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/**
* Cesium - https://github.com/CesiumGS/cesium
*
* Copyright 2011-2020 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/CesiumGS/cesium/blob/master/LICENSE.md for full licensing details.
*/
define(['exports', './when-8d13db60', './Check-70bec281', './Math-61ede240', './Cartographic-f2a06374', './Cartesian2-16a61632', './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;
});