js
import Cartesian3 from "./Cartesian3.js";
import Cartesian4 from "./Cartesian4.js";
import Check from "./Check.js";
import Frozen from "./Frozen.js";
import defined from "./defined.js";
import DeveloperError from "./DeveloperError.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.fromArray
* @see Matrix4.fromColumnMajorArray
* @see Matrix4.fromRowMajorArray
* @see Matrix4.fromRotationTranslation
* @see Matrix4.fromTranslationQuaternionRotationScale
* @see Matrix4.fromTranslationRotationScale
* @see Matrix4.fromTranslation
* @see Matrix4.fromScale
* @see Matrix4.fromUniformScale
* @see Matrix4.fromRotation
* @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] = column0Row0 ?? 0.0;
this[1] = column0Row1 ?? 0.0;
this[2] = column0Row2 ?? 0.0;
this[3] = column0Row3 ?? 0.0;
this[4] = column1Row0 ?? 0.0;
this[5] = column1Row1 ?? 0.0;
this[6] = column1Row2 ?? 0.0;
this[7] = column1Row3 ?? 0.0;
this[8] = column2Row0 ?? 0.0;
this[9] = column2Row1 ?? 0.0;
this[10] = column2Row2 ?? 0.0;
this[11] = column2Row3 ?? 0.0;
this[12] = column3Row0 ?? 0.0;
this[13] = column3Row1 ?? 0.0;
this[14] = column3Row2 ?? 0.0;
this[15] = 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 = 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 = 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;
};
/**
* Flattens an array of Matrix4s into an array of components. The components
* are stored in column-major order.
*
* @param {Matrix4[]} array The array of matrices to pack.
* @param {number[]} [result] The array onto which to store the result. If this is a typed array, it must have array.length * 16 components, else a {@link DeveloperError} will be thrown. If it is a regular array, it will be resized to have (array.length * 16) elements.
* @returns {number[]} The packed array.
*/
Matrix4.packArray = function (array, result) {
//>>includeStart('debug', pragmas.debug);
Check.defined("array", array);
//>>includeEnd('debug');
const length = array.length;
const resultLength = length * 16;
if (!defined(result)) {
result = new Array(resultLength);
} else if (!Array.isArray(result) && result.length !== resultLength) {
//>>includeStart('debug', pragmas.debug);
throw new DeveloperError(
"If result is a typed array, it must have exactly array.length * 16 elements",
);
//>>includeEnd('debug');
} else if (result.length !== resultLength) {
result.length = resultLength;
}
for (let i = 0; i < length; ++i) {
Matrix4.pack(array[i], result, i * 16);
}
return result;
};
/**
* Unpacks an array of column-major matrix components into an array of Matrix4s.
*
* @param {number[]} array The array of components to unpack.
* @param {Matrix4[]} [result] The array onto which to store the result.
* @returns {Matrix4[]} The unpacked array.
*/
Matrix4.unpackArray = function (array, result) {
//>>includeStart('debug', pragmas.debug);
Check.defined("array", array);
Check.typeOf.number.greaterThanOrEquals("array.length", array.length, 16);
if (array.length % 16 !== 0) {
throw new DeveloperError("array length must be a multiple of 16.");
}
//>>includeEnd('debug');
const length = array.length;
if (!defined(result)) {
result = new Array(length / 16);
} else {
result.length = length / 16;
}
for (let i = 0; i < length; i += 16) {
const index = i / 16;
result[index] = Matrix4.unpack(array, i, result[index]);
}
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]
*
* const 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];
* const m = Cesium.Matrix4.fromArray(v);
*
* // Create same Matrix4 with using an offset into an array
* const 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];
* const 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 = 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
* const 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();
}
const scaleX = scale.x;
const scaleY = scale.y;
const scaleZ = scale.z;
const x2 = rotation.x * rotation.x;
const xy = rotation.x * rotation.y;
const xz = rotation.x * rotation.z;
const xw = rotation.x * rotation.w;
const y2 = rotation.y * rotation.y;
const yz = rotation.y * rotation.z;
const yw = rotation.y * rotation.w;
const z2 = rotation.z * rotation.z;
const zw = rotation.z * rotation.w;
const w2 = rotation.w * rotation.w;
const m00 = x2 - y2 - z2 + w2;
const m01 = 2.0 * (xy - zw);
const m02 = 2.0 * (xz + yw);
const m10 = 2.0 * (xy + zw);
const m11 = -x2 + y2 - z2 + w2;
const m12 = 2.0 * (yz - xw);
const m20 = 2.0 * (xz - yw);
const m21 = 2.0 * (yz + xw);
const 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]
* const 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]
* const 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;
};
/**
* Creates a rotation matrix.
*
* @param {Matrix3} rotation The rotation matrix.
* @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.fromRotation = function (rotation, result) {
//>>includeStart('debug', pragmas.debug);
Check.typeOf.object("rotation", rotation);
//>>includeEnd('debug');
if (!defined(result)) {
result = new Matrix4();
}
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] = 0.0;
result[13] = 0.0;
result[14] = 0.0;
result[15] = 1.0;
return result;
};
const fromCameraF = new Cartesian3();
const fromCameraR = new Cartesian3();
const 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');
const position = camera.position;
const direction = camera.direction;
const 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,
);
const sX = fromCameraR.x;
const sY = fromCameraR.y;
const sZ = fromCameraR.z;
const fX = fromCameraF.x;
const fY = fromCameraF.y;
const fZ = fromCameraF.z;
const uX = fromCameraU.x;
const uY = fromCameraU.y;
const uZ = fromCameraU.z;
const positionX = position.x;
const positionY = position.y;
const positionZ = position.z;
const t0 = sX * -positionX + sY * -positionY + sZ * -positionZ;
const t1 = uX * -positionX + uY * -positionY + uZ * -positionZ;
const 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.
// const 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);
// const 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');
const bottom = Math.tan(fovY * 0.5);
const column1Row1 = 1.0 / bottom;
const column0Row0 = column1Row1 / aspectRatio;
const column2Row2 = (far + near) / (near - far);
const 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');
let a = 1.0 / (right - left);
let b = 1.0 / (top - bottom);
let c = 1.0 / (far - near);
const tx = -(right + left) * a;
const ty = -(top + bottom) * b;
const 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 the camera that will be in view.
* @param {number} top The number of meters above 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');
const column0Row0 = (2.0 * near) / (right - left);
const column1Row1 = (2.0 * near) / (top - bottom);
const column2Row0 = (right + left) / (right - left);
const column2Row1 = (top + bottom) / (top - bottom);
const column2Row2 = -(far + near) / (far - near);
const column2Row3 = -1.0;
const 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');
const column0Row0 = (2.0 * near) / (right - left);
const column1Row1 = (2.0 * near) / (top - bottom);
const column2Row0 = (right + left) / (right - left);
const column2Row1 = (top + bottom) / (top - bottom);
const column2Row2 = -1.0;
const column2Row3 = -1.0;
const 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.
* const 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 = viewport ?? Frozen.EMPTY_OBJECT;
const x = viewport.x ?? 0.0;
const y = viewport.y ?? 0.0;
const width = viewport.width ?? 0.0;
const height = viewport.height ?? 0.0;
nearDepthRange = nearDepthRange ?? 0.0;
farDepthRange = farDepthRange ?? 1.0;
const halfWidth = width * 0.5;
const halfHeight = height * 0.5;
const halfDepth = (farDepthRange - nearDepthRange) * 0.5;
const column0Row0 = halfWidth;
const column1Row1 = halfHeight;
const column2Row2 = halfDepth;
const column3Row0 = x + halfWidth;
const column3Row1 = y + halfHeight;
const column3Row2 = nearDepthRange + halfDepth;
const 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]
* const 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
* const myMatrix = new Cesium.Matrix4();
* const column1Row0Index = Cesium.Matrix4.getElementIndex(1, 0);
* const 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
* const a = Cesium.Matrix4.getColumn(m, 2, new Cesium.Cartesian4());
*
* @example
* //Example 2: Sets values for Cartesian instance
* const 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');
const startIndex = index * 4;
const x = matrix[startIndex];
const y = matrix[startIndex + 1];
const z = matrix[startIndex + 2];
const 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]
*
* const 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);
const startIndex = index * 4;
result[startIndex] = cartesian.x;
result[startIndex + 1] = cartesian.y;
result[startIndex + 2] = cartesian.z;
result[startIndex + 3] = cartesian.w;
return result;
};
/**
* Retrieves a copy of the matrix row at the provided index as a Cartesian4 instance.
*
* @param {Matrix4} matrix The matrix to use.
* @param {number} index The zero-based index of the row to retrieve.
* @param {Cartesian4} result The object onto which to store the result.
* @returns {Cartesian4} The modified result parameter.
*
* @exception {DeveloperError} index must be 0, 1, 2, or 3.
*
* @example
* //returns a Cartesian4 instance with values from the specified column
* // m = [10.0, 11.0, 12.0, 13.0]
* // [14.0, 15.0, 16.0, 17.0]
* // [18.0, 19.0, 20.0, 21.0]
* // [22.0, 23.0, 24.0, 25.0]
*
* //Example 1: Returns an instance of Cartesian
* const a = Cesium.Matrix4.getRow(m, 2, new Cesium.Cartesian4());
*
* @example
* //Example 2: Sets values for a Cartesian instance
* const 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');
const x = matrix[index];
const y = matrix[index + 4];
const z = matrix[index + 8];
const 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]
*
* const 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;
};
/**
* 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;
};
const scaleScratch1 = 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.
*
* @see Matrix4.setUniformScale
* @see Matrix4.fromScale
* @see Matrix4.fromUniformScale
* @see Matrix4.multiplyByScale
* @see Matrix4.multiplyByUniformScale
* @see Matrix4.getScale
*/
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');
const existingScale = Matrix4.getScale(matrix, scaleScratch1);
const scaleRatioX = scale.x / existingScale.x;
const scaleRatioY = scale.y / existingScale.y;
const scaleRatioZ = scale.z / existingScale.z;
result[0] = matrix[0] * scaleRatioX;
result[1] = matrix[1] * scaleRatioX;
result[2] = matrix[2] * scaleRatioX;
result[3] = matrix[3];
result[4] = matrix[4] * scaleRatioY;
result[5] = matrix[5] * scaleRatioY;
result[6] = matrix[6] * scaleRatioY;
result[7] = matrix[7];
result[8] = matrix[8] * scaleRatioZ;
result[9] = matrix[9] * scaleRatioZ;
result[10] = matrix[10] * scaleRatioZ;
result[11] = matrix[11];
result[12] = matrix[12];
result[13] = matrix[13];
result[14] = matrix[14];
result[15] = matrix[15];
return result;
};
const scaleScratch2 = new Cartesian3();
/**
* Computes a new matrix that replaces the scale with the provided uniform scale.
* This assumes the matrix is an affine transformation.
*
* @param {Matrix4} matrix The matrix to use.
* @param {number} scale The uniform 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.
*
* @see Matrix4.setScale
* @see Matrix4.fromScale
* @see Matrix4.fromUniformScale
* @see Matrix4.multiplyByScale
* @see Matrix4.multiplyByUniformScale
* @see Matrix4.getScale
*/
Matrix4.setUniformScale = 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');
const existingScale = Matrix4.getScale(matrix, scaleScratch2);
const scaleRatioX = scale / existingScale.x;
const scaleRatioY = scale / existingScale.y;
const scaleRatioZ = scale / existingScale.z;
result[0] = matrix[0] * scaleRatioX;
result[1] = matrix[1] * scaleRatioX;
result[2] = matrix[2] * scaleRatioX;
result[3] = matrix[3];
result[4] = matrix[4] * scaleRatioY;
result[5] = matrix[5] * scaleRatioY;
result[6] = matrix[6] * scaleRatioY;
result[7] = matrix[7];
result[8] = matrix[8] * scaleRatioZ;
result[9] = matrix[9] * scaleRatioZ;
result[10] = matrix[10] * scaleRatioZ;
result[11] = matrix[11];
result[12] = matrix[12];
result[13] = matrix[13];
result[14] = matrix[14];
result[15] = matrix[15];
return result;
};
const 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
*
* @see Matrix4.multiplyByScale
* @see Matrix4.multiplyByUniformScale
* @see Matrix4.fromScale
* @see Matrix4.fromUniformScale
* @see Matrix4.setScale
* @see Matrix4.setUniformScale
*/
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;
};
const scaleScratch3 = 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, scaleScratch3);
return Cartesian3.maximumComponent(scaleScratch3);
};
const scaleScratch4 = new Cartesian3();
/**
* Sets the rotation assuming the matrix is an affine transformation.
*
* @param {Matrix4} matrix The matrix.
* @param {Matrix3} rotation The rotation matrix.
* @param {Matrix4} result The object onto which to store the result.
* @returns {Matrix4} The modified result parameter.
*
* @see Matrix4.fromRotation
* @see Matrix4.getRotation
*/
Matrix4.setRotation = function (matrix, rotation, result) {
//>>includeStart('debug', pragmas.debug);
Check.typeOf.object("matrix", matrix);
Check.typeOf.object("result", result);
//>>includeEnd('debug');
const scale = Matrix4.getScale(matrix, scaleScratch4);
result[0] = rotation[0] * scale.x;
result[1] = rotation[1] * scale.x;
result[2] = rotation[2] * scale.x;
result[3] = matrix[3];
result[4] = rotation[3] * scale.y;
result[5] = rotation[4] * scale.y;
result[6] = rotation[5] * scale.y;
result[7] = matrix[7];
result[8] = rotation[6] * scale.z;
result[9] = rotation[7] * scale.z;
result[10] = rotation[8] * scale.z;
result[11] = matrix[11];
result[12] = matrix[12];
result[13] = matrix[13];
result[14] = matrix[14];
result[15] = matrix[15];
return result;
};
const scaleScratch5 = new Cartesian3();
/**
* Extracts the rotation matrix assuming the matrix is an affine transformation.
*
* @param {Matrix4} matrix The matrix.
* @param {Matrix3} result The object onto which to store the result.
* @returns {Matrix3} The modified result parameter.
*
* @see Matrix4.setRotation
* @see Matrix4.fromRotation
*/
Matrix4.getRotation = function (matrix, result) {
//>>includeStart('debug', pragmas.debug);
Check.typeOf.object("matrix", matrix);
Check.typeOf.object("result", result);
//>>includeEnd('debug');
const scale = Matrix4.getScale(matrix, scaleScratch5);
result[0] = matrix[0] / scale.x;
result[1] = matrix[1] / scale.x;
result[2] = matrix[2] / scale.x;
result[3] = matrix[4] / scale.y;
result[4] = matrix[5] / scale.y;
result[5] = matrix[6] / scale.y;
result[6] = matrix[8] / scale.z;
result[7] = matrix[9] / scale.z;
result[8] = matrix[10] / scale.z;
return result;
};
/**
* 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');
const left0 = left[0];
const left1 = left[1];
const left2 = left[2];
const left3 = left[3];
const left4 = left[4];
const left5 = left[5];
const left6 = left[6];
const left7 = left[7];
const left8 = left[8];
const left9 = left[9];
const left10 = left[10];
const left11 = left[11];
const left12 = left[12];
const left13 = left[13];
const left14 = left[14];
const left15 = left[15];
const right0 = right[0];
const right1 = right[1];
const right2 = right[2];
const right3 = right[3];
const right4 = right[4];
const right5 = right[5];
const right6 = right[6];
const right7 = right[7];
const right8 = right[8];
const right9 = right[9];
const right10 = right[10];
const right11 = right[11];
const right12 = right[12];
const right13 = right[13];
const right14 = right[14];
const right15 = right[15];
const column0Row0 =
left0 * right0 + left4 * right1 + left8 * right2 + left12 * right3;
const column0Row1 =
left1 * right0 + left5 * right1 + left9 * right2 + left13 * right3;
const column0Row2 =
left2 * right0 + left6 * right1 + left10 * right2 + left14 * right3;
const column0Row3 =
left3 * right0 + left7 * right1 + left11 * right2 + left15 * right3;
const column1Row0 =
left0 * right4 + left4 * right5 + left8 * right6 + left12 * right7;
const column1Row1 =
left1 * right4 + left5 * right5 + left9 * right6 + left13 * right7;
const column1Row2 =
left2 * right4 + left6 * right5 + left10 * right6 + left14 * right7;
const column1Row3 =
left3 * right4 + left7 * right5 + left11 * right6 + left15 * right7;
const column2Row0 =
left0 * right8 + left4 * right9 + left8 * right10 + left12 * right11;
const column2Row1 =
left1 * right8 + left5 * right9 + left9 * right10 + left13 * right11;
const column2Row2 =
left2 * right8 + left6 * right9 + left10 * right10 + left14 * right11;
const column2Row3 =
left3 * right8 + left7 * right9 + left11 * right10 + left15 * right11;
const column3Row0 =
left0 * right12 + left4 * right13 + left8 * right14 + left12 * right15;
const column3Row1 =
left1 * right12 + left5 * right13 + left9 * right14 + left13 * right15;
const column3Row2 =
left2 * right12 + left6 * right13 + left10 * right14 + left14 * right15;
const 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 any 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
* const 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);
* const m2 = Cesium.Transforms.eastNorthUpToFixedFrame(new Cesium.Cartesian3(1.0, 1.0, 1.0));
* const 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');
const left0 = left[0];
const left1 = left[1];
const left2 = left[2];
const left4 = left[4];
const left5 = left[5];
const left6 = left[6];
const left8 = left[8];
const left9 = left[9];
const left10 = left[10];
const left12 = left[12];
const left13 = left[13];
const left14 = left[14];
const right0 = right[0];
const right1 = right[1];
const right2 = right[2];
const right4 = right[4];
const right5 = right[5];
const right6 = right[6];
const right8 = right[8];
const right9 = right[9];
const right10 = right[10];
const right12 = right[12];
const right13 = right[13];
const right14 = right[14];
const column0Row0 = left0 * right0 + left4 * right1 + left8 * right2;
const column0Row1 = left1 * right0 + left5 * right1 + left9 * right2;
const column0Row2 = left2 * right0 + left6 * right1 + left10 * right2;
const column1Row0 = left0 * right4 + left4 * right5 + left8 * right6;
const column1Row1 = left1 * right4 + left5 * right5 + left9 * right6;
const column1Row2 = left2 * right4 + left6 * right5 + left10 * right6;
const column2Row0 = left0 * right8 + left4 * right9 + left8 * right10;
const column2Row1 = left1 * right8 + left5 * right9 + left9 * right10;
const column2Row2 = left2 * right8 + left6 * right9 + left10 * right10;
const column3Row0 =
left0 * right12 + left4 * right13 + left8 * right14 + left12;
const column3Row1 =
left1 * right12 + left5 * right13 + left9 * right14 + left13;
const 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');
const left0 = matrix[0];
const left1 = matrix[1];
const left2 = matrix[2];
const left4 = matrix[4];
const left5 = matrix[5];
const left6 = matrix[6];
const left8 = matrix[8];
const left9 = matrix[9];
const left10 = matrix[10];
const right0 = rotation[0];
const right1 = rotation[1];
const right2 = rotation[2];
const right4 = rotation[3];
const right5 = rotation[4];
const right6 = rotation[5];
const right8 = rotation[6];
const right9 = rotation[7];
const right10 = rotation[8];
const column0Row0 = left0 * right0 + left4 * right1 + left8 * right2;
const column0Row1 = left1 * right0 + left5 * right1 + left9 * right2;
const column0Row2 = left2 * right0 + left6 * right1 + left10 * right2;
const column1Row0 = left0 * right4 + left4 * right5 + left8 * right6;
const column1Row1 = left1 * right4 + left5 * right5 + left9 * right6;
const column1Row2 = left2 * right4 + left6 * right5 + left10 * right6;
const column2Row0 = left0 * right8 + left4 * right9 + left8 * right10;
const column2Row1 = left1 * right8 + left5 * right9 + left9 * right10;
const 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');
const x = translation.x;
const y = translation.y;
const z = translation.z;
const tx = x * matrix[0] + y * matrix[4] + z * matrix[8] + matrix[12];
const ty = x * matrix[1] + y * matrix[5] + z * matrix[9] + matrix[13];
const 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;
};
/**
* 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.multiplyByUniformScale
* @see Matrix4.fromScale
* @see Matrix4.fromUniformScale
* @see Matrix4.setScale
* @see Matrix4.setUniformScale
* @see Matrix4.getScale
*/
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');
const scaleX = scale.x;
const scaleY = scale.y;
const 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] = matrix[3];
result[4] = scaleY * matrix[4];
result[5] = scaleY * matrix[5];
result[6] = scaleY * matrix[6];
result[7] = matrix[7];
result[8] = scaleZ * matrix[8];
result[9] = scaleZ * matrix[9];
result[10] = scaleZ * 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 product of a matrix times a uniform scale, as if the scale were a scale matrix.
*
* @param {Matrix4} matrix The 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.multiplyByScale
* @see Matrix4.fromScale
* @see Matrix4.fromUniformScale
* @see Matrix4.setScale
* @see Matrix4.setUniformScale
* @see Matrix4.getScale
*/
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');
result[0] = matrix[0] * scale;
result[1] = matrix[1] * scale;
result[2] = matrix[2] * scale;
result[3] = matrix[3];
result[4] = matrix[4] * scale;
result[5] = matrix[5] * scale;
result[6] = matrix[6] * scale;
result[7] = matrix[7];
result[8] = matrix[8] * scale;
result[9] = matrix[9] * scale;
result[10] = matrix[10] * scale;
result[11] = matrix[11];
result[12] = matrix[12];
result[13] = matrix[13];
result[14] = matrix[14];
result[15] = matrix[15];
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');
const vX = cartesian.x;
const vY = cartesian.y;
const vZ = cartesian.z;
const vW = cartesian.w;
const x = matrix[0] * vX + matrix[4] * vY + matrix[8] * vZ + matrix[12] * vW;
const y = matrix[1] * vX + matrix[5] * vY + matrix[9] * vZ + matrix[13] * vW;
const z = matrix[2] * vX + matrix[6] * vY + matrix[10] * vZ + matrix[14] * vW;
const 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
* const p = new Cesium.Cartesian3(1.0, 2.0, 3.0);
* const 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');
const vX = cartesian.x;
const vY = cartesian.y;
const vZ = cartesian.z;
const x = matrix[0] * vX + matrix[4] * vY + matrix[8] * vZ;
const y = matrix[1] * vX + matrix[5] * vY + matrix[9] * vZ;
const 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
* const p = new Cesium.Cartesian3(1.0, 2.0, 3.0);
* const 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');
const vX = cartesian.x;
const vY = cartesian.y;
const vZ = cartesian.z;
const x = matrix[0] * vX + matrix[4] * vY + matrix[8] * vZ + matrix[12];
const y = matrix[1] * vX + matrix[5] * vY + matrix[9] * vZ + matrix[13];
const 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]
*
* const 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]
*
* const 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]
*
* const 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');
const matrix1 = matrix[1];
const matrix2 = matrix[2];
const matrix3 = matrix[3];
const matrix6 = matrix[6];
const matrix7 = matrix[7];
const 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 = 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 an 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 matrix of the provided 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]
*
* const 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;
};
const scratchInverseRotation = new Matrix3();
const scratchMatrix3Zero = new Matrix3();
const scratchBottomRow = new Cartesian4();
const 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 a proper rigid transformation, 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
//
const src0 = matrix[0];
const src1 = matrix[4];
const src2 = matrix[8];
const src3 = matrix[12];
const src4 = matrix[1];
const src5 = matrix[5];
const src6 = matrix[9];
const src7 = matrix[13];
const src8 = matrix[2];
const src9 = matrix[6];
const src10 = matrix[10];
const src11 = matrix[14];
const src12 = matrix[3];
const src13 = matrix[7];
const src14 = matrix[11];
const src15 = matrix[15];
// calculate pairs for first 8 elements (cofactors)
let tmp0 = src10 * src15;
let tmp1 = src11 * src14;
let tmp2 = src9 * src15;
let tmp3 = src11 * src13;
let tmp4 = src9 * src14;
let tmp5 = src10 * src13;
let tmp6 = src8 * src15;
let tmp7 = src11 * src12;
let tmp8 = src8 * src14;
let tmp9 = src10 * src12;
let tmp10 = src8 * src13;
let tmp11 = src9 * src12;
// calculate first 8 elements (cofactors)
const dst0 =
tmp0 * src5 +
tmp3 * src6 +
tmp4 * src7 -
(tmp1 * src5 + tmp2 * src6 + tmp5 * src7);
const dst1 =
tmp1 * src4 +
tmp6 * src6 +
tmp9 * src7 -
(tmp0 * src4 + tmp7 * src6 + tmp8 * src7);
const dst2 =
tmp2 * src4 +
tmp7 * src5 +
tmp10 * src7 -
(tmp3 * src4 + tmp6 * src5 + tmp11 * src7);
const dst3 =
tmp5 * src4 +
tmp8 * src5 +
tmp11 * src6 -
(tmp4 * src4 + tmp9 * src5 + tmp10 * src6);
const dst4 =
tmp1 * src1 +
tmp2 * src2 +
tmp5 * src3 -
(tmp0 * src1 + tmp3 * src2 + tmp4 * src3);
const dst5 =
tmp0 * src0 +
tmp7 * src2 +
tmp8 * src3 -
(tmp1 * src0 + tmp6 * src2 + tmp9 * src3);
const dst6 =
tmp3 * src0 +
tmp6 * src1 +
tmp11 * src3 -
(tmp2 * src0 + tmp7 * src1 + tmp10 * src3);
const 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)
const dst8 =
tmp0 * src13 +
tmp3 * src14 +
tmp4 * src15 -
(tmp1 * src13 + tmp2 * src14 + tmp5 * src15);
const dst9 =
tmp1 * src12 +
tmp6 * src14 +
tmp9 * src15 -
(tmp0 * src12 + tmp7 * src14 + tmp8 * src15);
const dst10 =
tmp2 * src12 +
tmp7 * src13 +
tmp10 * src15 -
(tmp3 * src12 + tmp6 * src13 + tmp11 * src15);
const dst11 =
tmp5 * src12 +
tmp8 * src13 +
tmp11 * src14 -
(tmp4 * src12 + tmp9 * src13 + tmp10 * src14);
const dst12 =
tmp2 * src10 +
tmp5 * src11 +
tmp1 * src9 -
(tmp4 * src11 + tmp0 * src9 + tmp3 * src10);
const dst13 =
tmp8 * src11 +
tmp0 * src8 +
tmp7 * src10 -
(tmp6 * src10 + tmp9 * src11 + tmp1 * src8);
const dst14 =
tmp6 * src9 +
tmp11 * src11 +
tmp3 * src8 -
(tmp10 * src11 + tmp2 * src8 + tmp7 * src9);
const dst15 =
tmp10 * src10 +
tmp4 * src8 +
tmp9 * src9 -
(tmp8 * src9 + tmp11 * src10 + tmp5 * src8);
// calculate determinant
let 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 a proper rigid 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.
//const rT = Matrix3.transpose(Matrix4.getMatrix3(matrix));
//const rTN = Matrix3.negate(rT);
//const rTT = Matrix3.multiplyByVector(rTN, Matrix4.getTranslation(matrix));
//return Matrix4.fromRotationTranslation(rT, rTT, result);
const matrix0 = matrix[0];
const matrix1 = matrix[1];
const matrix2 = matrix[2];
const matrix4 = matrix[4];
const matrix5 = matrix[5];
const matrix6 = matrix[6];
const matrix8 = matrix[8];
const matrix9 = matrix[9];
const matrix10 = matrix[10];
const vX = matrix[12];
const vY = matrix[13];
const vZ = matrix[14];
const x = -matrix0 * vX - matrix1 * vY - matrix2 * vZ;
const y = -matrix4 * vX - matrix5 * vY - matrix6 * vZ;
const 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;
};
const 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;这段代码实现了 Matrix4 类，代表一个 4x4 矩阵 ，采用列主序 存储（column-major order），是三维图形学中用于表示变换（平移、旋转、缩放）和投影矩阵的核心数学类型。它提供了丰富的静态方法，用于创建、操作、组合矩阵，并支持与 Cartesian3、Cartesian4、Matrix3 等类型的互操作。
1. 整体结构
js
function Matrix4(column0Row0, column1Row0, ... , column3Row3) {
this[0] = column0Row0 ?? 0.0;
this[1] = column0Row1 ?? 0.0;
// ... 共16个属性，以数值索引存储
}- 矩阵内部使用数组索引（0~15）存储 16 个元素，按列主序排列。
- 构造函数接受 16 个参数，但顺序是行主序（row-major），便于代码可读性；内部按列主序赋值。
- 实现了
ArrayLike<number>接口，因此可以像数组一样使用matrix[0]访问元素。 - 所有方法都是静态 的，但提供了实例方法的浅封装（如
clone、equals），方便链式调用。
2. 存储与序列化
2.1 列主序布局
js
// 索引映射：
// [0] = column0, row0
// [1] = column0, row1
// [2] = column0, row2
// [3] = column0, row3
// [4] = column1, row0
// [5] = column1, row1
// ...这种布局与 OpenGL / WebGL 的矩阵传递方式一致，可以直接传递给 shader。
2.2 Packable 接口
与 Cartesian3 类似，Matrix4 实现了 Packable 接口，支持序列化：
packedLength = 16pack(value, array, startingIndex)-- 将矩阵写入数组unpack(array, startingIndex, result)-- 从数组恢复packArray/unpackArray-- 批量处理
3. 核心功能分类
3.1 创建矩阵（静态工厂方法）
- 基础创建 ：
fromArray/fromColumnMajorArray/fromRowMajorArray-- 从数组创建clone-- 深拷贝
- 变换矩阵 ：
fromRotationTranslation(rotation, translation)-- 从旋转矩阵和平移向量创建fromTranslationQuaternionRotationScale-- 从平移、四元数旋转、非均匀缩放创建（高效）fromTranslationRotationScale-- 从TranslationRotationScale对象创建fromTranslation-- 纯平移矩阵fromScale-- 非均匀缩放矩阵fromUniformScale-- 均匀缩放矩阵fromRotation-- 从旋转矩阵创建
- 相机矩阵 ：
fromCamera(camera)-- 从Camera对象构建视图矩阵
- 投影矩阵 ：
computePerspectiveFieldOfView-- 透视投影（基于 FOV）computeOrthographicOffCenter-- 正交投影computePerspectiveOffCenter-- 非对称透视投影computeInfinitePerspectiveOffCenter-- 无限远透视投影computeViewportTransformation-- 视口变换矩阵computeView-- 视图矩阵（从位置、方向、上、右向量）
3.2 矩阵运算
- 代数运算 ：
multiply-- 矩阵乘法（通用 4x4）multiplyTransformation-- 针对仿射变换的优化乘法（忽略最后一行）add/subtract-- 逐元素加减multiplyByScalar-- 数乘negate-- 取负transpose-- 转置abs-- 绝对值inverse-- 通用求逆（Cramer 法则）inverseTransformation-- 仿射变换求逆（更快）inverseTranspose-- 逆转置
- 与向量/矩阵的乘法 ：
multiplyByMatrix3-- 左乘一个 3x3 矩阵（用于仿射变换）multiplyByTranslation-- 左乘一个平移矩阵multiplyByScale/multiplyByUniformScale-- 左乘缩放矩阵multiplyByVector-- 乘以Cartesian4multiplyByPoint-- 乘以Cartesian3（w=1）multiplyByPointAsVector-- 乘以Cartesian3（w=0，方向向量）
3.3 矩阵分解与访问
- 分量访问 ：
getElementIndex(column, row)-- 获取索引getColumn/setColumn-- 获取/设置列（Cartesian4）getRow/setRow-- 获取/设置行
- 仿射变换分解 ：
getTranslation-- 提取平移部分getMatrix3-- 提取左上角 3x3 矩阵getScale-- 计算非均匀缩放因子getMaximumScale-- 最大缩放因子setTranslation-- 设置平移setScale/setUniformScale-- 设置缩放（保留旋转）getRotation-- 提取旋转矩阵（归一化后）setRotation-- 设置旋转（保持缩放）
3.4 比较与容差
equals-- 严格相等equalsEpsilon-- 带容差比较- 实例方法
equals/equalsEpsilon委托给静态版本
3.5 常量与工具
Matrix4.IDENTITY-- 单位矩阵（冻结）Matrix4.ZERO-- 零矩阵- 预定义索引常量（如
COLUMN0ROW0），便于直接索引 toString()-- 按行打印矩阵
4. 设计亮点
4.1 性能优化
- 静态方法 + 可选的 result 参数：所有运算都允许传入预分配的对象，避免 GC 压力。
- 专用优化路径 ：
multiplyTransformation假定矩阵是仿射变换（最后一行 [0,0,0,1]），减少计算量。inverseTransformation利用旋转矩阵正交性，用转置替代通用求逆。- 矩阵乘法展开为显式公式，避免循环开销。
- Scratch 变量 ：内部使用静态临时变量（如
scratchInverseRotation）减少对象创建。 - 条件编译 ：通过
//>>includeStart('debug', pragmas.debug)包裹参数校验，在生产构建中可移除，提高运行时性能。
4.2 数值稳定性
- 求逆时检查行列式是否接近零，对零缩放矩阵做了特殊处理（如全零缩放时，返回平移取反的矩阵）。
- 使用
CesiumMath.EPSILON21等容差判断奇异性。 - 提供
equalsEpsilon方法，避免浮点误差。
4.3 易用性
- 灵活的构造函数：参数顺序按行主序，与数学表达式一致；使用默认值简化调用。
- 丰富的工厂方法：覆盖了三维图形中常见的矩阵创建场景（旋转、平移、缩放、投影、相机）。
- 与
Cartesian3/Cartesian4/Matrix3无缝集成：方法参数和返回值均使用这些类型，形成统一的数学库。
4.4 接口设计
- 实现了
ArrayLike<number>，可直接用于 WebGL 的uniformMatrix4fv等函数。 - 提供实例方法，便于在面向对象风格中使用。
5. 依赖与关系
Matrix4 依赖于：
Cartesian3-- 表示点/向量Cartesian4-- 表示齐次坐标Matrix3-- 表示旋转/缩放Check-- 参数校验defined-- 存在性检查DeveloperError/RuntimeError-- 异常类型CesiumMath-- 数学工具（如EPSILON21、clamp、equalsEpsilon）Frozen-- 提供空对象常量
这些依赖与之前分析的 defined、Check、DeveloperError 等工具类协同工作，构成了 Cesium 数学库的基础。
6. 使用示例
js
import Matrix4 from './Matrix4.js';
import Cartesian3 from './Cartesian3.js';
// 创建平移矩阵
const translation = new Cartesian3(10, 20, 30);
const T = Matrix4.fromTranslation(translation);
// 创建旋转矩阵（绕 X 轴 45 度）
const rotationX = Matrix3.fromRotationX(Math.PI / 4);
const R = Matrix4.fromRotation(rotationX);
// 组合：先旋转后平移
const M = Matrix4.multiply(T, R, new Matrix4());
// 变换点
const point = new Cartesian3(1, 2, 3);
const transformed = Matrix4.multiplyByPoint(M, point, new Cartesian3());
// 提取平移和缩放
const trans = Matrix4.getTranslation(M, new Cartesian3());
const scale = Matrix4.getScale(M, new Cartesian3());
// 创建透视投影矩阵
const perspective = Matrix4.computePerspectiveFieldOfView(
Math.PI / 4, // 45° FOV
16/9, // 宽高比
0.1, // 近平面
1000, // 远平面
new Matrix4()
);7. 总结
Matrix4 是 Cesium 数学库中最重要的类之一，它完整实现了 4x4 矩阵的各种运算，并针对三维图形应用进行了高度优化。通过列主序存储 、静态工厂方法 、可重用的 scratch 变量 、参数校验条件编译 等技巧，在保证正确性的同时兼顾了性能。与 Cartesian3、Matrix3 等类协同工作，为三维变换、投影、视图计算提供了坚实的基础。其设计模式（如 Packable 接口、可选的 result 参数）与之前分析的工具类一脉相承，体现了 Cesium 在可维护性和性能之间的平衡。