/*global define*/
define([
'./Cartesian3',
'./Cartesian4',
'./defaultValue',
'./defined',
'./defineProperties',
'./DeveloperError',
'./freezeObject',
'./Math',
'./Matrix3',
'./RuntimeError'
], function(
Cartesian3,
Cartesian4,
defaultValue,
defined,
defineProperties,
DeveloperError,
freezeObject,
CesiumMath,
Matrix3,
RuntimeError) {
'use strict';
/**
* 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] = defaultValue(column0Row0, 0.0);
this[1] = defaultValue(column0Row1, 0.0);
this[2] = defaultValue(column0Row2, 0.0);
this[3] = defaultValue(column0Row3, 0.0);
this[4] = defaultValue(column1Row0, 0.0);
this[5] = defaultValue(column1Row1, 0.0);
this[6] = defaultValue(column1Row2, 0.0);
this[7] = defaultValue(column1Row3, 0.0);
this[8] = defaultValue(column2Row0, 0.0);
this[9] = defaultValue(column2Row1, 0.0);
this[10] = defaultValue(column2Row2, 0.0);
this[11] = defaultValue(column2Row3, 0.0);
this[12] = defaultValue(column3Row0, 0.0);
this[13] = defaultValue(column3Row1, 0.0);
this[14] = defaultValue(column3Row2, 0.0);
this[15] = 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);
if (!defined(value)) {
throw new DeveloperError('value is required');
}
if (!defined(array)) {
throw new DeveloperError('array is required');
}
//>>includeEnd('debug');
startingIndex = 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);
if (!defined(array)) {
throw new DeveloperError('array is required');
}
//>>includeEnd('debug');
startingIndex = defaultValue(startingIndex, 0);
if (!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 (!defined(matrix)) {
return undefined;
}
if (!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);
if (!defined(values)) {
throw new DeveloperError('values is required');
}
//>>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);
if (!defined(values)) {
throw new DeveloperError('values is required.');
}
//>>includeEnd('debug');
if (!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);
if (!defined(rotation)) {
throw new DeveloperError('rotation is required.');
}
//>>includeEnd('debug');
translation = defaultValue(translation, Cartesian3.ZERO);
if (!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);
if (!defined(translation)) {
throw new DeveloperError('translation is required.');
}
if (!defined(rotation)) {
throw new DeveloperError('rotation is required.');
}
if (!defined(scale)) {
throw new DeveloperError('scale is required.');
}
//>>includeEnd('debug');
if (!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);
if (!defined(translationRotationScale)) {
throw new DeveloperError('translationRotationScale is required.');
}
//>>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);
if (!defined(translation)) {
throw new DeveloperError('translation is required.');
}
//>>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);
if (!defined(scale)) {
throw new DeveloperError('scale is required.');
}
//>>includeEnd('debug');
if (!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);
if (typeof scale !== 'number') {
throw new DeveloperError('scale is required.');
}
//>>includeEnd('debug');
if (!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 Cartesian3();
var fromCameraR = new Cartesian3();
var fromCameraU = new 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);
if (!defined(camera)) {
throw new DeveloperError('camera is required.');
}
//>>includeEnd('debug');
var position = camera.position;
var direction = camera.direction;
var up = camera.up;
//>>includeStart('debug', pragmas.debug);
if (!defined(position)) {
throw new DeveloperError('camera.position is required.');
}
if (!defined(direction)) {
throw new DeveloperError('camera.direction is required.');
}
if (!defined(up)) {
throw new DeveloperError('camera.up is required.');
}
//>>includeEnd('debug');
Cartesian3.normalize(direction, fromCameraF);
Cartesian3.normalize(Cartesian3.cross(fromCameraF, up, fromCameraR), fromCameraR);
Cartesian3.normalize(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 (!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);
if (fovY <= 0.0 || fovY > Math.PI) {
throw new DeveloperError('fovY must be in (0, PI].');
}
if (aspectRatio <= 0.0) {
throw new DeveloperError('aspectRatio must be greater than zero.');
}
if (near <= 0.0) {
throw new DeveloperError('near must be greater than zero.');
}
if (far <= 0.0) {
throw new DeveloperError('far must be greater than zero.');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
//>>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);
if (!defined(left)) {
throw new DeveloperError('left is required.');
}
if (!defined(right)) {
throw new DeveloperError('right is required.');
}
if (!defined(bottom)) {
throw new DeveloperError('bottom is required.');
}
if (!defined(top)) {
throw new DeveloperError('top is required.');
}
if (!defined(near)) {
throw new DeveloperError('near is required.');
}
if (!defined(far)) {
throw new DeveloperError('far is required.');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
//>>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);
if (!defined(left)) {
throw new DeveloperError('left is required.');
}
if (!defined(right)) {
throw new DeveloperError('right is required.');
}
if (!defined(bottom)) {
throw new DeveloperError('bottom is required.');
}
if (!defined(top)) {
throw new DeveloperError('top is required.');
}
if (!defined(near)) {
throw new DeveloperError('near is required.');
}
if (!defined(far)) {
throw new DeveloperError('far is required.');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
//>>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);
if (!defined(left)) {
throw new DeveloperError('left is required.');
}
if (!defined(right)) {
throw new DeveloperError('right is required.');
}
if (!defined(bottom)) {
throw new DeveloperError('bottom is required.');
}
if (!defined(top)) {
throw new DeveloperError('top is required.');
}
if (!defined(near)) {
throw new DeveloperError('near is required.');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
//>>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);
if (!defined(result)) {
throw new DeveloperError('result is required');
}
//>>includeEnd('debug');
viewport = defaultValue(viewport, defaultValue.EMPTY_OBJECT);
var x = defaultValue(viewport.x, 0.0);
var y = defaultValue(viewport.y, 0.0);
var width = defaultValue(viewport.width, 0.0);
var height = defaultValue(viewport.height, 0.0);
nearDepthRange = defaultValue(nearDepthRange, 0.0);
farDepthRange = 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);
if (!defined(position)) {
throw new DeveloperError('position is required');
}
if (!defined(direction)) {
throw new DeveloperError('direction is required');
}
if (!defined(up)) {
throw new DeveloperError('up is required');
}
if (!defined(right)) {
throw new DeveloperError('right is required');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
//>>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] = -Cartesian3.dot(right, position);
result[13] = -Cartesian3.dot(up, position);
result[14] = 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);
if (!defined(matrix)) {
throw new DeveloperError('matrix is required');
}
//>>includeEnd('debug');
if (!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);
if (typeof row !== 'number' || row < 0 || row > 3) {
throw new DeveloperError('row must be 0, 1, 2, or 3.');
}
if (typeof column !== 'number' || column < 0 || column > 3) {
throw new DeveloperError('column must be 0, 1, 2, or 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);
if (!defined(matrix)) {
throw new DeveloperError('matrix is required.');
}
if (typeof index !== 'number' || index < 0 || index > 3) {
throw new DeveloperError('index must be 0, 1, 2, or 3.');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
//>>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);
if (!defined(matrix)) {
throw new DeveloperError('matrix is required');
}
if (!defined(cartesian)) {
throw new DeveloperError('cartesian is required');
}
if (typeof index !== 'number' || index < 0 || index > 3) {
throw new DeveloperError('index must be 0, 1, 2, or 3.');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
//>>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 {Cartesian4} 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);
if (!defined(matrix)) {
throw new DeveloperError('matrix is required');
}
if (!defined(translation)) {
throw new DeveloperError('translation is required');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
//>>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;
};
/**
* 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);
if (!defined(matrix)) {
throw new DeveloperError('matrix is required.');
}
if (typeof index !== 'number' || index < 0 || index > 3) {
throw new DeveloperError('index must be 0, 1, 2, or 3.');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
//>>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);
if (!defined(matrix)) {
throw new DeveloperError('matrix is required');
}
if (!defined(cartesian)) {
throw new DeveloperError('cartesian is required');
}
if (typeof index !== 'number' || index < 0 || index > 3) {
throw new DeveloperError('index must be 0, 1, 2, or 3.');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
//>>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 = new 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);
if (!defined(matrix)) {
throw new DeveloperError('matrix is required.');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
//>>includeEnd('debug');
result.x = Cartesian3.magnitude(Cartesian3.fromElements(matrix[0], matrix[1], matrix[2], scratchColumn));
result.y = Cartesian3.magnitude(Cartesian3.fromElements(matrix[4], matrix[5], matrix[6], scratchColumn));
result.z = Cartesian3.magnitude(Cartesian3.fromElements(matrix[8], matrix[9], matrix[10], scratchColumn));
return result;
};
var scratchScale = new 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);
return Cartesian3.maximumComponent(scratchScale);
};
/**
* 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);
if (!defined(left)) {
throw new DeveloperError('left is required');
}
if (!defined(right)) {
throw new DeveloperError('right is required');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
//>>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);
if (!defined(left)) {
throw new DeveloperError('left is required');
}
if (!defined(right)) {
throw new DeveloperError('right is required');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
//>>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);
if (!defined(left)) {
throw new DeveloperError('left is required');
}
if (!defined(right)) {
throw new DeveloperError('right is required');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
//>>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);
if (!defined(left)) {
throw new DeveloperError('left is required');
}
if (!defined(right)) {
throw new DeveloperError('right is required');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
//>>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);
if (!defined(matrix)) {
throw new DeveloperError('matrix is required');
}
if (!defined(rotation)) {
throw new DeveloperError('rotation is required');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
//>>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);
if (!defined(matrix)) {
throw new DeveloperError('matrix is required');
}
if (!defined(translation)) {
throw new DeveloperError('translation is required');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
//>>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 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);
if (!defined(matrix)) {
throw new DeveloperError('matrix is required');
}
if (typeof scale !== 'number') {
throw new DeveloperError('scale is required');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
//>>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);
if (!defined(matrix)) {
throw new DeveloperError('matrix is required');
}
if (!defined(scale)) {
throw new DeveloperError('scale is required');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
//>>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);
if (!defined(matrix)) {
throw new DeveloperError('matrix is required');
}
if (!defined(cartesian)) {
throw new DeveloperError('cartesian is required');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
//>>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);
if (!defined(matrix)) {
throw new DeveloperError('matrix is required');
}
if (!defined(cartesian)) {
throw new DeveloperError('cartesian is required');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
//>>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);
if (!defined(matrix)) {
throw new DeveloperError('matrix is required');
}
if (!defined(cartesian)) {
throw new DeveloperError('cartesian is required');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
//>>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);
if (!defined(matrix)) {
throw new DeveloperError('matrix is required');
}
if (typeof scalar !== 'number') {
throw new DeveloperError('scalar must be a number');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
//>>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;
};
/**
* 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);
if (!defined(matrix)) {
throw new DeveloperError('matrix is required');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
//>>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);
if (!defined(matrix)) {
throw new DeveloperError('matrix is required');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
//>>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);
if (!defined(matrix)) {
throw new DeveloperError('matrix is required');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
//>>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) ||
(defined(left) &&
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);
if (typeof epsilon !== 'number') {
throw new DeveloperError('epsilon must be a number');
}
//>>includeEnd('debug');
return (left === right) ||
(defined(left) &&
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);
if (!defined(matrix)) {
throw new DeveloperError('matrix is required');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
//>>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 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);
if (!defined(matrix)) {
throw new DeveloperError('matrix is required');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
//>>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();
var scratchExpectedBottomRow = new 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);
if (!defined(matrix)) {
throw new DeveloperError('matrix is required');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
//>>includeEnd('debug');
// 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, CesiumMath.EPSILON7) &&
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;
}
//
// 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) < CesiumMath.EPSILON20) {
throw new 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);
if (!defined(matrix)) {
throw new DeveloperError('matrix is required');
}
if (!defined(result)) {
throw new DeveloperError('result is required');
}
//>>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 = freezeObject(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 = freezeObject(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;
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] +')';
};
return Matrix4;
});