaterThanOrEquals('index', index, 0);
- Check.Check.typeOf.number.lessThanOrEquals('index', index, 3);
- Check.Check.typeOf.object('cartesian', cartesian);
- Check.Check.typeOf.object('result', result);
- //>>includeEnd('debug');
- result = Matrix4.clone(matrix, result);
- result[index] = cartesian.x;
- result[index + 4] = cartesian.y;
- result[index + 8] = cartesian.z;
- result[index + 12] = cartesian.w;
- return result;
- };
- var scratchColumn$1 = new Cartographic.Cartesian3();
- /**
- * Extracts the non-uniform scale assuming the matrix is an affine transformation.
- *
- * @param {Matrix4} matrix The matrix.
- * @param {Cartesian3} result The object onto which to store the result.
- * @returns {Cartesian3} The modified result parameter
- */
- Matrix4.getScale = function(matrix, result) {
- //>>includeStart('debug', pragmas.debug);
- Check.Check.typeOf.object('matrix', matrix);
- Check.Check.typeOf.object('result', result);
- //>>includeEnd('debug');
- result.x = Cartographic.Cartesian3.magnitude(Cartographic.Cartesian3.fromElements(matrix[0], matrix[1], matrix[2], scratchColumn$1));
- result.y = Cartographic.Cartesian3.magnitude(Cartographic.Cartesian3.fromElements(matrix[4], matrix[5], matrix[6], scratchColumn$1));
- result.z = Cartographic.Cartesian3.magnitude(Cartographic.Cartesian3.fromElements(matrix[8], matrix[9], matrix[10], scratchColumn$1));
- return result;
- };
- var scratchScale$1 = new Cartographic.Cartesian3();
- /**
- * Computes the maximum scale assuming the matrix is an affine transformation.
- * The maximum scale is the maximum length of the column vectors in the upper-left
- * 3x3 matrix.
- *
- * @param {Matrix4} matrix The matrix.
- * @returns {Number} The maximum scale.
- */
- Matrix4.getMaximumScale = function(matrix) {
- Matrix4.getScale(matrix, scratchScale$1);
- return Cartographic.Cartesian3.maximumComponent(scratchScale$1);
- };
- /**
- * Computes the product of two matrices.
- *
- * @param {Matrix4} left The first matrix.
- * @param {Matrix4} right The second matrix.
- * @param {Matrix4} result The object onto which to store the result.
- * @returns {Matrix4} The modified result parameter.
- */
- Matrix4.multiply = function(left, right, result) {
- //>>includeStart('debug', pragmas.debug);
- Check.Check.typeOf.object('left', left);
- Check.Check.typeOf.object('right', right);
- Check.Check.typeOf.object('result', result);
- //>>includeEnd('debug');
- var left0 = left[0];
- var left1 = left[1];
- var left2 = left[2];
- var left3 = left[3];
- var left4 = left[4];
- var left5 = left[5];
- var left6 = left[6];
- var left7 = left[7];
- var left8 = left[8];
- var left9 = left[9];
- var left10 = left[10];
- var left11 = left[11];
- var left12 = left[12];
- var left13 = left[13];
- var left14 = left[14];
- var left15 = left[15];
- var right0 = right[0];
- var right1 = right[1];
- var right2 = right[2];
- var right3 = right[3];
- var right4 = right[4];
- var right5 = right[5];
- var right6 = right[6];
- var right7 = right[7];
- var right8 = right[8];
- var right9 = right[9];
- var right10 = right[10];
- var right11 = right[11];
- var right12 = right[12];
- var right13 = right[13];
- var right14 = right[14];
- var right15 = right[15];
- var column0Row0 = left0 * right0 + left4 * right1 + left8 * right2 + left12 * right3;
- var column0Row1 = left1 * right0 + left5 * right1 + left9 * right2 + left13 * right3;
- var column0Row2 = left2 * right0 + left6 * right1 + left10 * right2 + left14 * right3;
- var column0Row3 = left3 * right0 + left7 * right1 + left11 * right2 + left15 * right3;
- var column1Row0 = left0 * right4 + left4 * right5 + left8 * right6 + left12 * right7;
- var column1Row1 = left1 * right4 + left5 * right5 + left9 * right6 + left13 * right7;
- var column1Row2 = left2 * right4 + left6 * right5 + left10 * right6 + left14 * right7;
- var column1Row3 = left3 * right4 + left7 * right5 + left11 * right6 + left15 * right7;
- var column2Row0 = left0 * right8 + left4 * right9 + left8 * right10 + left12 * right11;
- var column2Row1 = left1 * right8 + left5 * right9 + left9 * right10 + left13 * right11;
- var column2Row2 = left2 * right8 + left6 * right9 + left10 * right10 + left14 * right11;
- var column2Row3 = left3 * right8 + left7 * right9 + left11 * right10 + left15 * right11;
- var column3Row0 = left0 * right12 + left4 * right13 + left8 * right14 + left12 * right15;
- var column3Row1 = left1 * right12 + left5 * right13 + left9 * right14 + left13 * right15;
- var column3Row2 = left2 * right12 + left6 * right13 + left10 * right14 + left14 * right15;
- var column3Row3 = left3 * right12 + left7 * right13 + left11 * right14 + left15 * right15;
- result[0] = column0Row0;
- result[1] = column0Row1;
- result[2] = column0Row2;
- result[3] = column0Row3;
- result[4] = column1Row0;
- result[5] = column1Row1;
- result[6] = column1Row2;
- result[7] = column1Row3;
- result[8] = column2Row0;
- result[9] = column2Row1;
- result[10] = column2Row2;
- result[11] = column2Row3;
- result[12] = column3Row0;
- result[13] = column3Row1;
- result[14] = column3Row2;
- result[15] = column3Row3;
- return result;
- };
- /**
- * Computes the sum of two matrices.
- *
- * @param {Matrix4} left The first matrix.
- * @param {Matrix4} right The second matrix.
- * @param {Matrix4} result The object onto which to store the result.
- * @returns {Matrix4} The modified result parameter.
- */
- Matrix4.add = function(left, right, result) {
- //>>includeStart('debug', pragmas.debug);
- Check.Check.typeOf.object('left', left);
- Check.Check.typeOf.object('right', right);
- Check.Check.typeOf.object('result', result);
- //>>includeEnd('debug');
- result[0] = left[0] + right[0];
- result[1] = left[1] + right[1];
- result[2] = left[2] + right[2];
- result[3] = left[3] + right[3];
- result[4] = left[4] + right[4];
- result[5] = left[5] + right[5];
- result[6] = left[6] + right[6];
- result[7] = left[7] + right[7];
- result[8] = left[8] + right[8];
- result[9] = left[9] + right[9];
- result[10] = left[10] + right[10];
- result[11] = left[11] + right[11];
- result[12] = left[12] + right[12];
- result[13] = left[13] + right[13];
- result[14] = left[14] + right[14];
- result[15] = left[15] + right[15];
- return result;
- };
- /**
- * Computes the difference of two matrices.
- *
- * @param {Matrix4} left The first matrix.
- * @param {Matrix4} right The second matrix.
- * @param {Matrix4} result The object onto which to store the result.
- * @returns {Matrix4} The modified result parameter.
- */
- Matrix4.subtract = function(left, right, result) {
- //>>includeStart('debug', pragmas.debug);
- Check.Check.typeOf.object('left', left);
- Check.Check.typeOf.object('right', right);
- Check.Check.typeOf.object('result', result);
- //>>includeEnd('debug');
- result[0] = left[0] - right[0];
- result[1] = left[1] - right[1];
- result[2] = left[2] - right[2];
- result[3] = left[3] - right[3];
- result[4] = left[4] - right[4];
- result[5] = left[5] - right[5];
- result[6] = left[6] - right[6];
- result[7] = left[7] - right[7];
- result[8] = left[8] - right[8];
- result[9] = left[9] - right[9];
- result[10] = left[10] - right[10];
- result[11] = left[11] - right[11];
- result[12] = left[12] - right[12];
- result[13] = left[13] - right[13];
- result[14] = left[14] - right[14];
- result[15] = left[15] - right[15];
- return result;
- };
- /**
- * Computes the product of two matrices assuming the matrices are
- * affine transformation matrices, where the upper left 3x3 elements
- * are a rotation matrix, and the upper three elements in the fourth
- * column are the translation. The bottom row is assumed to be [0, 0, 0, 1].
- * The matrix is not verified to be in the proper form.
- * This method is faster than computing the product for general 4x4
- * matrices using {@link Matrix4.multiply}.
- *
- * @param {Matrix4} left The first matrix.
- * @param {Matrix4} right The second matrix.
- * @param {Matrix4} result The object onto which to store the result.
- * @returns {Matrix4} The modified result parameter.
- *
- * @example
- * var m1 = new Cesium.Matrix4(1.0, 6.0, 7.0, 0.0, 2.0, 5.0, 8.0, 0.0, 3.0, 4.0, 9.0, 0.0, 0.0, 0.0, 0.0, 1.0);
- * var m2 = Cesium.Transforms.eastNorthUpToFixedFrame(new Cesium.Cartesian3(1.0, 1.0, 1.0));
- * var m3 = Cesium.Matrix4.multiplyTransformation(m1, m2, new Cesium.Matrix4());
- */
- Matrix4.multiplyTransformation = function(left, right, result) {
- //>>includeStart('debug', pragmas.debug);
- Check.Check.typeOf.object('left', left);
- Check.Check.typeOf.object('right', right);
- Check.Check.typeOf.object('result', result);
- //>>includeEnd('debug');
- var left0 = left[0];
- var left1 = left[1];
- var left2 = left[2];
- var left4 = left[4];
- var left5 = left[5];
- var left6 = left[6];
- var left8 = left[8];
- var left9 = left[9];
- var left10 = left[10];
- var left12 = left[12];
- var left13 = left[13];
- var left14 = left[14];
- var right0 = right[0];
- var right1 = right[1];
- var right2 = right[2];
- var right4 = right[4];
- var right5 = right[5];
- var right6 = right[6];
- var right8 = right[8];
- var right9 = right[9];
- var right10 = right[10];
- var right12 = right[12];
- var right13 = right[13];
- var right14 = right[14];
- var column0Row0 = left0 * right0 + left4 * right1 + left8 * right2;
- var column0Row1 = left1 * right0 + left5 * right1 + left9 * right2;
- var column0Row2 = left2 * right0 + left6 * right1 + left10 * right2;
- var column1Row0 = left0 * right4 + left4 * right5 + left8 * right6;
- var column1Row1 = left1 * right4 + left5 * right5 + left9 * right6;
- var column1Row2 = left2 * right4 + left6 * right5 + left10 * right6;
- var column2Row0 = left0 * right8 + left4 * right9 + left8 * right10;
- var column2Row1 = left1 * right8 + left5 * right9 + left9 * right10;
- var column2Row2 = left2 * right8 + left6 * right9 + left10 * right10;
- var column3Row0 = left0 * right12 + left4 * right13 + left8 * right14 + left12;
- var column3Row1 = left1 * right12 + left5 * right13 + left9 * right14 + left13;
- var column3Row2 = left2 * right12 + left6 * right13 + left10 * right14 + left14;
- result[0] = column0Row0;
- result[1] = column0Row1;
- result[2] = column0Row2;
- result[3] = 0.0;
- result[4] = column1Row0;
- result[5] = column1Row1;
- result[6] = column1Row2;
- result[7] = 0.0;
- result[8] = column2Row0;
- result[9] = column2Row1;
- result[10] = column2Row2;
- result[11] = 0.0;
- result[12] = column3Row0;
- result[13] = column3Row1;
- result[14] = column3Row2;
- result[15] = 1.0;
- return result;
- };
- /**
- * Multiplies a transformation matrix (with a bottom row of <code>[0.0, 0.0, 0.0, 1.0]</code>)
- * by a 3x3 rotation matrix. This is an optimization
- * for <code>Matrix4.multiply(m, Matrix4.fromRotationTranslation(rotation), m);</code> with less allocations and arithmetic operations.
- *
- * @param {Matrix4} matrix The matrix on the left-hand side.
- * @param {Matrix3} rotation The 3x3 rotation matrix on the right-hand side.
- * @param {Matrix4} result The object onto which to store the result.
- * @returns {Matrix4} The modified result parameter.
- *
- * @example
- * // Instead of Cesium.Matrix4.multiply(m, Cesium.Matrix4.fromRotationTranslation(rotation), m);
- * Cesium.Matrix4.multiplyByMatrix3(m, rotation, m);
- */
- Matrix4.multiplyByMatrix3 = function(matrix, rotation, result) {
- //>>includeStart('debug', pragmas.debug);
- Check.Check.typeOf.object('matrix', matrix);
- Check.Check.typeOf.object('rotation', rotation);
- Check.Check.typeOf.object('result', result);
- //>>includeEnd('debug');
- var left0 = matrix[0];
- var left1 = matrix[1];
- var left2 = matrix[2];
- var left4 = matrix[4];
- var left5 = matrix[5];
- var left6 = matrix[6];
- var left8 = matrix[8];
- var left9 = matrix[9];
- var left10 = matrix[10];
- var right0 = rotation[0];
- var right1 = rotation[1];
- var right2 = rotation[2];
- var right4 = rotation[3];
- var right5 = rotation[4];
- var right6 = rotation[5];
- var right8 = rotation[6];
- var right9 = rotation[7];
- var right10 = rotation[8];
- var column0Row0 = left0 * right0 + left4 * right1 + left8 * right2;
- var column0Row1 = left1 * right0 + left5 * right1 + left9 * right2;
- var column0Row2 = left2 * right0 + left6 * right1 + left10 * right2;
- var column1Row0 = left0 * right4 + left4 * right5 + left8 * right6;
- var column1Row1 = left1 * right4 + left5 * right5 + left9 * right6;
- var column1Row2 = left2 * right4 + left6 * right5 + left10 * right6;
- var column2Row0 = left0 * right8 + left4 * right9 + left8 * right10;
- var column2Row1 = left1 * right8 + left5 * right9 + left9 * right10;
- var column2Row2 = left2 * right8 + left6 * right9 + left10 * right10;
- result[0] = column0Row0;
- result[1] = column0Row1;
- result[2] = column0Row2;
- result[3] = 0.0;
- result[4] = column1Row0;
- result[5] = column1Row1;
- result[6] = column1Row2;
- result[7] = 0.0;
- result[8] = column2Row0;
- result[9] = column2Row1;
- result[10] = column2Row2;
- result[11] = 0.0;
- result[12] = matrix[12];
- result[13] = matrix[13];
- result[14] = matrix[14];
- result[15] = matrix[15];
- return result;
- };
- /**
- * Multiplies a transformation matrix (with a bottom row of <code>[0.0, 0.0, 0.0, 1.0]</code>)
- * by an implicit translation matrix defined by a {@link Cartesian3}. This is an optimization
- * for <code>Matrix4.multiply(m, Matrix4.fromTranslation(position), m);</code> with less allocations and arithmetic operations.
- *
- * @param {Matrix4} matrix The matrix on the left-hand side.
- * @param {Cartesian3} translation The translation on the right-hand side.
- * @param {Matrix4} result The object onto which to store the result.
- * @returns {Matrix4} The modified result parameter.
- *
- * @example
- * // Instead of Cesium.Matrix4.multiply(m, Cesium.Matrix4.fromTranslation(position), m);
- * Cesium.Matrix4.multiplyByTranslation(m, position, m);
- */
- Matrix4.multiplyByTranslation = function(matrix, translation, result) {
- //>>includeStart('debug', pragmas.debug);
- Check.Check.typeOf.object('matrix', matrix);
- Check.Check.typeOf.object('translation', translation);
- Check.Check.typeOf.object('result', result);
- //>>includeEnd('debug');
- var x = translation.x;
- var y = translation.y;
- var z = translation.z;
- var tx = (x * matrix[0]) + (y * matrix[4]) + (z * matrix[8]) + matrix[12];
- var ty = (x * matrix[1]) + (y * matrix[5]) + (z * matrix[9]) + matrix[13];
- var tz = (x * matrix[2]) + (y * matrix[6]) + (z * matrix[10]) + matrix[14];
- result[0] = matrix[0];
- result[1] = matrix[1];
- result[2] = matrix[2];
- result[3] = matrix[3];
- result[4] = matrix[4];
- result[5] = matrix[5];
- result[6] = matrix[6];
- result[7] = matrix[7];
- result[8] = matrix[8];
- result[9] = matrix[9];
- result[10] = matrix[10];
- result[11] = matrix[11];
- result[12] = tx;
- result[13] = ty;
- result[14] = tz;
- result[15] = matrix[15];
- return result;
- };
- var uniformScaleScratch = new Cartographic.Cartesian3();
- /**
- * Multiplies an affine transformation matrix (with a bottom row of <code>[0.0, 0.0, 0.0, 1.0]</code>)
- * by an implicit uniform scale matrix. This is an optimization
- * for <code>Matrix4.multiply(m, Matrix4.fromUniformScale(scale), m);</code>, where
- * <code>m</code> must be an affine matrix.
- * This function performs fewer allocations and arithmetic operations.
- *
- * @param {Matrix4} matrix The affine matrix on the left-hand side.
- * @param {Number} scale The uniform scale on the right-hand side.
- * @param {Matrix4} result The object onto which to store the result.
- * @returns {Matrix4} The modified result parameter.
- *
- *
- * @example
- * // Instead of Cesium.Matrix4.multiply(m, Cesium.Matrix4.fromUniformScale(scale), m);
- * Cesium.Matrix4.multiplyByUniformScale(m, scale, m);
- *
- * @see Matrix4.fromUniformScale
- * @see Matrix4.multiplyByScale
- */
- Matrix4.multiplyByUniformScale = function(matrix, scale, result) {
- //>>includeStart('debug', pragmas.debug);
- Check.Check.typeOf.object('matrix', matrix);
- Check.Check.typeOf.number('scale', scale);
- Check.Check.typeOf.object('result', result);
- //>>includeEnd('debug');
- uniformScaleScratch.x = scale;
- uniformScaleScratch.y = scale;
- uniformScaleScratch.z = scale;
- return Matrix4.multiplyByScale(matrix, uniformScaleScratch, result);
- };
- /**
- * Multiplies an affine transformation matrix (with a bottom row of <code>[0.0, 0.0, 0.0, 1.0]</code>)
- * by an implicit non-uniform scale matrix. This is an optimization
- * for <code>Matrix4.multiply(m, Matrix4.fromUniformScale(scale), m);</code>, where
- * <code>m</code> must be an affine matrix.
- * This function performs fewer allocations and arithmetic operations.
- *
- * @param {Matrix4} matrix The affine matrix on the left-hand side.
- * @param {Cartesian3} scale The non-uniform scale on the right-hand side.
- * @param {Matrix4} result The object onto which to store the result.
- * @returns {Matrix4} The modified result parameter.
- *
- *
- * @example
- * // Instead of Cesium.Matrix4.multiply(m, Cesium.Matrix4.fromScale(scale), m);
- * Cesium.Matrix4.multiplyByScale(m, scale, m);
- *
- * @see Matrix4.fromScale
- * @see Matrix4.multiplyByUniformScale
- */
- Matrix4.multiplyByScale = function(matrix, scale, result) {
- //>>includeStart('debug', pragmas.debug);
- Check.Check.typeOf.object('matrix', matrix);
- Check.Check.typeOf.object('scale', scale);
- Check.Check.typeOf.object('result', result);
- //>>includeEnd('debug');
- var scaleX = scale.x;
- var scaleY = scale.y;
- var scaleZ = scale.z;
- // Faster than Cartesian3.equals
- if ((scaleX === 1.0) && (scaleY === 1.0) && (scaleZ === 1.0)) {
- return Matrix4.clone(matrix, result);
- }
- result[0] = scaleX * matrix[0];
- result[1] = scaleX * matrix[1];
- result[2] = scaleX * matrix[2];
- result[3] = 0.0;
- result[4] = scaleY * matrix[4];
- result[5] = scaleY * matrix[5];
- result[6] = scaleY * matrix[6];
- result[7] = 0.0;
- result[8] = scaleZ * matrix[8];
- result[9] = scaleZ * matrix[9];
- result[10] = scaleZ * matrix[10];
- result[11] = 0.0;
- result[12] = matrix[12];
- result[13] = matrix[13];
- result[14] = matrix[14];
- result[15] = 1.0;
- return result;
- };
- /**
- * Computes the product of a matrix and a column vector.
- *
- * @param {Matrix4} matrix The matrix.
- * @param {Cartesian4} cartesian The vector.
- * @param {Cartesian4} result The object onto which to store the result.
- * @returns {Cartesian4} The modified result parameter.
- */
- Matrix4.multiplyByVector = function(matrix, cartesian, result) {
- //>>includeStart('debug', pragmas.debug);
- Check.Check.typeOf.object('matrix', matrix);
- Check.Check.typeOf.object('cartesian', cartesian);
- Check.Check.typeOf.object('result', result);
- //>>includeEnd('debug');
- var vX = cartesian.x;
- var vY = cartesian.y;
- var vZ = cartesian.z;
- var vW = cartesian.w;
- var x = matrix[0] * vX + matrix[4] * vY + matrix[8] * vZ + matrix[12] * vW;
- var y = matrix[1] * vX + matrix[5] * vY + matrix[9] * vZ + matrix[13] * vW;
- var z = matrix[2] * vX + matrix[6] * vY + matrix[10] * vZ + matrix[14] * vW;
- var w = matrix[3] * vX + matrix[7] * vY + matrix[11] * vZ + matrix[15] * vW;
- result.x = x;
- result.y = y;
- result.z = z;
- result.w = w;
- return result;
- };
- /**
- * Computes the product of a matrix and a {@link Cartesian3}. This is equivalent to calling {@link Matrix4.multiplyByVector}
- * with a {@link Cartesian4} with a <code>w</code> component of zero.
- *
- * @param {Matrix4} matrix The matrix.
- * @param {Cartesian3} cartesian The point.
- * @param {Cartesian3} result The object onto which to store the result.
- * @returns {Cartesian3} The modified result parameter.
- *
- * @example
- * var p = new Cesium.Cartesian3(1.0, 2.0, 3.0);
- * var result = Cesium.Matrix4.multiplyByPointAsVector(matrix, p, new Cesium.Cartesian3());
- * // A shortcut for
- * // Cartesian3 p = ...
- * // Cesium.Matrix4.multiplyByVector(matrix, new Cesium.Cartesian4(p.x, p.y, p.z, 0.0), result);
- */
- Matrix4.multiplyByPointAsVector = function(matrix, cartesian, result) {
- //>>includeStart('debug', pragmas.debug);
- Check.Check.typeOf.object('matrix', matrix);
- Check.Check.typeOf.object('cartesian', cartesian);
- Check.Check.typeOf.object('result', result);
- //>>includeEnd('debug');
- var vX = cartesian.x;
- var vY = cartesian.y;
- var vZ = cartesian.z;
- var x = matrix[0] * vX + matrix[4] * vY + matrix[8] * vZ;
- var y = matrix[1] * vX + matrix[5] * vY + matrix[9] * vZ;
- var z = matrix[2] * vX + matrix[6] * vY + matrix[10] * vZ;
- result.x = x;
- result.y = y;
- result.z = z;
- return result;
- };
- /**
- * Computes the product of a matrix and a {@link Cartesian3}. This is equivalent to calling {@link Matrix4.multiplyByVector}
- * with a {@link Cartesian4} with a <code>w</code> component of 1, but returns a {@link Cartesian3} instead of a {@link Cartesian4}.
- *
- * @param {Matrix4} matrix The matrix.
- * @param {Cartesian3} cartesian The point.
- * @param {Cartesian3} result The object onto which to store the result.
- * @returns {Cartesian3} The modified result parameter.
- *
- * @example
- * var p = new Cesium.Cartesian3(1.0, 2.0, 3.0);
- * var result = Cesium.Matrix4.multiplyByPoint(matrix, p, new Cesium.Cartesian3());
- */
- Matrix4.multiplyByPoint = function(matrix, cartesian, result) {
- //>>includeStart('debug', pragmas.debug);
- Check.Check.typeOf.object('matrix', matrix);
- Check.Check.typeOf.object('cartesian', cartesian);
- Check.Check.typeOf.object('result', result);
- //>>includeEnd('debug');
- var vX = cartesian.x;
- var vY = cartesian.y;
- var vZ = cartesian.z;
- var x = matrix[0] * vX + matrix[4] * vY + matrix[8] * vZ + matrix[12];
- var y = matrix[1] * vX + matrix[5] * vY + matrix[9] * vZ + matrix[13];
- var z = matrix[2] * vX + matrix[6] * vY + matrix[10] * vZ + matrix[14];
- result.x = x;
- result.y = y;
- result.z = z;
- return result;
- };
- /**
- * Computes the product of a matrix and a scalar.
- *
- * @param {Matrix4} matrix The matrix.
- * @param {Number} scalar The number to multiply by.
- * @param {Matrix4} result The object onto which to store the result.
- * @returns {Matrix4} The modified result parameter.
- *
- * @example
- * //create a Matrix4 instance which is a scaled version of the supplied Matrix4
- * // m = [10.0, 11.0, 12.0, 13.0]
- * // [14.0, 15.0, 16.0, 17.0]
- * // [18.0, 19.0, 20.0, 21.0]
- * // [22.0, 23.0, 24.0, 25.0]
- *
- * var a = Cesium.Matrix4.multiplyByScalar(m, -2, new Cesium.Matrix4());
- *
- * // m remains the same
- * // a = [-20.0, -22.0, -24.0, -26.0]
- * // [-28.0, -30.0, -32.0, -34.0]
- * // [-36.0, -38.0, -40.0, -42.0]
- * // [-44.0, -46.0, -48.0, -50.0]
- */
- Matrix4.multiplyByScalar = function(matrix, scalar, result) {
- //>>includeStart('debug', pragmas.debug);
- Check.Check.typeOf.object('matrix', matrix);
- Check.Check.typeOf.number('scalar', scalar);
- Check.Check.typeOf.object('result', result);
- //>>includeEnd('debug');
- result[0] = matrix[0] * scalar;
- result[1] = matrix[1] * scalar;
- result[2] = matrix[2] * scalar;
- result[3] = matrix[3] * scalar;
- result[4] = matrix[4] * scalar;
- result[5] = matrix[5] * scalar;
- result[6] = matrix[6] * scalar;
- result[7] = matrix[7] * scalar;
- result[8] = matrix[8] * scalar;
- result[9] = matrix[9] * scalar;
- result[10] = matrix[10] * scalar;
- result[11] = matrix[11] * scalar;
- result[12] = matrix[12] * scalar;
- result[13] = matrix[13] * scalar;
- result[14] = matrix[14] * scalar;
- result[15] = matrix[15] * scalar;
- return result;
- };
- /**
- * Compute the product of a matrix and a plane.
- * @param matrix
- * @param plane
- * @param result
- * @returns {*}
- */
- Matrix4.multiplyByPlane = function(matrix, plane, result) {
- //>>includeStart('debug', pragmas.debug);
- Check.Check.typeOf.object('matrix', matrix);
- Check.Check.typeOf.object('plane', plane);
- Check.Check.typeOf.object('result', result);
- //>>includeEnd('debug');
- var inverseMat = new Matrix4();
- var invTrans = new Matrix4();
- Matrix4.inverse(matrix, inverseMat);
- Matrix4.transpose(inverseMat, invTrans);
- var v4 = new Cartesian4.Cartesian4(plane.normal.x, plane.normal.y, plane.normal.z, plane.distance);
- Matrix4.multiplyByVector(invTrans, v4, v4);
- result.normal.x = v4.x;
- result.normal.y = v4.y;
- result.normal.z = v4.z;
- var length = Cartographic.Cartesian3.magnitude(result.normal);
- Cartographic.Cartesian3.normalize(result.normal, result.normal);
- result.distance = v4.w / length;
- return result;
- };
- /**
- * Computes a negated copy of the provided matrix.
- *
- * @param {Matrix4} matrix The matrix to negate.
- * @param {Matrix4} result The object onto which to store the result.
- * @returns {Matrix4} The modified result parameter.
- *
- * @example
- * //create a new Matrix4 instance which is a negation of a Matrix4
- * // m = [10.0, 11.0, 12.0, 13.0]
- * // [14.0, 15.0, 16.0, 17.0]
- * // [18.0, 19.0, 20.0, 21.0]
- * // [22.0, 23.0, 24.0, 25.0]
- *
- * var a = Cesium.Matrix4.negate(m, new Cesium.Matrix4());
- *
- * // m remains the same
- * // a = [-10.0, -11.0, -12.0, -13.0]
- * // [-14.0, -15.0, -16.0, -17.0]
- * // [-18.0, -19.0, -20.0, -21.0]
- * // [-22.0, -23.0, -24.0, -25.0]
- */
- Matrix4.negate = function(matrix, result) {
- //>>includeStart('debug', pragmas.debug);
- Check.Check.typeOf.object('matrix', matrix);
- Check.Check.typeOf.object('result', result);
- //>>includeEnd('debug');
- result[0] = -matrix[0];
- result[1] = -matrix[1];
- result[2] = -matrix[2];
- result[3] = -matrix[3];
- result[4] = -matrix[4];
- result[5] = -matrix[5];
- result[6] = -matrix[6];
- result[7] = -matrix[7];
- result[8] = -matrix[8];
- result[9] = -matrix[9];
- result[10] = -matrix[10];
- result[11] = -matrix[11];
- result[12] = -matrix[12];
- result[13] = -matrix[13];
- result[14] = -matrix[14];
- result[15] = -matrix[15];
- return result;
- };
- /**
- * Computes the transpose of the provided matrix.
- *
- * @param {Matrix4} matrix The matrix to transpose.
- * @param {Matrix4} result The object onto which to store the result.
- * @returns {Matrix4} The modified result parameter.
- *
- * @example
- * //returns transpose of a Matrix4
- * // m = [10.0, 11.0, 12.0, 13.0]
- * // [14.0, 15.0, 16.0, 17.0]
- * // [18.0, 19.0, 20.0, 21.0]
- * // [22.0, 23.0, 24.0, 25.0]
- *
- * var a = Cesium.Matrix4.transpose(m, new Cesium.Matrix4());
- *
- * // m remains the same
- * // a = [10.0, 14.0, 18.0, 22.0]
- * // [11.0, 15.0, 19.0, 23.0]
- * // [12.0, 16.0, 20.0, 24.0]
- * // [13.0, 17.0, 21.0, 25.0]
- */
- Matrix4.transpose = function(matrix, result) {
- //>>includeStart('debug', pragmas.debug);
- Check.Check.typeOf.object('matrix', matrix);
- Check.Check.typeOf.object('result', result);
- //>>includeEnd('debug');
- var matrix1 = matrix[1];
- var matrix2 = matrix[2];
- var matrix3 = matrix[3];
- var matrix6 = matrix[6];
- var matrix7 = matrix[7];
- var matrix11 = matrix[11];
- result[0] = matrix[0];
- result[1] = matrix[4];
- result[2] = matrix[8];
- result[3] = matrix[12];
- result[4] = matrix1;
- result[5] = matrix[5];
- result[6] = matrix[9];
- result[7] = matrix[13];
- result[8] = matrix2;
- result[9] = matrix6;
- result[10] = matrix[10];
- result[11] = matrix[14];
- result[12] = matrix3;
- result[13] = matrix7;
- result[14] = matrix11;
- result[15] = matrix[15];
- return result;
- };
- /**
- * Computes a matrix, which contains the absolute (unsigned) values of the provided matrix's elements.
- *
- * @param {Matrix4} matrix The matrix with signed elements.
- * @param {Matrix4} result The object onto which to store the result.
- * @returns {Matrix4} The modified result parameter.
- */
- Matrix4.abs = function(matrix, result) {
- //>>includeStart('debug', pragmas.debug);
- Check.Check.typeOf.object('matrix', matrix);
- Check.Check.typeOf.object('result', result);
- //>>includeEnd('debug');
- result[0] = Math.abs(matrix[0]);
- result[1] = Math.abs(matrix[1]);
- result[2] = Math.abs(matrix[2]);
- result[3] = Math.abs(matrix[3]);
- result[4] = Math.abs(matrix[4]);
- result[5] = Math.abs(matrix[5]);
- result[6] = Math.abs(matrix[6]);
- result[7] = Math.abs(matrix[7]);
- result[8] = Math.abs(matrix[8]);
- result[9] = Math.abs(matrix[9]);
- result[10] = Math.abs(matrix[10]);
- result[11] = Math.abs(matrix[11]);
- result[12] = Math.abs(matrix[12]);
- result[13] = Math.abs(matrix[13]);
- result[14] = Math.abs(matrix[14]);
- result[15] = Math.abs(matrix[15]);
- return result;
- };
- /**
- * Compares the provided matrices componentwise and returns
- * <code>true</code> if they are equal, <code>false</code> otherwise.
- *
- * @param {Matrix4} [left] The first matrix.
- * @param {Matrix4} [right] The second matrix.
- * @returns {Boolean} <code>true</code> if left and right are equal, <code>false</code> otherwise.
- *
- * @example
- * //compares two Matrix4 instances
- *
- * // a = [10.0, 14.0, 18.0, 22.0]
- * // [11.0, 15.0, 19.0, 23.0]
- * // [12.0, 16.0, 20.0, 24.0]
- * // [13.0, 17.0, 21.0, 25.0]
- *
- * // b = [10.0, 14.0, 18.0, 22.0]
- * // [11.0, 15.0, 19.0, 23.0]
- * // [12.0, 16.0, 20.0, 24.0]
- * // [13.0, 17.0, 21.0, 25.0]
- *
- * if(Cesium.Matrix4.equals(a,b)) {
- * console.log("Both matrices are equal");
- * } else {
- * console.log("They are not equal");
- * }
- *
- * //Prints "Both matrices are equal" on the console
- */
- Matrix4.equals = function(left, right) {
- // Given that most matrices will be transformation matrices, the elements
- // are tested in order such that the test is likely to fail as early
- // as possible. I _think_ this is just as friendly to the L1 cache
- // as testing in index order. It is certainty faster in practice.
- return (left === right) ||
- (when.defined(left) &&
- when.defined(right) &&
- // Translation
- left[12] === right[12] &&
- left[13] === right[13] &&
- left[14] === right[14] &&
- // Rotation/scale
- left[0] === right[0] &&
- left[1] === right[1] &&
- left[2] === right[2] &&
- left[4] === right[4] &&
- left[5] === right[5] &&
- left[6] === right[6] &&
- left[8] === right[8] &&
- left[9] === right[9] &&
- left[10] === right[10] &&
- // Bottom row
- left[3] === right[3] &&
- left[7] === right[7] &&
- left[11] === right[11] &&
- left[15] === right[15]);
- };
- /**
- * Compares the provided matrices componentwise and returns
- * <code>true</code> if they are within the provided epsilon,
- * <code>false</code> otherwise.
- *
- * @param {Matrix4} [left] The first matrix.
- * @param {Matrix4} [right] The second matrix.
- * @param {Number} epsilon The epsilon to use for equality testing.
- * @returns {Boolean} <code>true</code> if left and right are within the provided epsilon, <code>false</code> otherwise.
- *
- * @example
- * //compares two Matrix4 instances
- *
- * // a = [10.5, 14.5, 18.5, 22.5]
- * // [11.5, 15.5, 19.5, 23.5]
- * // [12.5, 16.5, 20.5, 24.5]
- * // [13.5, 17.5, 21.5, 25.5]
- *
- * // b = [10.0, 14.0, 18.0, 22.0]
- * // [11.0, 15.0, 19.0, 23.0]
- * // [12.0, 16.0, 20.0, 24.0]
- * // [13.0, 17.0, 21.0, 25.0]
- *
- * if(Cesium.Matrix4.equalsEpsilon(a,b,0.1)){
- * console.log("Difference between both the matrices is less than 0.1");
- * } else {
- * console.log("Difference between both the matrices is not less than 0.1");
- * }
- *
- * //Prints "Difference between both the matrices is not less than 0.1" on the console
- */
- Matrix4.equalsEpsilon = function(left, right, epsilon) {
- //>>includeStart('debug', pragmas.debug);
- Check.Check.typeOf.number('epsilon', epsilon);
- //>>includeEnd('debug');
- return (left === right) ||
- (when.defined(left) &&
- when.defined(right) &&
- Math.abs(left[0] - right[0]) <= epsilon &&
- Math.abs(left[1] - right[1]) <= epsilon &&
- Math.abs(left[2] - right[2]) <= epsilon &&
- Math.abs(left[3] - right[3]) <= epsilon &&
- Math.abs(left[4] - right[4]) <= epsilon &&
- Math.abs(left[5] - right[5]) <= epsilon &&
- Math.abs(left[6] - right[6]) <= epsilon &&
- Math.abs(left[7] - right[7]) <= epsilon &&
- Math.abs(left[8] - right[8]) <= epsilon &&
- Math.abs(left[9] - right[9]) <= epsilon &&
- Math.abs(left[10] - right[10]) <= epsilon &&
- Math.abs(left[11] - right[11]) <= epsilon &&
- Math.abs(left[12] - right[12]) <= epsilon &&
- Math.abs(left[13] - right[13]) <= epsilon &&
- Math.abs(left[14] - right[14]) <= epsilon &&
- Math.abs(left[15] - right[15]) <= epsilon);
- };
- /**
- * Gets the translation portion of the provided matrix, assuming the matrix is a affine transformation matrix.
- *
- * @param {Matrix4} matrix The matrix to use.
- * @param {Cartesian3} result The object onto which to store the result.
- * @returns {Cartesian3} The modified result parameter.
- */
- Matrix4.getTranslation = function(matrix, result) {
- //>>includeStart('debug', pragmas.debug);
- Check.Check.typeOf.object('matrix', matrix);
- Check.Check.typeOf.object('result', result);
- //>>includeEnd('debug');
- result.x = matrix[12];
- result.y = matrix[13];
- result.z = matrix[14];
- return result;
- };
- /**
- * Gets the upper left 3x3 rotation matrix of the provided matrix, assuming the matrix is an affine transformation matrix.
- *
- * @param {Matrix4} matrix The matrix to use.
- * @param {Matrix3} result The object onto which to store the result.
- * @returns {Matrix3} The modified result parameter.
- *
- * @example
- * // returns a Matrix3 instance from a Matrix4 instance
- *
- * // m = [10.0, 14.0, 18.0, 22.0]
- * // [11.0, 15.0, 19.0, 23.0]
- * // [12.0, 16.0, 20.0, 24.0]
- * // [13.0, 17.0, 21.0, 25.0]
- *
- * var b = new Cesium.Matrix3();
- * Cesium.Matrix4.getMatrix3(m,b);
- *
- * // b = [10.0, 14.0, 18.0]
- * // [11.0, 15.0, 19.0]
- * // [12.0, 16.0, 20.0]
- */
- Matrix4.getMatrix3 = function(matrix, result) {
- //>>includeStart('debug', pragmas.debug);
- Check.Check.typeOf.object('matrix', matrix);
- Check.Check.typeOf.object('result', result);
- //>>includeEnd('debug');
- result[0] = matrix[0];
- result[1] = matrix[1];
- result[2] = matrix[2];
- result[3] = matrix[4];
- result[4] = matrix[5];
- result[5] = matrix[6];
- result[6] = matrix[8];
- result[7] = matrix[9];
- result[8] = matrix[10];
- return result;
- };
- /**
- * Gets the upper left 3x3 rotation matrix of the provided matrix, assuming the matrix is a affine transformation matrix.
- *
- * @param {Matrix4} matrix The matrix to use.
- * @param {Matrix3} result The object onto which to store the result.
- * @returns {Matrix3} The modified result parameter.
- *
- * @example
- * // returns a Matrix3 instance from a Matrix4 instance
- *
- * // m = [10.0, 14.0, 18.0, 22.0]
- * // [11.0, 15.0, 19.0, 23.0]
- * // [12.0, 16.0, 20.0, 24.0]
- * // [13.0, 17.0, 21.0, 25.0]
- *
- * var b = new Cesium.Matrix3();
- * Cesium.Matrix4.getRotation(m,b);
- *
- * // b = [10.0, 14.0, 18.0]
- * // [11.0, 15.0, 19.0]
- * // [12.0, 16.0, 20.0]
- */
- Matrix4.getRotation = function(matrix, result) {
- //>>includeStart('debug', pragmas.debug);
- Check.Check.typeOf.object('matrix', matrix);
- Check.Check.typeOf.object('result', result);
- //>>includeEnd('debug');
- result[0] = matrix[0];
- result[1] = matrix[1];
- result[2] = matrix[2];
- result[3] = matrix[4];
- result[4] = matrix[5];
- result[5] = matrix[6];
- result[6] = matrix[8];
- result[7] = matrix[9];
- result[8] = matrix[10];
- return result;
- };
- var scratchInverseRotation = new Matrix3();
- var scratchMatrix3Zero = new Matrix3();
- var scratchBottomRow = new Cartesian4.Cartesian4();
- var scratchExpectedBottomRow = new Cartesian4.Cartesian4(0.0, 0.0, 0.0, 1.0);
- /**
- * Computes the inverse of the provided matrix using Cramers Rule.
- * If the determinant is zero, the matrix can not be inverted, and an exception is thrown.
- * If the matrix is an affine transformation matrix, it is more efficient
- * to invert it with {@link Matrix4.inverseTransformation}.
- *
- * @param {Matrix4} matrix The matrix to invert.
- * @param {Matrix4} result The object onto which to store the result.
- * @returns {Matrix4} The modified result parameter.
- *
- * @exception {RuntimeError} matrix is not invertible because its determinate is zero.
- */
- Matrix4.inverse = function(matrix, result) {
- //>>includeStart('debug', pragmas.debug);
- Check.Check.typeOf.object('matrix', matrix);
- Check.Check.typeOf.object('result', result);
- //>>includeEnd('debug');
- //
- // Ported from:
- // ftp://download.intel.com/design/PentiumIII/sml/24504301.pdf
- //
- var src0 = matrix[0];
- var src1 = matrix[4];
- var src2 = matrix[8];
- var src3 = matrix[12];
- var src4 = matrix[1];
- var src5 = matrix[5];
- var src6 = matrix[9];
- var src7 = matrix[13];
- var src8 = matrix[2];
- var src9 = matrix[6];
- var src10 = matrix[10];
- var src11 = matrix[14];
- var src12 = matrix[3];
- var src13 = matrix[7];
- var src14 = matrix[11];
- var src15 = matrix[15];
- // calculate pairs for first 8 elements (cofactors)
- var tmp0 = src10 * src15;
- var tmp1 = src11 * src14;
- var tmp2 = src9 * src15;
- var tmp3 = src11 * src13;
- var tmp4 = src9 * src14;
- var tmp5 = src10 * src13;
- var tmp6 = src8 * src15;
- var tmp7 = src11 * src12;
- var tmp8 = src8 * src14;
- var tmp9 = src10 * src12;
- var tmp10 = src8 * src13;
- var tmp11 = src9 * src12;
- // calculate first 8 elements (cofactors)
- var dst0 = (tmp0 * src5 + tmp3 * src6 + tmp4 * src7) - (tmp1 * src5 + tmp2 * src6 + tmp5 * src7);
- var dst1 = (tmp1 * src4 + tmp6 * src6 + tmp9 * src7) - (tmp0 * src4 + tmp7 * src6 + tmp8 * src7);
- var dst2 = (tmp2 * src4 + tmp7 * src5 + tmp10 * src7) - (tmp3 * src4 + tmp6 * src5 + tmp11 * src7);
- var dst3 = (tmp5 * src4 + tmp8 * src5 + tmp11 * src6) - (tmp4 * src4 + tmp9 * src5 + tmp10 * src6);
- var dst4 = (tmp1 * src1 + tmp2 * src2 + tmp5 * src3) - (tmp0 * src1 + tmp3 * src2 + tmp4 * src3);
- var dst5 = (tmp0 * src0 + tmp7 * src2 + tmp8 * src3) - (tmp1 * src0 + tmp6 * src2 + tmp9 * src3);
- var dst6 = (tmp3 * src0 + tmp6 * src1 + tmp11 * src3) - (tmp2 * src0 + tmp7 * src1 + tmp10 * src3);
- var dst7 = (tmp4 * src0 + tmp9 * src1 + tmp10 * src2) - (tmp5 * src0 + tmp8 * src1 + tmp11 * src2);
- // calculate pairs for second 8 elements (cofactors)
- tmp0 = src2 * src7;
- tmp1 = src3 * src6;
- tmp2 = src1 * src7;
- tmp3 = src3 * src5;
- tmp4 = src1 * src6;
- tmp5 = src2 * src5;
- tmp6 = src0 * src7;
- tmp7 = src3 * src4;
- tmp8 = src0 * src6;
- tmp9 = src2 * src4;
- tmp10 = src0 * src5;
- tmp11 = src1 * src4;
- // calculate second 8 elements (cofactors)
- var dst8 = (tmp0 * src13 + tmp3 * src14 + tmp4 * src15) - (tmp1 * src13 + tmp2 * src14 + tmp5 * src15);
- var dst9 = (tmp1 * src12 + tmp6 * src14 + tmp9 * src15) - (tmp0 * src12 + tmp7 * src14 + tmp8 * src15);
- var dst10 = (tmp2 * src12 + tmp7 * src13 + tmp10 * src15) - (tmp3 * src12 + tmp6 * src13 + tmp11 * src15);
- var dst11 = (tmp5 * src12 + tmp8 * src13 + tmp11 * src14) - (tmp4 * src12 + tmp9 * src13 + tmp10 * src14);
- var dst12 = (tmp2 * src10 + tmp5 * src11 + tmp1 * src9) - (tmp4 * src11 + tmp0 * src9 + tmp3 * src10);
- var dst13 = (tmp8 * src11 + tmp0 * src8 + tmp7 * src10) - (tmp6 * src10 + tmp9 * src11 + tmp1 * src8);
- var dst14 = (tmp6 * src9 + tmp11 * src11 + tmp3 * src8) - (tmp10 * src11 + tmp2 * src8 + tmp7 * src9);
- var dst15 = (tmp10 * src10 + tmp4 * src8 + tmp9 * src9) - (tmp8 * src9 + tmp11 * src10 + tmp5 * src8);
- // calculate determinant
- var det = src0 * dst0 + src1 * dst1 + src2 * dst2 + src3 * dst3;
- if (Math.abs(det) < _Math.CesiumMath.EPSILON21) {
- // Special case for a zero scale matrix that can occur, for example,
- // when a model's node has a [0, 0, 0] scale.
- if (Matrix3.equalsEpsilon(Matrix4.getRotation(matrix, scratchInverseRotation), scratchMatrix3Zero, _Math.CesiumMath.EPSILON7) &&
- Cartesian4.Cartesian4.equals(Matrix4.getRow(matrix, 3, scratchBottomRow), scratchExpectedBottomRow)) {
- result[0] = 0.0;
- result[1] = 0.0;
- result[2] = 0.0;
- result[3] = 0.0;
- result[4] = 0.0;
- result[5] = 0.0;
- result[6] = 0.0;
- result[7] = 0.0;
- result[8] = 0.0;
- result[9] = 0.0;
- result[10] = 0.0;
- result[11] = 0.0;
- result[12] = -matrix[12];
- result[13] = -matrix[13];
- result[14] = -matrix[14];
- result[15] = 1.0;
- return result;
- }
- throw new RuntimeError.RuntimeError('matrix is not invertible because its determinate is zero.');
- }
- // calculate matrix inverse
- det = 1.0 / det;
- result[0] = dst0 * det;
- result[1] = dst1 * det;
- result[2] = dst2 * det;
- result[3] = dst3 * det;
- result[4] = dst4 * det;
- result[5] = dst5 * det;
- result[6] = dst6 * det;
- result[7] = dst7 * det;
- result[8] = dst8 * det;
- result[9] = dst9 * det;
- result[10] = dst10 * det;
- result[11] = dst11 * det;
- result[12] = dst12 * det;
- result[13] = dst13 * det;
- result[14] = dst14 * det;
- result[15] = dst15 * det;
- return result;
- };
- /**
- * Computes the inverse of the provided matrix assuming it is
- * an affine transformation matrix, where the upper left 3x3 elements
- * are a rotation matrix, and the upper three elements in the fourth
- * column are the translation. The bottom row is assumed to be [0, 0, 0, 1].
- * The matrix is not verified to be in the proper form.
- * This method is faster than computing the inverse for a general 4x4
- * matrix using {@link Matrix4.inverse}.
- *
- * @param {Matrix4} matrix The matrix to invert.
- * @param {Matrix4} result The object onto which to store the result.
- * @returns {Matrix4} The modified result parameter.
- */
- Matrix4.inverseTransformation = function(matrix, result) {
- //>>includeStart('debug', pragmas.debug);
- Check.Check.typeOf.object('matrix', matrix);
- Check.Check.typeOf.object('result', result);
- //>>includeEnd('debug');
- //This function is an optimized version of the below 4 lines.
- //var rT = Matrix3.transpose(Matrix4.getRotation(matrix));
- //var rTN = Matrix3.negate(rT);
- //var rTT = Matrix3.multiplyByVector(rTN, Matrix4.getTranslation(matrix));
- //return Matrix4.fromRotationTranslation(rT, rTT, result);
- var matrix0 = matrix[0];
- var matrix1 = matrix[1];
- var matrix2 = matrix[2];
- var matrix4 = matrix[4];
- var matrix5 = matrix[5];
- var matrix6 = matrix[6];
- var matrix8 = matrix[8];
- var matrix9 = matrix[9];
- var matrix10 = matrix[10];
- var vX = matrix[12];
- var vY = matrix[13];
- var vZ = matrix[14];
- var x = -matrix0 * vX - matrix1 * vY - matrix2 * vZ;
- var y = -matrix4 * vX - matrix5 * vY - matrix6 * vZ;
- var z = -matrix8 * vX - matrix9 * vY - matrix10 * vZ;
- result[0] = matrix0;
- result[1] = matrix4;
- result[2] = matrix8;
- result[3] = 0.0;
- result[4] = matrix1;
- result[5] = matrix5;
- result[6] = matrix9;
- result[7] = 0.0;
- result[8] = matrix2;
- result[9] = matrix6;
- result[10] = matrix10;
- result[11] = 0.0;
- result[12] = x;
- result[13] = y;
- result[14] = z;
- result[15] = 1.0;
- return result;
- };
- /**
- * An immutable Matrix4 instance initialized to the identity matrix.
- *
- * @type {Matrix4}
- * @constant
- */
- Matrix4.IDENTITY = Object.freeze(new Matrix4(1.0, 0.0, 0.0, 0.0,
- 0.0, 1.0, 0.0, 0.0,
- 0.0, 0.0, 1.0, 0.0,
- 0.0, 0.0, 0.0, 1.0));
- /**
- * An immutable Matrix4 instance initialized to the zero matrix.
- *
- * @type {Matrix4}
- * @constant
- */
- Matrix4.ZERO = Object.freeze(new Matrix4(0.0, 0.0, 0.0, 0.0,
- 0.0, 0.0, 0.0, 0.0,
- 0.0, 0.0, 0.0, 0.0,
- 0.0, 0.0, 0.0, 0.0));
- /**
- * The index into Matrix4 for column 0, row 0.
- *
- * @type {Number}
- * @constant
- */
- Matrix4.COLUMN0ROW0 = 0;
- /**
- * The index into Matrix4 for column 0, row 1.
- *
- * @type {Number}
- * @constant
- */
- Matrix4.COLUMN0ROW1 = 1;
- /**
- * The index into Matrix4 for column 0, row 2.
- *
- * @type {Number}
- * @constant
- */
- Matrix4.COLUMN0ROW2 = 2;
- /**
- * The index into Matrix4 for column 0, row 3.
- *
- * @type {Number}
- * @constant
- */
- Matrix4.COLUMN0ROW3 = 3;
- /**
- * The index into Matrix4 for column 1, row 0.
- *
- * @type {Number}
- * @constant
- */
- Matrix4.COLUMN1ROW0 = 4;
- /**
- * The index into Matrix4 for column 1, row 1.
- *
- * @type {Number}
- * @constant
- */
- Matrix4.COLUMN1ROW1 = 5;
- /**
- * The index into Matrix4 for column 1, row 2.
- *
- * @type {Number}
- * @constant
- */
- Matrix4.COLUMN1ROW2 = 6;
- /**
- * The index into Matrix4 for column 1, row 3.
- *
- * @type {Number}
- * @constant
- */
- Matrix4.COLUMN1ROW3 = 7;
- /**
- * The index into Matrix4 for column 2, row 0.
- *
- * @type {Number}
- * @constant
- */
- Matrix4.COLUMN2ROW0 = 8;
- /**
- * The index into Matrix4 for column 2, row 1.
- *
- * @type {Number}
- * @constant
- */
- Matrix4.COLUMN2ROW1 = 9;
- /**
- * The index into Matrix4 for column 2, row 2.
- *
- * @type {Number}
- * @constant
- */
- Matrix4.COLUMN2ROW2 = 10;
- /**
- * The index into Matrix4 for column 2, row 3.
- *
- * @type {Number}
- * @constant
- */
- Matrix4.COLUMN2ROW3 = 11;
- /**
- * The index into Matrix4 for column 3, row 0.
- *
- * @type {Number}
- * @constant
- */
- Matrix4.COLUMN3ROW0 = 12;
- /**
- * The index into Matrix4 for column 3, row 1.
- *
- * @type {Number}
- * @constant
- */
- Matrix4.COLUMN3ROW1 = 13;
- /**
- * The index into Matrix4 for column 3, row 2.
- *
- * @type {Number}
- * @constant
- */
- Matrix4.COLUMN3ROW2 = 14;
- /**
- * The index into Matrix4 for column 3, row 3.
- *
- * @type {Number}
- * @constant
- */
- Matrix4.COLUMN3ROW3 = 15;
- Object.defineProperties(Matrix4.prototype, {
- /**
- * Gets the number of items in the collection.
- * @memberof Matrix4.prototype
- *
- * @type {Number}
- */
- length : {
- get : function() {
- return Matrix4.packedLength;
- }
- }
- });
- /**
- * Duplicates the provided Matrix4 instance.
- *
- * @param {Matrix4} [result] The object onto which to store the result.
- * @returns {Matrix4} The modified result parameter or a new Matrix4 instance if one was not provided.
- */
- Matrix4.prototype.clone = function(result) {
- return Matrix4.clone(this, result);
- };
- /**
- * Compares this matrix to the provided matrix componentwise and returns
- * <code>true</code> if they are equal, <code>false</code> otherwise.
- *
- * @param {Matrix4} [right] The right hand side matrix.
- * @returns {Boolean} <code>true</code> if they are equal, <code>false</code> otherwise.
- */
- Matrix4.prototype.equals = function(right) {
- return Matrix4.equals(this, right);
- };
- /**
- * @private
- */
- Matrix4.equalsArray = function(matrix, array, offset) {
- return matrix[0] === array[offset] &&
- matrix[1] === array[offset + 1] &&
- matrix[2] === array[offset + 2] &&
- matrix[3] === array[offset + 3] &&
- matrix[4] === array[offset + 4] &&
- matrix[5] === array[offset + 5] &&
- matrix[6] === array[offset + 6] &&
- matrix[7] === array[offset + 7] &&
- matrix[8] === array[offset + 8] &&
- matrix[9] === array[offset + 9] &&
- matrix[10] === array[offset + 10] &&
- matrix[11] === array[offset + 11] &&
- matrix[12] === array[offset + 12] &&
- matrix[13] === array[offset + 13] &&
- matrix[14] === array[offset + 14] &&
- matrix[15] === array[offset + 15];
- };
- /**
- * Compares this matrix to the provided matrix componentwise and returns
- * <code>true</code> if they are within the provided epsilon,
- * <code>false</code> otherwise.
- *
- * @param {Matrix4} [right] The right hand side matrix.
- * @param {Number} epsilon The epsilon to use for equality testing.
- * @returns {Boolean} <code>true</code> if they are within the provided epsilon, <code>false</code> otherwise.
- */
- Matrix4.prototype.equalsEpsilon = function(right, epsilon) {
- return Matrix4.equalsEpsilon(this, right, epsilon);
- };
- /**
- * Computes a string representing this Matrix with each row being
- * on a separate line and in the format '(column0, column1, column2, column3)'.
- *
- * @returns {String} A string representing the provided Matrix with each row being on a separate line and in the format '(column0, column1, column2, column3)'.
- */
- Matrix4.prototype.toString = function() {
- return '(' + this[0] + ', ' + this[4] + ', ' + this[8] + ', ' + this[12] +')\n' +
- '(' + this[1] + ', ' + this[5] + ', ' + this[9] + ', ' + this[13] +')\n' +
- '(' + this[2] + ', ' + this[6] + ', ' + this[10] + ', ' + this[14] +')\n' +
- '(' + this[3] + ', ' + this[7] + ', ' + this[11] + ', ' + this[15] +')';
- };
- /**
- * A bounding sphere with a center and a radius.
- * @alias BoundingSphere
- * @constructor
- *
- * @param {Cartesian3} [center=Cartesian3.ZERO] The center of the bounding sphere.
- * @param {Number} [radius=0.0] The radius of the bounding sphere.
- *
- * @see AxisAlignedBoundingBox
- * @see BoundingRectangle
- * @see Packable
- */
- function BoundingSphere(center, radius) {
- /**
- * The center point of the sphere.
- * @type {Cartesian3}
- * @default {@link Cartesian3.ZERO}
- */
- this.center = Cartographic.Cartesian3.clone(when.defaultValue(center, Cartographic.Cartesian3.ZERO));
- /**
- * The radius of the sphere.
- * @type {Number}
- * @default 0.0
- */
- this.radius = when.defaultValue(radius, 0.0);
- }
- var fromPointsXMin = new Cartographic.Cartesian3();
- var fromPointsYMin = new Cartographic.Cartesian3();
- var fromPointsZMin = new Cartographic.Cartesian3();
- var fromPointsXMax = new Cartographic.Cartesian3();
- var fromPointsYMax = new Cartographic.Cartesian3();
- var fromPointsZMax = new Cartographic.Cartesian3();
- var fromPointsCurrentPos = new Cartographic.Cartesian3();
- var fromPointsScratch = new Cartographic.Cartesian3();
- var fromPointsRitterCenter = new Cartographic.Cartesian3();
- var fromPointsMinBoxPt = new Cartographic.Cartesian3();
- var fromPointsMaxBoxPt = new Cartographic.Cartesian3();
- var fromPointsNaiveCenterScratch = new Cartographic.Cartesian3();
- var volumeConstant = (4.0 / 3.0) * _Math.CesiumMath.PI;
- /**
- * Computes a tight-fitting bounding sphere enclosing a list of 3D Cartesian points.
- * The bounding sphere is computed by running two algorithms, a naive algorithm and
- * Ritter's algorithm. The smaller of the two spheres is used to ensure a tight fit.
- *
- * @param {Cartesian3[]} [positions] An array of points that the bounding sphere will enclose. Each point must have <code>x</code>, <code>y</code>, and <code>z</code> properties.
- * @param {BoundingSphere} [result] The object onto which to store the result.
- * @returns {BoundingSphere} The modified result parameter or a new BoundingSphere instance if one was not provided.
- *
- * @see {@link http://help.agi.com/AGIComponents/html/BlogBoundingSphere.htm|Bounding Sphere computation article}
- */
- BoundingSphere.fromPoints = function(positions, result) {
- if (!when.defined(result)) {
- result = new BoundingSphere();
- }
- if (!when.defined(positions) || positions.length === 0) {
- result.center = Cartographic.Cartesian3.clone(Cartographic.Cartesian3.ZERO, result.center);
- result.radius = 0.0;
- return result;
- }
- var currentPos = Cartographic.Cartesian3.clone(positions[0], fromPointsCurrentPos);
- var xMin = Cartographic.Cartesian3.clone(currentPos, fromPointsXMin);
- var yMin = Cartographic.Cartesian3.clone(currentPos, fromPointsYMin);
- var zMin = Cartographic.Cartesian3.clone(currentPos, fromPointsZMin);
- var xMax = Cartographic.Cartesian3.clone(currentPos, fromPointsXMax);
- var yMax = Cartographic.Cartesian3.clone(currentPos, fromPointsYMax);
- var zMax = Cartographic.Cartesian3.clone(currentPos, fromPointsZMax);
- var numPositions = positions.length;
- var i;
- for (i = 1; i < numPositions; i++) {
- Cartographic.Cartesian3.clone(positions[i], currentPos);
- var x = currentPos.x;
- var y = currentPos.y;
- var z = currentPos.z;
- // Store points containing the the smallest and largest components
- if (x < xMin.x) {
- Cartographic.Cartesian3.clone(currentPos, xMin);
- }
- if (x > xMax.x) {
- Cartographic.Cartesian3.clone(currentPos, xMax);
- }
- if (y < yMin.y) {
- Cartographic.Cartesian3.clone(currentPos, yMin);
- }
- if (y > yMax.y) {
- Cartographic.Cartesian3.clone(currentPos, yMax);
- }
- if (z < zMin.z) {
- Cartographic.Cartesian3.clone(currentPos, zMin);
- }
- if (z > zMax.z) {
- Cartographic.Cartesian3.clone(currentPos, zMax);
- }
- }
- // Compute x-, y-, and z-spans (Squared distances b/n each component's min. and max.).
- var xSpan = Cartographic.Cartesian3.magnitudeSquared(Cartographic.Cartesian3.subtract(xMax, xMin, fromPointsScratch));
- var ySpan = Cartographic.Cartesian3.magnitudeSquared(Cartographic.Cartesian3.subtract(yMax, yMin, fromPointsScratch));
- var zSpan = Cartographic.Cartesian3.magnitudeSquared(Cartographic.Cartesian3.subtract(zMax, zMin, fromPointsScratch));
- // Set the diameter endpoints to the largest span.
- var diameter1 = xMin;
- var diameter2 = xMax;
- var maxSpan = xSpan;
- if (ySpan > maxSpan) {
- maxSpan = ySpan;
- diameter1 = yMin;
- diameter2 = yMax;
- }
- if (zSpan > maxSpan) {
- maxSpan = zSpan;
- diameter1 = zMin;
- diameter2 = zMax;
- }
- // Calculate the center of the initial sphere found by Ritter's algorithm
- var ritterCenter = fromPointsRitterCenter;
- ritterCenter.x = (diameter1.x + diameter2.x) * 0.5;
- ritterCenter.y = (diameter1.y + diameter2.y) * 0.5;
- ritterCenter.z = (diameter1.z + diameter2.z) * 0.5;
- // Calculate the radius of the initial sphere found by Ritter's algorithm
- var radiusSquared = Cartographic.Cartesian3.magnitudeSquared(Cartographic.Cartesian3.subtract(diameter2, ritterCenter, fromPointsScratch));
- var ritterRadius = Math.sqrt(radiusSquared);
- // Find the center of the sphere found using the Naive method.
- var minBoxPt = fromPointsMinBoxPt;
- minBoxPt.x = xMin.x;
- minBoxPt.y = yMin.y;
- minBoxPt.z = zMin.z;
- var maxBoxPt = fromPointsMaxBoxPt;
- maxBoxPt.x = xMax.x;
- maxBoxPt.y = yMax.y;
- maxBoxPt.z = zMax.z;
- var naiveCenter = Cartographic.Cartesian3.midpoint(minBoxPt, maxBoxPt, fromPointsNaiveCenterScratch);
- // Begin 2nd pass to find naive radius and modify the ritter sphere.
- var naiveRadius = 0;
- for (i = 0; i < numPositions; i++) {
- Cartographic.Cartesian3.clone(positions[i], currentPos);
- // Find the furthest point from the naive center to calculate the naive radius.
- var r = Cartographic.Cartesian3.magnitude(Cartographic.Cartesian3.subtract(currentPos, naiveCenter, fromPointsScratch));
- if (r > naiveRadius) {
- naiveRadius = r;
- }
- // Make adjustments to the Ritter Sphere to include all points.
- var oldCenterToPointSquared = Cartographic.Cartesian3.magnitudeSquared(Cartographic.Cartesian3.subtract(currentPos, ritterCenter, fromPointsScratch));
- if (oldCenterToPointSquared > radiusSquared) {
- var oldCenterToPoint = Math.sqrt(oldCenterToPointSquared);
- // Calculate new radius to include the point that lies outside
- ritterRadius = (ritterRadius + oldCenterToPoint) * 0.5;
- radiusSquared = ritterRadius * ritterRadius;
- // Calculate center of new Ritter sphere
- var oldToNew = oldCenterToPoint - ritterRadius;
- ritterCenter.x = (ritterRadius * ritterCenter.x + oldToNew * currentPos.x) / oldCenterToPoint;
- ritterCenter.y = (ritterRadius * ritterCenter.y + oldToNew * currentPos.y) / oldCenterToPoint;
- ritterCenter.z = (ritterRadius * ritterCenter.z + oldToNew * currentPos.z) / oldCenterToPoint;
- }
- }
- if (ritterRadius < naiveRadius) {
- Cartographic.Cartesian3.clone(ritterCenter, result.center);
- result.radius = ritterRadius;
- } else {
- Cartographic.Cartesian3.clone(naiveCenter, result.center);
- result.radius = naiveRadius;
- }
- return result;
- };
- var defaultProjection = new GeographicProjection();
- var fromRectangle2DLowerLeft = new Cartographic.Cartesian3();
- var fromRectangle2DUpperRight = new Cartographic.Cartesian3();
- var fromRectangle2DSouthwest = new Cartographic.Cartographic();
- var fromRectangle2DNortheast = new Cartographic.Cartographic();
- /**
- * Computes a bounding sphere from a rectangle projected in 2D.
- *
- * @param {Rectangle} [rectangle] The rectangle around which to create a bounding sphere.
- * @param {Object} [projection=GeographicProjection] The projection used to project the rectangle into 2D.
- * @param {BoundingSphere} [result] The object onto which to store the result.
- * @returns {BoundingSphere} The modified result parameter or a new BoundingSphere instance if none was provided.
- */
- BoundingSphere.fromRectangle2D = function(rectangle, projection, result) {
- return BoundingSphere.fromRectangleWithHeights2D(rectangle, projection, 0.0, 0.0, result);
- };
- /**
- * Computes a bounding sphere from a rectangle projected in 2D. The bounding sphere accounts for the
- * object's minimum and maximum heights over the rectangle.
- *
- * @param {Rectangle} [rectangle] The rectangle around which to create a bounding sphere.
- * @param {Object} [projection=GeographicProjection] The projection used to project the rectangle into 2D.
- * @param {Number} [minimumHeight=0.0] The minimum height over the rectangle.
- * @param {Number} [maximumHeight=0.0] The maximum height over the rectangle.
- * @param {BoundingSphere} [result] The object onto which to store the result.
- * @returns {BoundingSphere} The modified result parameter or a new BoundingSphere instance if none was provided.
- */
- BoundingSphere.fromRectangleWithHeights2D = function(rectangle, projection, minimumHeight, maximumHeight, result) {
- if (!when.defined(result)) {
- result = new BoundingSphere();
- }
- if (!when.defined(rectangle)) {
- result.center = Cartographic.Cartesian3.clone(Cartographic.Cartesian3.ZERO, result.center);
- result.radius = 0.0;
- return result;
- }
- projection = when.defaultValue(projection, defaultProjection);
- Cartesian2.Rectangle.southwest(rectangle, fromRectangle2DSouthwest);
- fromRectangle2DSouthwest.height = minimumHeight;
- Cartesian2.Rectangle.northeast(rectangle, fromRectangle2DNortheast);
- fromRectangle2DNortheast.height = maximumHeight;
- var lowerLeft = projection.project(fromRectangle2DSouthwest, fromRectangle2DLowerLeft);
- var upperRight = projection.project(fromRectangle2DNortheast, fromRectangle2DUpperRight);
- var width = upperRight.x - lowerLeft.x;
- var height = upperRight.y - lowerLeft.y;
- var elevation = upperRight.z - lowerLeft.z;
- result.radius = Math.sqrt(width * width + height * height + elevation * elevation) * 0.5;
- var center = result.center;
- center.x = lowerLeft.x + width * 0.5;
- center.y = lowerLeft.y + height * 0.5;
- center.z = lowerLeft.z + elevation * 0.5;
- return result;
- };
- var fromRectangle3DScratch = [];
- /**
- * Computes a bounding sphere from a rectangle in 3D. The bounding sphere is created using a subsample of points
- * on the ellipsoid and contained in the rectangle. It may not be accurate for all rectangles on all types of ellipsoids.
- *
- * @param {Rectangle} [rectangle] The valid rectangle used to create a bounding sphere.
- * @param {Ellipsoid} [ellipsoid=Ellipsoid.WGS84] The ellipsoid used to determine positions of the rectangle.
- * @param {Number} [surfaceHeight=0.0] The height above the surface of the ellipsoid.
- * @param {BoundingSphere} [result] The object onto which to store the result.
- * @returns {BoundingSphere} The modified result parameter or a new BoundingSphere instance if none was provided.
- */
- BoundingSphere.fromRectangle3D = function(rectangle, ellipsoid, surfaceHeight, result) {
- ellipsoid = when.defaultValue(ellipsoid, Cartesian2.Ellipsoid.WGS84);
- surfaceHeight = when.defaultValue(surfaceHeight, 0.0);
- if (!when.defined(result)) {
- result = new BoundingSphere();
- }
- if (!when.defined(rectangle)) {
- result.center = Cartographic.Cartesian3.clone(Cartographic.Cartesian3.ZERO, result.center);
- result.radius = 0.0;
- return result;
- }
- var positions = Cartesian2.Rectangle.subsample(rectangle, ellipsoid, surfaceHeight, fromRectangle3DScratch);
- return BoundingSphere.fromPoints(positions, result);
- };
- /**
- * Computes a tight-fitting bounding sphere enclosing a list of 3D points, where the points are
- * stored in a flat array in X, Y, Z, order. The bounding sphere is computed by running two
- * algorithms, a naive algorithm and Ritter's algorithm. The smaller of the two spheres is used to
- * ensure a tight fit.
- *
- * @param {Number[]} [positions] An array of points that the bounding sphere will enclose. Each point
- * is formed from three elements in the array in the order X, Y, Z.
- * @param {Cartesian3} [center=Cartesian3.ZERO] The position to which the positions are relative, which need not be the
- * origin of the coordinate system. This is useful when the positions are to be used for
- * relative-to-center (RTC) rendering.
- * @param {Number} [stride=3] The number of array elements per vertex. It must be at least 3, but it may
- * be higher. Regardless of the value of this parameter, the X coordinate of the first position
- * is at array index 0, the Y coordinate is at array index 1, and the Z coordinate is at array index
- * 2. When stride is 3, the X coordinate of the next position then begins at array index 3. If
- * the stride is 5, however, two array elements are skipped and the next position begins at array
- * index 5.
- * @param {BoundingSphere} [result] The object onto which to store the result.
- * @returns {BoundingSphere} The modified result parameter or a new BoundingSphere instance if one was not provided.
- *
- * @example
- * // Compute the bounding sphere from 3 positions, each specified relative to a center.
- * // In addition to the X, Y, and Z coordinates, the points array contains two additional
- * // elements per point which are ignored for the purpose of computing the bounding sphere.
- * var center = new Cesium.Cartesian3(1.0, 2.0, 3.0);
- * var points = [1.0, 2.0, 3.0, 0.1, 0.2,
- * 4.0, 5.0, 6.0, 0.1, 0.2,
- * 7.0, 8.0, 9.0, 0.1, 0.2];
- * var sphere = Cesium.BoundingSphere.fromVertices(points, center, 5);
- *
- * @see {@link http://blogs.agi.com/insight3d/index.php/2008/02/04/a-bounding/|Bounding Sphere computation article}
- */
- BoundingSphere.fromVertices = function(positions, center, stride, result) {
- if (!when.defined(result)) {
- result = new BoundingSphere();
- }
- if (!when.defined(positions) || positions.length === 0) {
- result.center = Cartographic.Cartesian3.clone(Cartographic.Cartesian3.ZERO, result.center);
- result.radius = 0.0;
- return result;
- }
- center = when.defaultValue(center, Cartographic.Cartesian3.ZERO);
- stride = when.defaultValue(stride, 3);
- //>>includeStart('debug', pragmas.debug);
- Check.Check.typeOf.number.greaterThanOrEquals('stride', stride, 3);
- //>>includeEnd('debug');
- var currentPos = fromPointsCurrentPos;
- currentPos.x = positions[0] + center.x;
- currentPos.y = positions[1] + center.y;
- currentPos.z = positions[2] + center.z;
- var xMin = Cartographic.Cartesian3.clone(currentPos, fromPointsXMin);
- var yMin = Cartographic.Cartesian3.clone(currentPos, fromPointsYMin);
- var zMin = Cartographic.Cartesian3.clone(currentPos, fromPointsZMin);
- var xMax = Cartographic.Cartesian3.clone(currentPos, fromPointsXMax);
- var yMax = Cartographic.Cartesian3.clone(currentPos, fromPointsYMax);
- var zMax = Cartographic.Cartesian3.clone(currentPos, fromPointsZMax);
- var numElements = positions.length;
- var i;
- for (i = 0; i < numElements; i += stride) {
- var x = positions[i] + center.x;
- var y = positions[i + 1] + center.y;
- var z = positions[i + 2] + center.z;
- currentPos.x = x;
- currentPos.y = y;
- currentPos.z = z;
- // Store points containing the the smallest and largest components
- if (x < xMin.x) {
- Cartographic.Cartesian3.clone(currentPos, xMin);
- }
- if (x > xMax.x) {
- Cartographic.Cartesian3.clone(currentPos, xMax);
- }
- if (y < yMin.y) {
- Cartographic.Cartesian3.clone(currentPos, yMin);
- }
- if (y > yMax.y) {
- Cartographic.Cartesian3.clone(currentPos, yMax);
- }
- if (z < zMin.z) {
- Cartographic.Cartesian3.clone(currentPos, zMin);
- }
- if (z > zMax.z) {
- Cartographic.Cartesian3.clone(currentPos, zMax);
- }
- }
- // Compute x-, y-, and z-spans (Squared distances b/n each component's min. and max.).
- var xSpan = Cartographic.Cartesian3.magnitudeSquared(Cartographic.Cartesian3.subtract(xMax, xMin, fromPointsScratch));
- var ySpan = Cartographic.Cartesian3.magnitudeSquared(Cartographic.Cartesian3.subtract(yMax, yMin, fromPointsScratch));
- var zSpan = Cartographic.Cartesian3.magnitudeSquared(Cartographic.Cartesian3.subtract(zMax, zMin, fromPointsScratch));
- // Set the diameter endpoints to the largest span.
- var diameter1 = xMin;
- var diameter2 = xMax;
- var maxSpan = xSpan;
- if (ySpan > maxSpan) {
- maxSpan = ySpan;
- diameter1 = yMin;
- diameter2 = yMax;
- }
- if (zSpan > maxSpan) {
- maxSpan = zSpan;
- diameter1 = zMin;
- diameter2 = zMax;
- }
- // Calculate the center of the initial sphere found by Ritter's algorithm
- var ritterCenter = fromPointsRitterCenter;
- ritterCenter.x = (diameter1.x + diameter2.x) * 0.5;
- ritterCenter.y = (diameter1.y + diameter2.y) * 0.5;
- ritterCenter.z = (diameter1.z + diameter2.z) * 0.5;
- // Calculate the radius of the initial sphere found by Ritter's algorithm
- var radiusSquared = Cartographic.Cartesian3.magnitudeSquared(Cartographic.Cartesian3.subtract(diameter2, ritterCenter, fromPointsScratch));
- var ritterRadius = Math.sqrt(radiusSquared);
- // Find the center of the sphere found using the Naive method.
- var minBoxPt = fromPointsMinBoxPt;
- minBoxPt.x = xMin.x;
- minBoxPt.y = yMin.y;
- minBoxPt.z = zMin.z;
- var maxBoxPt = fromPointsMaxBoxPt;
- maxBoxPt.x = xMax.x;
- maxBoxPt.y = yMax.y;
- maxBoxPt.z = zMax.z;
- var naiveCenter = Cartographic.Cartesian3.midpoint(minBoxPt, maxBoxPt, fromPointsNaiveCenterScratch);
- // Begin 2nd pass to find naive radius and modify the ritter sphere.
- var naiveRadius = 0;
- for (i = 0; i < numElements; i += stride) {
- currentPos.x = positions[i] + center.x;
- currentPos.y = positions[i + 1] + center.y;
- currentPos.z = positions[i + 2] + center.z;
- // Find the furthest point from the naive center to calculate the naive radius.
- var r = Cartographic.Cartesian3.magnitude(Cartographic.Cartesian3.subtract(currentPos, naiveCenter, fromPointsScratch));
- if (r > naiveRadius) {
- naiveRadius = r;
- }
- // Make adjustments to the Ritter Sphere to include all points.
- var oldCenterToPointSquared = Cartographic.Cartesian3.magnitudeSquared(Cartographic.Cartesian3.subtract(currentPos, ritterCenter, fromPointsScratch));
- if (oldCenterToPointSquared > radiusSquared) {
- var oldCenterToPoint = Math.sqrt(oldCenterToPointSquared);
- // Calculate new radius to include the point that lies outside
- ritterRadius = (ritterRadius + oldCenterToPoint) * 0.5;
- radiusSquared = ritterRadius * ritterRadius;
- // Calculate center of new Ritter sphere
- var oldToNew = oldCenterToPoint - ritterRadius;
- ritterCenter.x = (ritterRadius * ritterCenter.x + oldToNew * currentPos.x) / oldCenterToPoint;
- ritterCenter.y = (ritterRadius * ritterCenter.y + oldToNew * currentPos.y) / oldCenterToPoint;
- ritterCenter.z = (ritterRadius * ritterCenter.z + oldToNew * currentPos.z) / oldCenterToPoint;
- }
- }
- if (ritterRadius < naiveRadius) {
- Cartographic.Cartesian3.clone(ritterCenter, result.center);
- result.radius = ritterRadius;
- } else {
- Cartographic.Cartesian3.clone(naiveCenter, result.center);
- result.radius = naiveRadius;
- }
- return result;
- };
- /**
- * Computes a tight-fitting bounding sphere enclosing a list of EncodedCartesian3s, where the points are
- * stored in parallel flat arrays in X, Y, Z, order. The bounding sphere is computed by running two
- * algorithms, a naive algorithm and Ritter's algorithm. The smaller of the two spheres is used to
- * ensure a tight fit.
- *
- * @param {Number[]} [positionsHigh] An array of high bits of the encoded cartesians that the bounding sphere will enclose. Each point
- * is formed from three elements in the array in the order X, Y, Z.
- * @param {Number[]} [positionsLow] An array of low bits of the encoded cartesians that the bounding sphere will enclose. Each point
- * is formed from three elements in the array in the order X, Y, Z.
- * @param {BoundingSphere} [result] The object onto which to store the result.
- * @returns {BoundingSphere} The modified result parameter or a new BoundingSphere instance if one was not provided.
- *
- * @see {@link http://blogs.agi.com/insight3d/index.php/2008/02/04/a-bounding/|Bounding Sphere computation article}
- */
- BoundingSphere.fromEncodedCartesianVertices = function(positionsHigh, positionsLow, result) {
- if (!when.defined(result)) {
- result = new BoundingSphere();
- }
- if (!when.defined(positionsHigh) || !when.defined(positionsLow) || positionsHigh.length !== positionsLow.length || positionsHigh.length === 0) {
- result.center = Cartographic.Cartesian3.clone(Cartographic.Cartesian3.ZERO, result.center);
- result.radius = 0.0;
- return result;
- }
- var currentPos = fromPointsCurrentPos;
- currentPos.x = positionsHigh[0] + positionsLow[0];
- currentPos.y = positionsHigh[1] + positionsLow[1];
- currentPos.z = positionsHigh[2] + positionsLow[2];
- var xMin = Cartographic.Cartesian3.clone(currentPos, fromPointsXMin);
- var yMin = Cartographic.Cartesian3.clone(currentPos, fromPointsYMin);
- var zMin = Cartographic.Cartesian3.clone(currentPos, fromPointsZMin);
- var xMax = Cartographic.Cartesian3.clone(currentPos, fromPointsXMax);
- var yMax = Cartographic.Cartesian3.clone(currentPos, fromPointsYMax);
- var zMax = Cartographic.Cartesian3.clone(currentPos, fromPointsZMax);
- var numElements = positionsHigh.length;
- var i;
- for (i = 0; i < numElements; i += 3) {
- var x = positionsHigh[i] + positionsLow[i];
- var y = positionsHigh[i + 1] + positionsLow[i + 1];
- var z = positionsHigh[i + 2] + positionsLow[i + 2];
- currentPos.x = x;
- currentPos.y = y;
- currentPos.z = z;
- // Store points containing the the smallest and largest components
- if (x < xMin.x) {
- Cartographic.Cartesian3.clone(currentPos, xMin);
- }
- if (x > xMax.x) {
- Cartographic.Cartesian3.clone(currentPos, xMax);
- }
- if (y < yMin.y) {
- Cartographic.Cartesian3.clone(currentPos, yMin);
- }
- if (y > yMax.y) {
- Cartographic.Cartesian3.clone(currentPos, yMax);
- }
- if (z < zMin.z) {
- Cartographic.Cartesian3.clone(currentPos, zMin);
- }
- if (z > zMax.z) {
- Cartographic.Cartesian3.clone(currentPos, zMax);
- }
- }
- // Compute x-, y-, and z-spans (Squared distances b/n each component's min. and max.).
- var xSpan = Cartographic.Cartesian3.magnitudeSquared(Cartographic.Cartesian3.subtract(xMax, xMin, fromPointsScratch));
- var ySpan = Cartographic.Cartesian3.magnitudeSquared(Cartographic.Cartesian3.subtract(yMax, yMin, fromPointsScratch));
- var zSpan = Cartographic.Cartesian3.magnitudeSquared(Cartographic.Cartesian3.subtract(zMax, zMin, fromPointsScratch));
- // Set the diameter endpoints to the largest span.
- var diameter1 = xMin;
- var diameter2 = xMax;
- var maxSpan = xSpan;
- if (ySpan > maxSpan) {
- maxSpan = ySpan;
- diameter1 = yMin;
- diameter2 = yMax;
- }
- if (zSpan > maxSpan) {
- maxSpan = zSpan;
- diameter1 = zMin;
- diameter2 = zMax;
- }
- // Calculate the center of the initial sphere found by Ritter's algorithm
- var ritterCenter = fromPointsRitterCenter;
- ritterCenter.x = (diameter1.x + diameter2.x) * 0.5;
- ritterCenter.y = (diameter1.y + diameter2.y) * 0.5;
- ritterCenter.z = (diameter1.z + diameter2.z) * 0.5;
- // Calculate the radius of the initial sphere found by Ritter's algorithm
- var radiusSquared = Cartographic.Cartesian3.magnitudeSquared(Cartographic.Cartesian3.subtract(diameter2, ritterCenter, fromPointsScratch));
- var ritterRadius = Math.sqrt(radiusSquared);
- // Find the center of the sphere found using the Naive method.
- var minBoxPt = fromPointsMinBoxPt;
- minBoxPt.x = xMin.x;
- minBoxPt.y = yMin.y;
- minBoxPt.z = zMin.z;
- var maxBoxPt = fromPointsMaxBoxPt;
- maxBoxPt.x = xMax.x;
- maxBoxPt.y = yMax.y;
- maxBoxPt.z = zMax.z;
- var naiveCenter = Cartographic.Cartesian3.midpoint(minBoxPt, maxBoxPt, fromPointsNaiveCenterScratch);
- // Begin 2nd pass to find naive radius and modify the ritter sphere.
- var naiveRadius = 0;
- for (i = 0; i < numElements; i += 3) {
- currentPos.x = positionsHigh[i] + positionsLow[i];
- currentPos.y = positionsHigh[i + 1] + positionsLow[i + 1];
- currentPos.z = positionsHigh[i + 2] + positionsLow[i + 2];
- // Find the furthest point from the naive center to calculate the naive radius.
- var r = Cartographic.Cartesian3.magnitude(Cartographic.Cartesian3.subtract(currentPos, naiveCenter, fromPointsScratch));
- if (r > naiveRadius) {
- naiveRadius = r;
- }
- // Make adjustments to the Ritter Sphere to include all points.
- var oldCenterToPointSquared = Cartographic.Cartesian3.magnitudeSquared(Cartographic.Cartesian3.subtract(currentPos, ritterCenter, fromPointsScratch));
- if (oldCenterToPointSquared > radiusSquared) {
- var oldCenterToPoint = Math.sqrt(oldCenterToPointSquared);
- // Calculate new radius to include the point that lies outside
- ritterRadius = (ritterRadius + oldCenterToPoint) * 0.5;
- radiusSquared = ritterRadius * ritterRadius;
- // Calculate center of new Ritter sphere
- var oldToNew = oldCenterToPoint - ritterRadius;
- ritterCenter.x = (ritterRadius * ritterCenter.x + oldToNew * currentPos.x) / oldCenterToPoint;
- ritterCenter.y = (ritterRadius * ritterCenter.y + oldToNew * currentPos.y) / oldCenterToPoint;
- ritterCenter.z = (ritterRadius * ritterCenter.z + oldToNew * currentPos.z) / oldCenterToPoint;
- }
- }
- if (ritterRadius < naiveRadius) {
- Cartographic.Cartesian3.clone(ritterCenter, result.center);
- result.radius = ritterRadius;
- } else {
- Cartographic.Cartesian3.clone(naiveCenter, result.center);
- result.radius = naiveRadius;
- }
- return result;
- };
- /**
- * Computes a bounding sphere from the corner points of an axis-aligned bounding box. The sphere
- * tighly and fully encompases the box.
- *
- * @param {Cartesian3} [corner] The minimum height over the rectangle.
- * @param {Cartesian3} [oppositeCorner] The maximum height over the rectangle.
- * @param {BoundingSphere} [result] The object onto which to store the result.
- * @returns {BoundingSphere} The modified result parameter or a new BoundingSphere instance if none was provided.
- *
- * @example
- * // Create a bounding sphere around the unit cube
- * var sphere = Cesium.BoundingSphere.fromCornerPoints(new Cesium.Cartesian3(-0.5, -0.5, -0.5), new Cesium.Cartesian3(0.5, 0.5, 0.5));
- */
- BoundingSphere.fromCornerPoints = function(corner, oppositeCorner, result) {
- //>>includeStart('debug', pragmas.debug);
- Check.Check.typeOf.object('corner', corner);
- Check.Check.typeOf.object('oppositeCorner', oppositeCorner);
- //>>includeEnd('debug');
- if (!when.defined(result)) {
- result = new BoundingSphere();
- }
- var center = Cartographic.Cartesian3.midpoint(corner, oppositeCorner, result.center);
- result.radius = Cartographic.Cartesian3.distance(center, oppositeCorner);
- return result;
- };
- /**
- * Creates a bounding sphere encompassing an ellipsoid.
- *
- * @param {Ellipsoid} ellipsoid The ellipsoid around which to create a bounding sphere.
- * @param {BoundingSphere} [result] The object onto which to store the result.
- * @returns {BoundingSphere} The modified result parameter or a new BoundingSphere instance if none was provided.
- *
- * @example
- * var boundingSphere = Cesium.BoundingSphere.fromEllipsoid(ellipsoid);
- */
- BoundingSphere.fromEllipsoid = function(ellipsoid, result) {
- //>>includeStart('debug', pragmas.debug);
- Check.Check.typeOf.object('ellipsoid', ellipsoid);
- //>>includeEnd('debug');
- if (!when.defined(result)) {
- result = new BoundingSphere();
- }
- Cartographic.Cartesian3.clone(Cartographic.Cartesian3.ZERO, result.center);
- result.radius = ellipsoid.maximumRadius;
- return result;
- };
- var fromBoundingSpheresScratch = new Cartographic.Cartesian3();
- /**
- * Computes a tight-fitting bounding sphere enclosing the provided array of bounding spheres.
- *
- * @param {BoundingSphere[]} [boundingSpheres] The array of bounding spheres.
- * @param {BoundingSphere} [result] The object onto which to store the result.
- * @returns {BoundingSphere} The modified result parameter or a new BoundingSphere instance if none was provided.
- */
- BoundingSphere.fromBoundingSpheres = function(boundingSpheres, result) {
- if (!when.defined(result)) {
- result = new BoundingSphere();
- }
- if (!when.defined(boundingSpheres) || boundingSpheres.length === 0) {
- result.center = Cartographic.Cartesian3.clone(Cartographic.Cartesian3.ZERO, result.center);
- result.radius = 0.0;
- return result;
- }
- var length = boundingSpheres.length;
- if (length === 1) {
- return BoundingSphere.clone(boundingSpheres[0], result);
- }
- if (length === 2) {
- return BoundingSphere.union(boundingSpheres[0], boundingSpheres[1], result);
- }
- var positions = [];
- var i;
- for (i = 0; i < length; i++) {
- positions.push(boundingSpheres[i].center);
- }
- result = BoundingSphere.fromPoints(positions, result);
- var center = result.center;
- var radius = result.radius;
- for (i = 0; i < length; i++) {
- var tmp = boundingSpheres[i];
- radius = Math.max(radius, Cartographic.Cartesian3.distance(center, tmp.center, fromBoundingSpheresScratch) + tmp.radius);
- }
- result.radius = radius;
- return result;
- };
- var fromOrientedBoundingBoxScratchU = new Cartographic.Cartesian3();
- var fromOrientedBoundingBoxScratchV = new Cartographic.Cartesian3();
- var fromOrientedBoundingBoxScratchW = new Cartographic.Cartesian3();
- /**
- * Computes a tight-fitting bounding sphere enclosing the provided oriented bounding box.
- *
- * @param {OrientedBoundingBox} orientedBoundingBox The oriented bounding box.
- * @param {BoundingSphere} [result] The object onto which to store the result.
- * @returns {BoundingSphere} The modified result parameter or a new BoundingSphere instance if none was provided.
- */
- BoundingSphere.fromOrientedBoundingBox = function(orientedBoundingBox, result) {
- //>>includeStart('debug', pragmas.debug);
- Check.Check.defined('orientedBoundingBox', orientedBoundingBox);
- //>>includeEnd('debug');
- if (!when.defined(result)) {
- result = new BoundingSphere();
- }
- var halfAxes = orientedBoundingBox.halfAxes;
- var u = Matrix3.getColumn(halfAxes, 0, fromOrientedBoundingBoxScratchU);
- var v = Matrix3.getColumn(halfAxes, 1, fromOrientedBoundingBoxScratchV);
- var w = Matrix3.getColumn(halfAxes, 2, fromOrientedBoundingBoxScratchW);
- Cartographic.Cartesian3.add(u, v, u);
- Cartographic.Cartesian3.add(u, w, u);
- result.center = Cartographic.Cartesian3.clone(orientedBoundingBox.center, result.center);
- result.radius = Cartographic.Cartesian3.magnitude(u);
- return result;
- };
- /**
- * Duplicates a BoundingSphere instance.
- *
- * @param {BoundingSphere} sphere The bounding sphere to duplicate.
- * @param {BoundingSphere} [result] The object onto which to store the result.
- * @returns {BoundingSphere} The modified result parameter or a new BoundingSphere instance if none was provided. (Returns undefined if sphere is undefined)
- */
- BoundingSphere.clone = function(sphere, result) {
- if (!when.defined(sphere)) {
- return undefined;
- }
- if (!when.defined(result)) {
- return new BoundingSphere(sphere.center, sphere.radius);
- }
- result.center = Cartographic.Cartesian3.clone(sphere.center, result.center);
- result.radius = sphere.radius;
- return result;
- };
- /**
- * The number of elements used to pack the object into an array.
- * @type {Number}
- */
- BoundingSphere.packedLength = 4;
- /**
- * Stores the provided instance into the provided array.
- *
- * @param {BoundingSphere} value The value to pack.
- * @param {Number[]} array The array to pack into.
- * @param {Number} [startingIndex=0] The index into the array at which to start packing the elements.
- *
- * @returns {Number[]} The array that was packed into
- */
- BoundingSphere.pack = function(value, array, startingIndex) {
- //>>includeStart('debug', pragmas.debug);
- Check.Check.typeOf.object('value', value);
- Check.Check.defined('array', array);
- //>>includeEnd('debug');
- startingIndex = when.defaultValue(startingIndex, 0);
- var center = value.center;
- array[startingIndex++] = center.x;
- array[startingIndex++] = center.y;
- array[startingIndex++] = center.z;
- array[startingIndex] = value.radius;
- return array;
- };
- /**
- * Retrieves an instance from a packed array.
- *
- * @param {Number[]} array The packed array.
- * @param {Number} [startingIndex=0] The starting index of the element to be unpacked.
- * @param {BoundingSphere} [result] The object into which to store the result.
- * @returns {BoundingSphere} The modified result parameter or a new BoundingSphere instance if one was not provided.
- */
- BoundingSphere.unpack = function(array, startingIndex, result) {
- //>>includeStart('debug', pragmas.debug);
- Check.Check.defined('array', array);
- //>>includeEnd('debug');
- startingIndex = when.defaultValue(startingIndex, 0);
- if (!when.defined(result)) {
- result = new BoundingSphere();
- }
- var center = result.center;
- center.x = array[startingIndex++];
- center.y = array[startingIndex++];
- center.z = array[startingIndex++];
- result.radius = array[startingIndex];
- return result;
- };
- var unionScratch = new Cartographic.Cartesian3();
- var unionScratchCenter = new Cartographic.Cartesian3();
- /**
- * Computes a bounding sphere that contains both the left and right bounding spheres.
- *
- * @param {BoundingSphere} left A sphere to enclose in a bounding sphere.
- * @param {BoundingSphere} right A sphere to enclose in a bounding sphere.
- * @param {BoundingSphere} [result] The object onto which to store the result.
- * @returns {BoundingSphere} The modified result parameter or a new BoundingSphere instance if none was provided.
- */
- BoundingSphere.union = function(left, right, result) {
- //>>includeStart('debug', pragmas.debug);
- Check.Check.typeOf.object('left', left);
- Check.Check.typeOf.object('right', right);
- //>>includeEnd('debug');
- if (!when.defined(result)) {
- result = new BoundingSphere();
- }
- var leftCenter = left.center;
- var leftRadius = left.radius;
- var rightCenter = right.center;
- var rightRadius = right.radius;
- var toRightCenter = Cartographic.Cartesian3.subtract(rightCenter, leftCenter, unionScratch);
- var centerSeparation = Cartographic.Cartesian3.magnitude(toRightCenter);
- if (leftRadius >= (centerSeparation + rightRadius)) {
- // Left sphere wins.
- left.clone(result);
- return result;
- }
- if (rightRadius >= (centerSeparation + leftRadius)) {
- // Right sphere wins.
- right.clone(result);
- return result;
- }
- // There are two tangent points, one on far side of each sphere.
- var halfDistanceBetweenTangentPoints = (leftRadius + centerSeparation + rightRadius) * 0.5;
- // Compute the center point halfway between the two tangent points.
- var center = Cartographic.Cartesian3.multiplyByScalar(toRightCenter,
- (-leftRadius + halfDistanceBetweenTangentPoints) / centerSeparation, unionScratchCenter);
- Cartographic.Cartesian3.add(center, leftCenter, center);
- Cartographic.Cartesian3.clone(center, result.center);
- result.radius = halfDistanceBetweenTangentPoints;
- return result;
- };
- var expandScratch = new Cartographic.Cartesian3();
- /**
- * Computes a bounding sphere by enlarging the provided sphere to contain the provided point.
- *
- * @param {BoundingSphere} sphere A sphere to expand.
- * @param {Cartesian3} point A point to enclose in a bounding sphere.
- * @param {BoundingSphere} [result] The object onto which to store the result.
- * @returns {BoundingSphere} The modified result parameter or a new BoundingSphere instance if none was provided.
- */
- BoundingSphere.expand = function(sphere, point, result) {
- //>>includeStart('debug', pragmas.debug);
- Check.Check.typeOf.object('sphere', sphere);
- Check.Check.typeOf.object('point', point);
- //>>includeEnd('debug');
- result = BoundingSphere.clone(sphere, result);
- var radius = Cartographic.Cartesian3.magnitude(Cartographic.Cartesian3.subtract(point, result.center, expandScratch));
- if (radius > result.radius) {
- result.radius = radius;
- }
- return result;
- };
- /**
- * Determines which side of a plane a sphere is located.
- *
- * @param {BoundingSphere} sphere The bounding sphere to test.
- * @param {Plane} plane The plane to test against.
- * @returns {Intersect} {@link Intersect.INSIDE} if the entire sphere is on the side of the plane
- * the normal is pointing, {@link Intersect.OUTSIDE} if the entire sphere is
- * on the opposite side, and {@link Intersect.INTERSECTING} if the sphere
- * intersects the plane.
- */
- BoundingSphere.intersectPlane = function(sphere, plane) {
- //>>includeStart('debug', pragmas.debug);
- Check.Check.typeOf.object('sphere', sphere);
- Check.Check.typeOf.object('plane', plane);
- //>>includeEnd('debug');
- var center = sphere.center;
- var radius = sphere.radius;
- var normal = plane.normal;
- var distanceToPlane = Cartographic.Cartesian3.dot(normal, center) + plane.distance;
- if (distanceToPlane < -radius) {
- // The center point is negative side of the plane normal
- return Intersect$1.OUTSIDE;
- } else if (distanceToPlane < radius) {
- // The center point is positive side of the plane, but radius extends beyond it; partial overlap
- return Intersect$1.INTERSECTING;
- }
- return Intersect$1.INSIDE;
- };
- /**
- * Applies a 4x4 affine transformation matrix to a bounding sphere.
- *
- * @param {BoundingSphere} sphere The bounding sphere to apply the transformation to.
- * @param {Matrix4} transform The transformation matrix to apply to the bounding sphere.
- * @param {BoundingSphere} [result] The object onto which to store the result.
- * @returns {BoundingSphere} The modified result parameter or a new BoundingSphere instance if none was provided.
- */
- BoundingSphere.transform = function(sphere, transform, result) {
- //>>includeStart('debug', pragmas.debug);
- Check.Check.typeOf.object('sphere', sphere);
- Check.Check.typeOf.object('transform', transform);
- //>>includeEnd('debug');
- if (!when.defined(result)) {
- result = new BoundingSphere();
- }
- result.center = Matrix4.multiplyByPoint(transform, sphere.center, result.center);
- result.radius = Matrix4.getMaximumScale(transform) * sphere.radius;
- return result;
- };
- var distanceSquaredToScratch = new Cartographic.Cartesian3();
- /**
- * Computes the estimated distance squared from the closest point on a bounding sphere to a point.
- *
- * @param {BoundingSphere} sphere The sphere.
- * @param {Cartesian3} cartesian The point
- * @returns {Number} The estimated distance squared from the bounding sphere to the point.
- *
- * @example
- * // Sort bounding spheres from back to front
- * spheres.sort(function(a, b) {
- * return Cesium.BoundingSphere.distanceSquaredTo(b, camera.positionWC) - Cesium.BoundingSphere.distanceSquaredTo(a, camera.positionWC);
- * });
- */
- BoundingSphere.distanceSquaredTo = function(sphere, cartesian) {
- //>>includeStart('debug', pragmas.debug);
- Check.Check.typeOf.object('sphere', sphere);
- Check.Check.typeOf.object('cartesian', cartesian);
- //>>includeEnd('debug');
- var diff = Cartographic.Cartesian3.subtract(sphere.center, cartesian, distanceSquaredToScratch);
- return Cartographic.Cartesian3.magnitudeSquared(diff) - sphere.radius * sphere.radius;
- };
- /**
- * Applies a 4x4 affine transformation matrix to a bounding sphere where there is no scale
- * The transformation matrix is not verified to have a uniform scale of 1.
- * This method is faster than computing the general bounding sphere transform using {@link BoundingSphere.transform}.
- *
- * @param {BoundingSphere} sphere The bounding sphere to apply the transformation to.
- * @param {Matrix4} transform The transformation matrix to apply to the bounding sphere.
- * @param {BoundingSphere} [result] The object onto which to store the result.
- * @returns {BoundingSphere} The modified result parameter or a new BoundingSphere instance if none was provided.
- *
- * @example
- * var modelMatrix = Cesium.Transforms.eastNorthUpToFixedFrame(positionOnEllipsoid);
- * var boundingSphere = new Cesium.BoundingSphere();
- * var newBoundingSphere = Cesium.BoundingSphere.transformWithoutScale(boundingSphere, modelMatrix);
- */
- BoundingSphere.transformWithoutScale = function(sphere, transform, result) {
- //>>includeStart('debug', pragmas.debug);
- Check.Check.typeOf.object('sphere', sphere);
- Check.Check.typeOf.object('transform', transform);
- //>>includeEnd('debug');
- if (!when.defined(result)) {
- result = new BoundingSphere();
- }
- result.center = Matrix4.multiplyByPoint(transform, sphere.center, result.center);
- result.radius = sphere.radius;
- return result;
- };
- var scratchCartesian3 = new Cartographic.Cartesian3();
- /**
- * The distances calculated by the vector from the center of the bounding sphere to position projected onto direction
- * plus/minus the radius of the bounding sphere.
- * <br>
- * If you imagine the infinite number of planes with normal direction, this computes the smallest distance to the
- * closest and farthest planes from position that intersect the bounding sphere.
- *
- * @param {BoundingSphere} sphere The bounding sphere to calculate the distance to.
- * @param {Cartesian3} position The position to calculate the distance from.
- * @param {Cartesian3} direction The direction from position.
- * @param {Interval} [result] A Interval to store the nearest and farthest distances.
- * @returns {Interval} The nearest and farthest distances on the bounding sphere from position in direction.
- */
- BoundingSphere.computePlaneDistances = function(sphere, position, direction, result) {
- //>>includeStart('debug', pragmas.debug);
- Check.Check.typeOf.object('sphere', sphere);
- Check.Check.typeOf.object('position', position);
- Check.Check.typeOf.object('direction', direction);
- //>>includeEnd('debug');
- if (!when.defined(result)) {
- result = new Interval();
- }
- var toCenter = Cartographic.Cartesian3.subtract(sphere.center, position, scratchCartesian3);
- var mag = Cartographic.Cartesian3.dot(direction, toCenter);
- result.start = mag - sphere.radius;
- result.stop = mag + sphere.radius;
- return result;
- };
- var projectTo2DNormalScratch = new Cartographic.Cartesian3();
- var projectTo2DEastScratch = new Cartographic.Cartesian3();
- var projectTo2DNorthScratch = new Cartographic.Cartesian3();
- var projectTo2DWestScratch = new Cartographic.Cartesian3();
- var projectTo2DSouthScratch = new Cartographic.Cartesian3();
- var projectTo2DCartographicScratch = new Cartographic.Cartographic();
- var projectTo2DPositionsScratch = new Array(8);
- for (var n = 0; n < 8; ++n) {
- projectTo2DPositionsScratch[n] = new Cartographic.Cartesian3();
- }
- var projectTo2DProjection = new GeographicProjection();
- /**
- * Creates a bounding sphere in 2D from a bounding sphere in 3D world coordinates.
- *
- * @param {BoundingSphere} sphere The bounding sphere to transform to 2D.
- * @param {Object} [projection=GeographicProjection] The projection to 2D.
- * @param {BoundingSphere} [result] The object onto which to store the result.
- * @returns {BoundingSphere} The modified result parameter or a new BoundingSphere instance if none was provided.
- */
- BoundingSphere.projectTo2D = function(sphere, projection, result) {
- //>>includeStart('debug', pragmas.debug);
- Check.Check.typeOf.object('sphere', sphere);
- //>>includeEnd('debug');
- projection = when.defaultValue(projection, projectTo2DProjection);
- var ellipsoid = projection.ellipsoid;
- var center = sphere.center;
- var radius = sphere.radius;
- var normal;
- if (Cartographic.Cartesian3.equals(center, Cartographic.Cartesian3.ZERO)) {
- // Bounding sphere is at the center. The geodetic surface normal is not
- // defined here so pick the x-axis as a fallback.
- normal = Cartographic.Cartesian3.clone(Cartographic.Cartesian3.UNIT_X, projectTo2DNormalScratch);
- } else {
- normal = ellipsoid.geodeticSurfaceNormal(center, projectTo2DNormalScratch);
- }
- var east = Cartographic.Cartesian3.cross(Cartographic.Cartesian3.UNIT_Z, normal, projectTo2DEastScratch);
- Cartographic.Cartesian3.normalize(east, east);
- var north = Cartographic.Cartesian3.cross(normal, east, projectTo2DNorthScratch);
- Cartographic.Cartesian3.normalize(north, north);
- Cartographic.Cartesian3.multiplyByScalar(normal, radius, normal);
- Cartographic.Cartesian3.multiplyByScalar(north, radius, north);
- Cartographic.Cartesian3.multiplyByScalar(east, radius, east);
- var south = Cartographic.Cartesian3.negate(north, projectTo2DSouthScratch);
- var west = Cartographic.Cartesian3.negate(east, projectTo2DWestScratch);
- var positions = projectTo2DPositionsScratch;
- // top NE corner
- var corner = positions[0];
- Cartographic.Cartesian3.add(normal, north, corner);
- Cartographic.Cartesian3.add(corner, east, corner);
- // top NW corner
- corner = positions[1];
- Cartographic.Cartesian3.add(normal, north, corner);
- Cartographic.Cartesian3.add(corner, west, corner);
- // top SW corner
- corner = positions[2];
- Cartographic.Cartesian3.add(normal, south, corner);
- Cartographic.Cartesian3.add(corner, west, corner);
- // top SE corner
- corner = positions[3];
- Cartographic.Cartesian3.add(normal, south, corner);
- Cartographic.Cartesian3.add(corner, east, corner);
- Cartographic.Cartesian3.negate(normal, normal);
- // bottom NE corner
- corner = positions[4];
- Cartographic.Cartesian3.add(normal, north, corner);
- Cartographic.Cartesian3.add(corner, east, corner);
- // bottom NW corner
- corner = positions[5];
- Cartographic.Cartesian3.add(normal, north, corner);
- Cartographic.Cartesian3.add(corner, west, corner);
- // bottom SW corner
- corner = positions[6];
- Cartographic.Cartesian3.add(normal, south, corner);
- Cartographic.Cartesian3.add(corner, west, corner);
- // bottom SE corner
- corner = positions[7];
- Cartographic.Cartesian3.add(normal, south, corner);
- Cartographic.Cartesian3.add(corner, east, corner);
- var length = positions.length;
- for (var i = 0; i < length; ++i) {
- var position = positions[i];
- Cartographic.Cartesian3.add(center, position, position);
- var cartographic = ellipsoid.cartesianToCartographic(position, projectTo2DCartographicScratch);
- projection.project(cartographic, position);
- }
- result = BoundingSphere.fromPoints(positions, result);
- // swizzle center components
- center = result.center;
- var x = center.x;
- var y = center.y;
- var z = center.z;
- center.x = z;
- center.y = x;
- center.z = y;
- return result;
- };
- /**
- * Determines whether or not a sphere is hidden from view by the occluder.
- *
- * @param {BoundingSphere} sphere The bounding sphere surrounding the occludee object.
- * @param {Occluder} occluder The occluder.
- * @returns {Boolean} <code>true</code> if the sphere is not visible; otherwise <code>false</code>.
- */
- BoundingSphere.isOccluded = function(sphere, occluder) {
- //>>includeStart('debug', pragmas.debug);
- Check.Check.typeOf.object('sphere', sphere);
- Check.Check.typeOf.object('occluder', occluder);
- //>>includeEnd('debug');
- return !occluder.isBoundingSphereVisible(sphere);
- };
- /**
- * Compares the provided BoundingSphere componentwise and returns
- * <code>true</code> if they are equal, <code>false</code> otherwise.
- *
- * @param {BoundingSphere} [left] The first BoundingSphere.
- * @param {BoundingSphere} [right] The second BoundingSphere.
- * @returns {Boolean} <code>true</code> if left and right are equal, <code>false</code> otherwise.
- */
- BoundingSphere.equals = function(left, right) {
- return (left === right) ||
- ((when.defined(left)) &&
- (when.defined(right)) &&
- Cartographic.Cartesian3.equals(left.center, right.center) &&
- left.radius === right.radius);
- };
- /**
- * Determines which side of a plane the sphere is located.
- *
- * @param {Plane} plane The plane to test against.
- * @returns {Intersect} {@link Intersect.INSIDE} if the entire sphere is on the side of the plane
- * the normal is pointing, {@link Intersect.OUTSIDE} if the entire sphere is
- * on the opposite side, and {@link Intersect.INTERSECTING} if the sphere
- * intersects the plane.
- */
- BoundingSphere.prototype.intersectPlane = function(plane) {
- return BoundingSphere.intersectPlane(this, plane);
- };
- /**
- * Computes the estimated distance squared from the closest point on a bounding sphere to a point.
- *
- * @param {Cartesian3} cartesian The point
- * @returns {Number} The estimated distance squared from the bounding sphere to the point.
- *
- * @example
- * // Sort bounding spheres from back to front
- * spheres.sort(function(a, b) {
- * return b.distanceSquaredTo(camera.positionWC) - a.distanceSquaredTo(camera.positionWC);
- * });
- */
- BoundingSphere.prototype.distanceSquaredTo = function(cartesian) {
- return BoundingSphere.distanceSquaredTo(this, cartesian);
- };
- /**
- * The distances calculated by the vector from the center of the bounding sphere to position projected onto direction
- * plus/minus the radius of the bounding sphere.
- * <br>
- * If you imagine the infinite number of planes with normal direction, this computes the smallest distance to the
- * closest and farthest planes from position that intersect the bounding sphere.
- *
- * @param {Cartesian3} position The position to calculate the distance from.
- * @param {Cartesian3} direction The direction from position.
- * @param {Interval} [result] A Interval to store the nearest and farthest distances.
- * @returns {Interval} The nearest and farthest distances on the bounding sphere from position in direction.
- */
- BoundingSphere.prototype.computePlaneDistances = function(position, direction, result) {
- return BoundingSphere.computePlaneDistances(this, position, direction, result);
- };
- /**
- * Determines whether or not a sphere is hidden from view by the occluder.
- *
- * @param {Occluder} occluder The occluder.
- * @returns {Boolean} <code>true</code> if the sphere is not visible; otherwise <code>false</code>.
- */
- BoundingSphere.prototype.isOccluded = function(occluder) {
- return BoundingSphere.isOccluded(this, occluder);
- };
- /**
- * Compares this BoundingSphere against the provided BoundingSphere componentwise and returns
- * <code>true</code> if they are equal, <code>false</code> otherwise.
- *
- * @param {BoundingSphere} [right] The right hand side BoundingSphere.
- * @returns {Boolean} <code>true</code> if they are equal, <code>false</code> otherwise.
- */
- BoundingSphere.prototype.equals = function(right) {
- return BoundingSphere.equals(this, right);
- };
- /**
- * Duplicates this BoundingSphere instance.
- *
- * @param {BoundingSphere} [result] The object onto which to store the result.
- * @returns {BoundingSphere} The modified result parameter or a new BoundingSphere instance if none was provided.
- */
- BoundingSphere.prototype.clone = function(result) {
- return BoundingSphere.clone(this, result);
- };
- /**
- * Computes the radius of the BoundingSphere.
- * @returns {Number} The radius of the BoundingSphere.
- */
- BoundingSphere.prototype.volume = function() {
- var radius = this.radius;
- return volumeConstant * radius * radius * radius;
- };
- exports.BoundingSphere = BoundingSphere;
- exports.GeographicProjection = GeographicProjection;
- exports.Intersect = Intersect$1;
- exports.Interval = Interval;
- exports.Matrix3 = Matrix3;
- exports.Matrix4 = Matrix4;
- });
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