@cesium/engine
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CesiumJS is a JavaScript library for creating 3D globes and 2D maps in a web browser without a plugin.
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JavaScript
// @ts-check
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";
/** @import Quaternion from "./Quaternion.js"; */
/** @import TranslationRotationScale from "./TranslationRotationScale.js"; */
/** @import Camera from "../Scene/Camera.js"; */
/**
* @typedef {object} Viewport
* @property {number} [x]
* @property {number} [y]
* @property {number} [width]
* @property {number} [height]
*/
/**
* A 4x4 matrix, indexable as a column-major order array.
* Constructor parameters are in row-major order for code readability.
*
* @implements {ArrayLike<number>}
*
* @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
*/
// @ts-expect-error TODO(tsd-jsdoc): Requires index signature support.
class Matrix4 {
/**
* @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.
*/
constructor(
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;
}
/**
* 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
*/
static pack(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.
*/
static unpack(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.
*/
static packArray(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);
// @ts-expect-error TODO(tsd-jsdoc): Requires conditional TypedArray types.
} 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) {
/** @type {number[]} */ (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.
*/
static unpackArray(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)
*/
static clone(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;
}
/**
* 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.
*/
static fromColumnMajorArray(values, result) {
//>>includeStart('debug', pragmas.debug);
Check.defined("values", values);
//>>includeEnd('debug');
// @ts-expect-error TODO(tsd-jsdoc): Requires index signature support.
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.
*/
static fromRowMajorArray(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.
*/
static fromRotationTranslation(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);
*/
static fromTranslationQuaternionRotationScale(
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.
*/
static fromTranslationRotationScale(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
*/
static fromTranslation(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));
*/
static fromScale(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);
*/
static fromUniformScale(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.
*/
static fromRotation(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;
}
/**
* 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.
*/
static fromCamera(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.
*/
static computePerspectiveFieldOfView(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.
*/
static computeOrthographicOffCenter(
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.
*/
static computePerspectiveOffCenter(
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.
*/
static computeInfinitePerspectiveOffCenter(
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 {Viewport} [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());
*/
static computeViewportTransformation(
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.
*/
static computeView(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]
*/
static toArray(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;
*/
static getElementIndex(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;
*/
static getColumn(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;
// @ts-expect-error TODO(tsd-jsdoc): Requires index signature support.
const x = matrix[startIndex];
// @ts-expect-error TODO(tsd-jsdoc): Requires index signature support.
const y = matrix[startIndex + 1];
// @ts-expect-error TODO(tsd-jsdoc): Requires index signature support.
const z = matrix[startIndex + 2];
// @ts-expect-error TODO(tsd-jsdoc): Requires index signature support.
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]
*/
static setColumn(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;
// @ts-expect-error TODO(tsd-jsdoc): Requires index signature support.
result[startIndex] = cartesian.x;
// @ts-expect-error TODO(tsd-jsdoc): Requires index signature support.
result[startIndex + 1] = cartesian.y;
// @ts-expect-error TODO(tsd-jsdoc): Requires index signature support.
result[startIndex + 2] = cartesian.z;
// @ts-expect-error TODO(tsd-jsdoc): Requires index signature support.
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;
*/
static getRow(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');
// @ts-expect-error TODO(tsd-jsdoc): Requires index signature support.
const x = matrix[index];
// @ts-expect-error TODO(tsd-jsdoc): Requires index signature support.
const y = matrix[index + 4];
// @ts-expect-error TODO(tsd-jsdoc): Requires index signature support.
const z = matrix[index + 8];
// @ts-expect-error TODO(tsd-jsdoc): Requires index signature support.
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]
*/
static setRow(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);
// @ts-expect-error TODO(tsd-jsdoc): Requires index signature support.
result[index] = cartesian.x;
// @ts-expect-error TODO(tsd-jsdoc): Requires index signature support.
result[index + 4] = cartesian.y;
// @ts-expect-error TODO(tsd-jsdoc): Requires index signature support.
result[index + 8] = cartesian.z;
// @ts-expect-error TODO(tsd-jsdoc): Requires index signature support.
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.
*/
static setTranslation(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;
}
/**
* 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
*/
static setScale(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;
}
/**
* 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
*/
static setUniformScale(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 scaleRat