You cannot select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
2972 lines
86 KiB
JavaScript
2972 lines
86 KiB
JavaScript
import Cartesian3 from "./Cartesian3.js";
|
|
import Cartesian4 from "./Cartesian4.js";
|
|
import Check from "./Check.js";
|
|
import defaultValue from "./defaultValue.js";
|
|
import defined from "./defined.js";
|
|
import CesiumMath from "./Math.js";
|
|
import Matrix3 from "./Matrix3.js";
|
|
import RuntimeError from "./RuntimeError.js";
|
|
|
|
/**
|
|
* A 4x4 matrix, indexable as a column-major order array.
|
|
* Constructor parameters are in row-major order for code readability.
|
|
* @alias Matrix4
|
|
* @constructor
|
|
* @implements {ArrayLike<number>}
|
|
*
|
|
* @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);
|
|
Check.typeOf.object("value", value);
|
|
Check.defined("array", array);
|
|
//>>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);
|
|
Check.defined("array", array);
|
|
//>>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);
|
|
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.defined("values", values);
|
|
//>>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);
|
|
Check.typeOf.object("rotation", rotation);
|
|
//>>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);
|
|
Check.typeOf.object("translation", translation);
|
|
Check.typeOf.object("rotation", rotation);
|
|
Check.typeOf.object("scale", scale);
|
|
//>>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);
|
|
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.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.typeOf.object("scale", scale);
|
|
//>>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);
|
|
Check.typeOf.number("scale", scale);
|
|
//>>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);
|
|
Check.typeOf.object("camera", camera);
|
|
//>>includeEnd('debug');
|
|
|
|
var position = camera.position;
|
|
var direction = camera.direction;
|
|
var up = camera.up;
|
|
|
|
//>>includeStart('debug', pragmas.debug);
|
|
Check.typeOf.object("camera.position", position);
|
|
Check.typeOf.object("camera.direction", direction);
|
|
Check.typeOf.object("camera.up", up);
|
|
//>>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);
|
|
Check.typeOf.number.greaterThan("fovY", fovY, 0.0);
|
|
Check.typeOf.number.lessThan("fovY", fovY, Math.PI);
|
|
Check.typeOf.number.greaterThan("near", near, 0.0);
|
|
Check.typeOf.number.greaterThan("far", far, 0.0);
|
|
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.typeOf.number("left", left);
|
|
Check.typeOf.number("right", right);
|
|
Check.typeOf.number("bottom", bottom);
|
|
Check.typeOf.number("top", top);
|
|
Check.typeOf.number("near", near);
|
|
Check.typeOf.number("far", far);
|
|
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.typeOf.number("left", left);
|
|
Check.typeOf.number("right", right);
|
|
Check.typeOf.number("bottom", bottom);
|
|
Check.typeOf.number("top", top);
|
|
Check.typeOf.number("near", near);
|
|
Check.typeOf.number("far", far);
|
|
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.typeOf.number("left", left);
|
|
Check.typeOf.number("right", right);
|
|
Check.typeOf.number("bottom", bottom);
|
|
Check.typeOf.number("top", top);
|
|
Check.typeOf.number("near", near);
|
|
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
|
|
) {
|
|
if (!defined(result)) {
|
|
result = new Matrix4();
|
|
}
|
|
|
|
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);
|
|
Check.typeOf.object("position", position);
|
|
Check.typeOf.object("direction", direction);
|
|
Check.typeOf.object("up", up);
|
|
Check.typeOf.object("right", right);
|
|
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] = -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);
|
|
Check.typeOf.object("matrix", matrix);
|
|
//>>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);
|
|
Check.typeOf.number.greaterThanOrEquals("row", row, 0);
|
|
Check.typeOf.number.lessThanOrEquals("row", row, 3);
|
|
|
|
Check.typeOf.number.greaterThanOrEquals("column", column, 0);
|
|
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.typeOf.object("matrix", matrix);
|
|
|
|
Check.typeOf.number.greaterThanOrEquals("index", index, 0);
|
|
Check.typeOf.number.lessThanOrEquals("index", index, 3);
|
|
|
|
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.typeOf.object("matrix", matrix);
|
|
|
|
Check.typeOf.number.greaterThanOrEquals("index", index, 0);
|
|
Check.typeOf.number.lessThanOrEquals("index", index, 3);
|
|
|
|
Check.typeOf.object("cartesian", cartesian);
|
|
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.typeOf.object("matrix", matrix);
|
|
Check.typeOf.object("translation", translation);
|
|
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 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.typeOf.object("matrix", matrix);
|
|
Check.typeOf.object("scale", scale);
|
|
Check.typeOf.object("result", result);
|
|
//>>includeEnd('debug');
|
|
|
|
var existingScale = Matrix4.getScale(matrix, scaleScratch);
|
|
var newScale = 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.typeOf.object("matrix", matrix);
|
|
|
|
Check.typeOf.number.greaterThanOrEquals("index", index, 0);
|
|
Check.typeOf.number.lessThanOrEquals("index", index, 3);
|
|
|
|
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.typeOf.object("matrix", matrix);
|
|
|
|
Check.typeOf.number.greaterThanOrEquals("index", index, 0);
|
|
Check.typeOf.number.lessThanOrEquals("index", index, 3);
|
|
|
|
Check.typeOf.object("cartesian", cartesian);
|
|
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 = 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);
|
|
Check.typeOf.object("matrix", matrix);
|
|
Check.typeOf.object("result", result);
|
|
//>>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);
|
|
Check.typeOf.object("left", left);
|
|
Check.typeOf.object("right", right);
|
|
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.typeOf.object("left", left);
|
|
Check.typeOf.object("right", right);
|
|
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.typeOf.object("left", left);
|
|
Check.typeOf.object("right", right);
|
|
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.typeOf.object("left", left);
|
|
Check.typeOf.object("right", right);
|
|
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.typeOf.object("matrix", matrix);
|
|
Check.typeOf.object("rotation", rotation);
|
|
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.typeOf.object("matrix", matrix);
|
|
Check.typeOf.object("translation", translation);
|
|
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 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.typeOf.object("matrix", matrix);
|
|
Check.typeOf.number("scale", scale);
|
|
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.typeOf.object("matrix", matrix);
|
|
Check.typeOf.object("scale", scale);
|
|
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.typeOf.object("matrix", matrix);
|
|
Check.typeOf.object("cartesian", cartesian);
|
|
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.typeOf.object("matrix", matrix);
|
|
Check.typeOf.object("cartesian", cartesian);
|
|
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.typeOf.object("matrix", matrix);
|
|
Check.typeOf.object("cartesian", cartesian);
|
|
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.typeOf.object("matrix", matrix);
|
|
Check.typeOf.number("scalar", scalar);
|
|
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;
|
|
};
|
|
|
|
/**
|
|
* 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.typeOf.object("matrix", matrix);
|
|
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.typeOf.object("matrix", matrix);
|
|
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.typeOf.object("matrix", matrix);
|
|
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 ||
|
|
(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=0] 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) {
|
|
epsilon = defaultValue(epsilon, 0);
|
|
|
|
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);
|
|
Check.typeOf.object("matrix", matrix);
|
|
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.typeOf.object("matrix", matrix);
|
|
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();
|
|
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);
|
|
Check.typeOf.object("matrix", matrix);
|
|
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) < 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.getMatrix3(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;
|
|
}
|
|
|
|
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);
|
|
Check.typeOf.object("matrix", matrix);
|
|
Check.typeOf.object("result", result);
|
|
//>>includeEnd('debug');
|
|
|
|
//This function is an optimized version of the below 4 lines.
|
|
//var rT = Matrix3.transpose(Matrix4.getMatrix3(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;
|
|
};
|
|
|
|
var scratchTransposeMatrix = new Matrix4();
|
|
|
|
/**
|
|
* Computes the inverse transpose of a matrix.
|
|
*
|
|
* @param {Matrix4} matrix The matrix to transpose and invert.
|
|
* @param {Matrix4} result The object onto which to store the result.
|
|
* @returns {Matrix4} The modified result parameter.
|
|
*/
|
|
Matrix4.inverseTranspose = function (matrix, result) {
|
|
//>>includeStart('debug', pragmas.debug);
|
|
Check.typeOf.object("matrix", matrix);
|
|
Check.typeOf.object("result", result);
|
|
//>>includeEnd('debug');
|
|
|
|
return Matrix4.inverse(
|
|
Matrix4.transpose(matrix, scratchTransposeMatrix),
|
|
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=0] 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] +
|
|
")"
|
|
);
|
|
};
|
|
export default Matrix4;
|