true if they are equal, false otherwise.
*
* @param {Cartesian3} [left] The first Cartesian.
* @param {Cartesian3} [right] The second Cartesian.
* @returns {boolean} true if left and right are equal, false otherwise.
*/
static equals(left, right) {
return left === right || defined_default(left) && defined_default(right) && left.x === right.x && left.y === right.y && left.z === right.z;
}
/**
* @param {Cartesian3} cartesian
* @param {number[]} array
* @param {number} offset
* @ignore
*/
static equalsArray(cartesian, array, offset) {
return cartesian.x === array[offset] && cartesian.y === array[offset + 1] && cartesian.z === array[offset + 2];
}
/**
* Compares the provided Cartesians componentwise and returns
* true if they pass an absolute or relative tolerance test,
* false otherwise.
*
* @param {Cartesian3} [left] The first Cartesian.
* @param {Cartesian3} [right] The second Cartesian.
* @param {number} [relativeEpsilon=0] The relative epsilon tolerance to use for equality testing.
* @param {number} [absoluteEpsilon=relativeEpsilon] The absolute epsilon tolerance to use for equality testing.
* @returns {boolean} true if left and right are within the provided epsilon, false otherwise.
*/
static equalsEpsilon(left, right, relativeEpsilon, absoluteEpsilon) {
return left === right || defined_default(left) && defined_default(right) && Math_default.equalsEpsilon(
left.x,
right.x,
relativeEpsilon,
absoluteEpsilon
) && Math_default.equalsEpsilon(
left.y,
right.y,
relativeEpsilon,
absoluteEpsilon
) && Math_default.equalsEpsilon(
left.z,
right.z,
relativeEpsilon,
absoluteEpsilon
);
}
/**
* Computes the cross (outer) product of two Cartesians.
*
* @param {Cartesian3} left The first Cartesian.
* @param {Cartesian3} right The second Cartesian.
* @param {Cartesian3} result The object onto which to store the result.
* @returns {Cartesian3} The cross product.
*/
static cross(left, right, result) {
Check_default.typeOf.object("left", left);
Check_default.typeOf.object("right", right);
Check_default.typeOf.object("result", result);
const leftX = left.x;
const leftY = left.y;
const leftZ = left.z;
const rightX = right.x;
const rightY = right.y;
const rightZ = right.z;
const x = leftY * rightZ - leftZ * rightY;
const y = leftZ * rightX - leftX * rightZ;
const z = leftX * rightY - leftY * rightX;
result.x = x;
result.y = y;
result.z = z;
return result;
}
/**
* Computes the midpoint between the right and left Cartesian.
* @param {Cartesian3} left The first Cartesian.
* @param {Cartesian3} right The second Cartesian.
* @param {Cartesian3} result The object onto which to store the result.
* @returns {Cartesian3} The midpoint.
*/
static midpoint(left, right, result) {
Check_default.typeOf.object("left", left);
Check_default.typeOf.object("right", right);
Check_default.typeOf.object("result", result);
result.x = (left.x + right.x) * 0.5;
result.y = (left.y + right.y) * 0.5;
result.z = (left.z + right.z) * 0.5;
return result;
}
/**
* Returns a Cartesian3 position from longitude and latitude values given in degrees.
*
* @param {number} longitude The longitude, in degrees
* @param {number} latitude The latitude, in degrees
* @param {number} [height=0.0] The height, in meters, above the ellipsoid.
* @param {Ellipsoid} [ellipsoid=Ellipsoid.default] The ellipsoid on which the position lies.
* @param {Cartesian3} [result] The object onto which to store the result.
* @returns {Cartesian3} The position
*
* @example
* const position = Cesium.Cartesian3.fromDegrees(-115.0, 37.0);
*/
static fromDegrees(longitude, latitude, height, ellipsoid, result) {
Check_default.typeOf.number("longitude", longitude);
Check_default.typeOf.number("latitude", latitude);
longitude = Math_default.toRadians(longitude);
latitude = Math_default.toRadians(latitude);
return _Cartesian3.fromRadians(
longitude,
latitude,
height,
ellipsoid,
result
);
}
/**
* Returns a Cartesian3 position from longitude and latitude values given in radians.
*
* @param {number} longitude The longitude, in radians
* @param {number} latitude The latitude, in radians
* @param {number} [height=0.0] The height, in meters, above the ellipsoid.
* @param {Ellipsoid} [ellipsoid=Ellipsoid.default] The ellipsoid on which the position lies.
* @param {Cartesian3} [result] The object onto which to store the result.
* @returns {Cartesian3} The position
*
* @example
* const position = Cesium.Cartesian3.fromRadians(-2.007, 0.645);
*/
static fromRadians(longitude, latitude, height, ellipsoid, result) {
Check_default.typeOf.number("longitude", longitude);
Check_default.typeOf.number("latitude", latitude);
height = height ?? 0;
const radiiSquared = !defined_default(ellipsoid) ? _Cartesian3._ellipsoidRadiiSquared : ellipsoid.radiiSquared;
const cosLatitude = Math.cos(latitude);
scratchN.x = cosLatitude * Math.cos(longitude);
scratchN.y = cosLatitude * Math.sin(longitude);
scratchN.z = Math.sin(latitude);
scratchN = _Cartesian3.normalize(scratchN, scratchN);
_Cartesian3.multiplyComponents(radiiSquared, scratchN, scratchK);
const gamma = Math.sqrt(_Cartesian3.dot(scratchN, scratchK));
scratchK = _Cartesian3.divideByScalar(scratchK, gamma, scratchK);
scratchN = _Cartesian3.multiplyByScalar(scratchN, height, scratchN);
if (!defined_default(result)) {
result = new _Cartesian3();
}
return _Cartesian3.add(scratchK, scratchN, result);
}
/**
* Returns an array of Cartesian3 positions given an array of longitude and latitude values given in degrees.
*
* @param {number[]} coordinates A list of longitude and latitude values. Values alternate [longitude, latitude, longitude, latitude...].
* @param {Ellipsoid} [ellipsoid=Ellipsoid.default] The ellipsoid on which the coordinates lie.
* @param {Cartesian3[]} [result] An array of Cartesian3 objects to store the result.
* @returns {Cartesian3[]} The array of positions.
*
* @example
* const positions = Cesium.Cartesian3.fromDegreesArray([-115.0, 37.0, -107.0, 33.0]);
*/
static fromDegreesArray(coordinates, ellipsoid, result) {
Check_default.defined("coordinates", coordinates);
if (coordinates.length < 2 || coordinates.length % 2 !== 0) {
throw new DeveloperError_default(
"the number of coordinates must be a multiple of 2 and at least 2"
);
}
const length = coordinates.length;
if (!defined_default(result)) {
result = new Array(length / 2);
} else {
result.length = length / 2;
}
for (let i = 0; i < length; i += 2) {
const longitude = coordinates[i];
const latitude = coordinates[i + 1];
const index = i / 2;
result[index] = _Cartesian3.fromDegrees(
longitude,
latitude,
0,
ellipsoid,
result[index]
);
}
return result;
}
/**
* Returns an array of Cartesian3 positions given an array of longitude and latitude values given in radians.
*
* @param {number[]} coordinates A list of longitude and latitude values. Values alternate [longitude, latitude, longitude, latitude...].
* @param {Ellipsoid} [ellipsoid=Ellipsoid.default] The ellipsoid on which the coordinates lie.
* @param {Cartesian3[]} [result] An array of Cartesian3 objects to store the result.
* @returns {Cartesian3[]} The array of positions.
*
* @example
* const positions = Cesium.Cartesian3.fromRadiansArray([-2.007, 0.645, -1.867, .575]);
*/
static fromRadiansArray(coordinates, ellipsoid, result) {
Check_default.defined("coordinates", coordinates);
if (coordinates.length < 2 || coordinates.length % 2 !== 0) {
throw new DeveloperError_default(
"the number of coordinates must be a multiple of 2 and at least 2"
);
}
const length = coordinates.length;
if (!defined_default(result)) {
result = new Array(length / 2);
} else {
result.length = length / 2;
}
for (let i = 0; i < length; i += 2) {
const longitude = coordinates[i];
const latitude = coordinates[i + 1];
const index = i / 2;
result[index] = _Cartesian3.fromRadians(
longitude,
latitude,
0,
ellipsoid,
result[index]
);
}
return result;
}
/**
* Returns an array of Cartesian3 positions given an array of longitude, latitude and height values where longitude and latitude are given in degrees.
*
* @param {number[]} coordinates A list of longitude, latitude and height values. Values alternate [longitude, latitude, height, longitude, latitude, height...].
* @param {Ellipsoid} [ellipsoid=Ellipsoid.default] The ellipsoid on which the position lies.
* @param {Cartesian3[]} [result] An array of Cartesian3 objects to store the result.
* @returns {Cartesian3[]} The array of positions.
*
* @example
* const positions = Cesium.Cartesian3.fromDegreesArrayHeights([-115.0, 37.0, 100000.0, -107.0, 33.0, 150000.0]);
*/
static fromDegreesArrayHeights(coordinates, ellipsoid, result) {
Check_default.defined("coordinates", coordinates);
if (coordinates.length < 3 || coordinates.length % 3 !== 0) {
throw new DeveloperError_default(
"the number of coordinates must be a multiple of 3 and at least 3"
);
}
const length = coordinates.length;
if (!defined_default(result)) {
result = new Array(length / 3);
} else {
result.length = length / 3;
}
for (let i = 0; i < length; i += 3) {
const longitude = coordinates[i];
const latitude = coordinates[i + 1];
const height = coordinates[i + 2];
const index = i / 3;
result[index] = _Cartesian3.fromDegrees(
longitude,
latitude,
height,
ellipsoid,
result[index]
);
}
return result;
}
/**
* Returns an array of Cartesian3 positions given an array of longitude, latitude and height values where longitude and latitude are given in radians.
*
* @param {number[]} coordinates A list of longitude, latitude and height values. Values alternate [longitude, latitude, height, longitude, latitude, height...].
* @param {Ellipsoid} [ellipsoid=Ellipsoid.default] The ellipsoid on which the position lies.
* @param {Cartesian3[]} [result] An array of Cartesian3 objects to store the result.
* @returns {Cartesian3[]} The array of positions.
*
* @example
* const positions = Cesium.Cartesian3.fromRadiansArrayHeights([-2.007, 0.645, 100000.0, -1.867, .575, 150000.0]);
*/
static fromRadiansArrayHeights(coordinates, ellipsoid, result) {
Check_default.defined("coordinates", coordinates);
if (coordinates.length < 3 || coordinates.length % 3 !== 0) {
throw new DeveloperError_default(
"the number of coordinates must be a multiple of 3 and at least 3"
);
}
const length = coordinates.length;
if (!defined_default(result)) {
result = new Array(length / 3);
} else {
result.length = length / 3;
}
for (let i = 0; i < length; i += 3) {
const longitude = coordinates[i];
const latitude = coordinates[i + 1];
const height = coordinates[i + 2];
const index = i / 3;
result[index] = _Cartesian3.fromRadians(
longitude,
latitude,
height,
ellipsoid,
result[index]
);
}
return result;
}
/**
* Duplicates this Cartesian3 instance.
*
* @param {Cartesian3} [result] The object onto which to store the result.
* @returns {Cartesian3} The modified result parameter or a new Cartesian3 instance if one was not provided.
*/
clone(result) {
return _Cartesian3.clone(this, result);
}
/**
* Compares this Cartesian against the provided Cartesian componentwise and returns
* true if they are equal, false otherwise.
*
* @param {Cartesian3} [right] The right hand side Cartesian.
* @returns {boolean} true if they are equal, false otherwise.
*/
equals(right) {
return _Cartesian3.equals(this, right);
}
/**
* Compares this Cartesian against the provided Cartesian componentwise and returns
* true if they pass an absolute or relative tolerance test,
* false otherwise.
*
* @param {Cartesian3} [right] The right hand side Cartesian.
* @param {number} [relativeEpsilon=0] The relative epsilon tolerance to use for equality testing.
* @param {number} [absoluteEpsilon=relativeEpsilon] The absolute epsilon tolerance to use for equality testing.
* @returns {boolean} true if they are within the provided epsilon, false otherwise.
*/
equalsEpsilon(right, relativeEpsilon, absoluteEpsilon) {
return _Cartesian3.equalsEpsilon(
this,
right,
relativeEpsilon,
absoluteEpsilon
);
}
/**
* Creates a string representing this Cartesian in the format '(x, y, z)'.
*
* @returns {string} A string representing this Cartesian in the format '(x, y, z)'.
*/
toString() {
return `(${this.x}, ${this.y}, ${this.z})`;
}
};
Cartesian3.fromCartesian4 = Cartesian3.clone;
Cartesian3.packedLength = 3;
Cartesian3.fromArray = Cartesian3.unpack;
var distanceScratch = new Cartesian3();
var lerpScratch = new Cartesian3();
var angleBetweenScratch = new Cartesian3();
var angleBetweenScratch2 = new Cartesian3();
var mostOrthogonalAxisScratch = new Cartesian3();
var scratchN = new Cartesian3();
var scratchK = new Cartesian3();
Cartesian3._ellipsoidRadiiSquared = new Cartesian3(
6378137 * 6378137,
6378137 * 6378137,
6356752314245179e-9 * 6356752314245179e-9
);
Cartesian3.ZERO = Object.freeze(new Cartesian3(0, 0, 0));
Cartesian3.ONE = Object.freeze(new Cartesian3(1, 1, 1));
Cartesian3.UNIT_X = Object.freeze(new Cartesian3(1, 0, 0));
Cartesian3.UNIT_Y = Object.freeze(new Cartesian3(0, 1, 0));
Cartesian3.UNIT_Z = Object.freeze(new Cartesian3(0, 0, 1));
var Cartesian3_default = Cartesian3;
// packages/engine/Source/Core/Matrix3.js
var Matrix3 = class _Matrix3 {
/**
* @param {number} [column0Row0=0.0] The value for column 0, row 0.
* @param {number} [column1Row0=0.0] The value for column 1, row 0.
* @param {number} [column2Row0=0.0] The value for column 2, row 0.
* @param {number} [column0Row1=0.0] The value for column 0, row 1.
* @param {number} [column1Row1=0.0] The value for column 1, row 1.
* @param {number} [column2Row1=0.0] The value for column 2, row 1.
* @param {number} [column0Row2=0.0] The value for column 0, row 2.
* @param {number} [column1Row2=0.0] The value for column 1, row 2.
* @param {number} [column2Row2=0.0] The value for column 2, row 2.
*/
constructor(column0Row0, column1Row0, column2Row0, column0Row1, column1Row1, column2Row1, column0Row2, column1Row2, column2Row2) {
this[0] = column0Row0 ?? 0;
this[1] = column0Row1 ?? 0;
this[2] = column0Row2 ?? 0;
this[3] = column1Row0 ?? 0;
this[4] = column1Row1 ?? 0;
this[5] = column1Row2 ?? 0;
this[6] = column2Row0 ?? 0;
this[7] = column2Row1 ?? 0;
this[8] = column2Row2 ?? 0;
}
/**
* Stores the provided instance into the provided array.
*
* @param {Matrix3} value The value to pack.
* @param {number[]} array The array to pack into.
* @param {number} [startingIndex=0] The index into the array at which to start packing the elements.
*
* @returns {number[]} The array that was packed into
*/
static pack(value, array, startingIndex) {
Check_default.typeOf.object("value", value);
Check_default.defined("array", array);
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];
return array;
}
/**
* Retrieves an instance from a packed array.
*
* @param {number[]} array The packed array.
* @param {number} [startingIndex=0] The starting index of the element to be unpacked.
* @param {Matrix3} [result] The object into which to store the result.
* @returns {Matrix3} The modified result parameter or a new Matrix3 instance if one was not provided.
*/
static unpack(array, startingIndex, result) {
Check_default.defined("array", array);
startingIndex = startingIndex ?? 0;
if (!defined_default(result)) {
result = new _Matrix3();
}
result[0] = array[startingIndex++];
result[1] = array[startingIndex++];
result[2] = array[startingIndex++];
result[3] = array[startingIndex++];
result[4] = array[startingIndex++];
result[5] = array[startingIndex++];
result[6] = array[startingIndex++];
result[7] = array[startingIndex++];
result[8] = array[startingIndex++];
return result;
}
/**
* Flattens an array of Matrix3s into an array of components. The components
* are stored in column-major order.
*
* @param {Matrix3[]} 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 * 9 components, else a {@link DeveloperError} will be thrown. If it is a regular array, it will be resized to have (array.length * 9) elements.
* @returns {number[]} The packed array.
*/
static packArray(array, result) {
Check_default.defined("array", array);
const length = array.length;
const resultLength = length * 9;
if (!defined_default(result)) {
result = new Array(resultLength);
} else if (!Array.isArray(result) && result.length !== resultLength) {
throw new DeveloperError_default(
"If result is a typed array, it must have exactly array.length * 9 elements"
);
} else if (result.length !== resultLength) {
result.length = resultLength;
}
for (let i = 0; i < length; ++i) {
_Matrix3.pack(array[i], result, i * 9);
}
return result;
}
/**
* Unpacks an array of column-major matrix components into an array of Matrix3s.
*
* @param {number[]} array The array of components to unpack.
* @param {Matrix3[]} [result] The array onto which to store the result.
* @returns {Matrix3[]} The unpacked array.
*/
static unpackArray(array, result) {
Check_default.defined("array", array);
Check_default.typeOf.number.greaterThanOrEquals("array.length", array.length, 9);
if (array.length % 9 !== 0) {
throw new DeveloperError_default("array length must be a multiple of 9.");
}
const length = array.length;
if (!defined_default(result)) {
result = new Array(length / 9);
} else {
result.length = length / 9;
}
for (let i = 0; i < length; i += 9) {
const index = i / 9;
result[index] = _Matrix3.unpack(array, i, result[index]);
}
return result;
}
/**
* Duplicates a Matrix3 instance.
*
* @param {Matrix3} matrix The matrix to duplicate.
* @param {Matrix3} [result] The object onto which to store the result.
* @returns {Matrix3} The modified result parameter or a new Matrix3 instance if one was not provided. (Returns undefined if matrix is undefined)
*/
static clone(matrix, result) {
if (!defined_default(matrix)) {
return void 0;
}
if (!defined_default(result)) {
return new _Matrix3(
matrix[0],
matrix[3],
matrix[6],
matrix[1],
matrix[4],
matrix[7],
matrix[2],
matrix[5],
matrix[8]
);
}
result[0] = matrix[0];
result[1] = matrix[1];
result[2] = matrix[2];
result[3] = matrix[3];
result[4] = matrix[4];
result[5] = matrix[5];
result[6] = matrix[6];
result[7] = matrix[7];
result[8] = matrix[8];
return result;
}
/**
* Creates a Matrix3 instance from a column-major order array.
*
* @param {number[]} values The column-major order array.
* @param {Matrix3} [result] The object in which the result will be stored, if undefined a new instance will be created.
* @returns {Matrix3} The modified result parameter, or a new Matrix3 instance if one was not provided.
*/
static fromColumnMajorArray(values, result) {
Check_default.defined("values", values);
return _Matrix3.clone(values, result);
}
/**
* Creates a Matrix3 instance from a row-major order array.
* The resulting matrix will be in column-major order.
*
* @param {number[]} values The row-major order array.
* @param {Matrix3} [result] The object in which the result will be stored, if undefined a new instance will be created.
* @returns {Matrix3} The modified result parameter, or a new Matrix3 instance if one was not provided.
*/
static fromRowMajorArray(values, result) {
Check_default.defined("values", values);
if (!defined_default(result)) {
return new _Matrix3(
values[0],
values[1],
values[2],
values[3],
values[4],
values[5],
values[6],
values[7],
values[8]
);
}
result[0] = values[0];
result[1] = values[3];
result[2] = values[6];
result[3] = values[1];
result[4] = values[4];
result[5] = values[7];
result[6] = values[2];
result[7] = values[5];
result[8] = values[8];
return result;
}
/**
* Computes a 3x3 rotation matrix from the provided quaternion.
*
* @param {Quaternion} quaternion the quaternion to use.
* @param {Matrix3} [result] The object in which the result will be stored, if undefined a new instance will be created.
* @returns {Matrix3} The 3x3 rotation matrix from this quaternion.
*/
static fromQuaternion(quaternion, result) {
Check_default.typeOf.object("quaternion", quaternion);
const x2 = quaternion.x * quaternion.x;
const xy = quaternion.x * quaternion.y;
const xz = quaternion.x * quaternion.z;
const xw = quaternion.x * quaternion.w;
const y2 = quaternion.y * quaternion.y;
const yz = quaternion.y * quaternion.z;
const yw = quaternion.y * quaternion.w;
const z2 = quaternion.z * quaternion.z;
const zw = quaternion.z * quaternion.w;
const w2 = quaternion.w * quaternion.w;
const m00 = x2 - y2 - z2 + w2;
const m01 = 2 * (xy - zw);
const m02 = 2 * (xz + yw);
const m10 = 2 * (xy + zw);
const m11 = -x2 + y2 - z2 + w2;
const m12 = 2 * (yz - xw);
const m20 = 2 * (xz - yw);
const m21 = 2 * (yz + xw);
const m22 = -x2 - y2 + z2 + w2;
if (!defined_default(result)) {
return new _Matrix3(m00, m01, m02, m10, m11, m12, m20, m21, m22);
}
result[0] = m00;
result[1] = m10;
result[2] = m20;
result[3] = m01;
result[4] = m11;
result[5] = m21;
result[6] = m02;
result[7] = m12;
result[8] = m22;
return result;
}
/**
* Computes a 3x3 rotation matrix from the provided headingPitchRoll. (see http://en.wikipedia.org/wiki/Conversion_between_quaternions_and_Euler_angles )
*
* @param {HeadingPitchRoll} headingPitchRoll the headingPitchRoll to use.
* @param {Matrix3} [result] The object in which the result will be stored, if undefined a new instance will be created.
* @returns {Matrix3} The 3x3 rotation matrix from this headingPitchRoll.
*/
static fromHeadingPitchRoll(headingPitchRoll, result) {
Check_default.typeOf.object("headingPitchRoll", headingPitchRoll);
const cosTheta = Math.cos(-headingPitchRoll.pitch);
const cosPsi = Math.cos(-headingPitchRoll.heading);
const cosPhi = Math.cos(headingPitchRoll.roll);
const sinTheta = Math.sin(-headingPitchRoll.pitch);
const sinPsi = Math.sin(-headingPitchRoll.heading);
const sinPhi = Math.sin(headingPitchRoll.roll);
const m00 = cosTheta * cosPsi;
const m01 = -cosPhi * sinPsi + sinPhi * sinTheta * cosPsi;
const m02 = sinPhi * sinPsi + cosPhi * sinTheta * cosPsi;
const m10 = cosTheta * sinPsi;
const m11 = cosPhi * cosPsi + sinPhi * sinTheta * sinPsi;
const m12 = -sinPhi * cosPsi + cosPhi * sinTheta * sinPsi;
const m20 = -sinTheta;
const m21 = sinPhi * cosTheta;
const m22 = cosPhi * cosTheta;
if (!defined_default(result)) {
return new _Matrix3(m00, m01, m02, m10, m11, m12, m20, m21, m22);
}
result[0] = m00;
result[1] = m10;
result[2] = m20;
result[3] = m01;
result[4] = m11;
result[5] = m21;
result[6] = m02;
result[7] = m12;
result[8] = m22;
return result;
}
/**
* Computes a Matrix3 instance representing a non-uniform scale.
*
* @param {Cartesian3} scale The x, y, and z scale factors.
* @param {Matrix3} [result] The object in which the result will be stored, if undefined a new instance will be created.
* @returns {Matrix3} The modified result parameter, or a new Matrix3 instance if one was not provided.
*
* @example
* // Creates
* // [7.0, 0.0, 0.0]
* // [0.0, 8.0, 0.0]
* // [0.0, 0.0, 9.0]
* const m = Cesium.Matrix3.fromScale(new Cesium.Cartesian3(7.0, 8.0, 9.0));
*/
static fromScale(scale, result) {
Check_default.typeOf.object("scale", scale);
if (!defined_default(result)) {
return new _Matrix3(
scale.x,
0,
0,
0,
scale.y,
0,
0,
0,
scale.z
);
}
result[0] = scale.x;
result[1] = 0;
result[2] = 0;
result[3] = 0;
result[4] = scale.y;
result[5] = 0;
result[6] = 0;
result[7] = 0;
result[8] = scale.z;
return result;
}
/**
* Computes a Matrix3 instance representing a uniform scale.
*
* @param {number} scale The uniform scale factor.
* @param {Matrix3} [result] The object in which the result will be stored, if undefined a new instance will be created.
* @returns {Matrix3} The modified result parameter, or a new Matrix3 instance if one was not provided.
*
* @example
* // Creates
* // [2.0, 0.0, 0.0]
* // [0.0, 2.0, 0.0]
* // [0.0, 0.0, 2.0]
* const m = Cesium.Matrix3.fromUniformScale(2.0);
*/
static fromUniformScale(scale, result) {
Check_default.typeOf.number("scale", scale);
if (!defined_default(result)) {
return new _Matrix3(scale, 0, 0, 0, scale, 0, 0, 0, scale);
}
result[0] = scale;
result[1] = 0;
result[2] = 0;
result[3] = 0;
result[4] = scale;
result[5] = 0;
result[6] = 0;
result[7] = 0;
result[8] = scale;
return result;
}
/**
* Computes a Matrix3 instance representing the cross product equivalent matrix of a Cartesian3 vector.
*
* @param {Cartesian3} vector the vector on the left hand side of the cross product operation.
* @param {Matrix3} [result] The object in which the result will be stored, if undefined a new instance will be created.
* @returns {Matrix3} The modified result parameter, or a new Matrix3 instance if one was not provided.
*
* @example
* // Creates
* // [0.0, -9.0, 8.0]
* // [9.0, 0.0, -7.0]
* // [-8.0, 7.0, 0.0]
* const m = Cesium.Matrix3.fromCrossProduct(new Cesium.Cartesian3(7.0, 8.0, 9.0));
*/
static fromCrossProduct(vector, result) {
Check_default.typeOf.object("vector", vector);
if (!defined_default(result)) {
return new _Matrix3(
0,
-vector.z,
vector.y,
vector.z,
0,
-vector.x,
-vector.y,
vector.x,
0
);
}
result[0] = 0;
result[1] = vector.z;
result[2] = -vector.y;
result[3] = -vector.z;
result[4] = 0;
result[5] = vector.x;
result[6] = vector.y;
result[7] = -vector.x;
result[8] = 0;
return result;
}
/**
* Creates a rotation matrix around the x-axis.
*
* @param {number} angle The angle, in radians, of the rotation. Positive angles are counterclockwise.
* @param {Matrix3} [result] The object in which the result will be stored, if undefined a new instance will be created.
* @returns {Matrix3} The modified result parameter, or a new Matrix3 instance if one was not provided.
*
* @example
* // Rotate a point 45 degrees counterclockwise around the x-axis.
* const p = new Cesium.Cartesian3(5, 6, 7);
* const m = Cesium.Matrix3.fromRotationX(Cesium.Math.toRadians(45.0));
* const rotated = Cesium.Matrix3.multiplyByVector(m, p, new Cesium.Cartesian3());
*/
static fromRotationX(angle, result) {
Check_default.typeOf.number("angle", angle);
const cosAngle = Math.cos(angle);
const sinAngle = Math.sin(angle);
if (!defined_default(result)) {
return new _Matrix3(
1,
0,
0,
0,
cosAngle,
-sinAngle,
0,
sinAngle,
cosAngle
);
}
result[0] = 1;
result[1] = 0;
result[2] = 0;
result[3] = 0;
result[4] = cosAngle;
result[5] = sinAngle;
result[6] = 0;
result[7] = -sinAngle;
result[8] = cosAngle;
return result;
}
/**
* Creates a rotation matrix around the y-axis.
*
* @param {number} angle The angle, in radians, of the rotation. Positive angles are counterclockwise.
* @param {Matrix3} [result] The object in which the result will be stored, if undefined a new instance will be created.
* @returns {Matrix3} The modified result parameter, or a new Matrix3 instance if one was not provided.
*
* @example
* // Rotate a point 45 degrees counterclockwise around the y-axis.
* const p = new Cesium.Cartesian3(5, 6, 7);
* const m = Cesium.Matrix3.fromRotationY(Cesium.Math.toRadians(45.0));
* const rotated = Cesium.Matrix3.multiplyByVector(m, p, new Cesium.Cartesian3());
*/
static fromRotationY(angle, result) {
Check_default.typeOf.number("angle", angle);
const cosAngle = Math.cos(angle);
const sinAngle = Math.sin(angle);
if (!defined_default(result)) {
return new _Matrix3(
cosAngle,
0,
sinAngle,
0,
1,
0,
-sinAngle,
0,
cosAngle
);
}
result[0] = cosAngle;
result[1] = 0;
result[2] = -sinAngle;
result[3] = 0;
result[4] = 1;
result[5] = 0;
result[6] = sinAngle;
result[7] = 0;
result[8] = cosAngle;
return result;
}
/**
* Creates a rotation matrix around the z-axis.
*
* @param {number} angle The angle, in radians, of the rotation. Positive angles are counterclockwise.
* @param {Matrix3} [result] The object in which the result will be stored, if undefined a new instance will be created.
* @returns {Matrix3} The modified result parameter, or a new Matrix3 instance if one was not provided.
*
* @example
* // Rotate a point 45 degrees counterclockwise around the z-axis.
* const p = new Cesium.Cartesian3(5, 6, 7);
* const m = Cesium.Matrix3.fromRotationZ(Cesium.Math.toRadians(45.0));
* const rotated = Cesium.Matrix3.multiplyByVector(m, p, new Cesium.Cartesian3());
*/
static fromRotationZ(angle, result) {
Check_default.typeOf.number("angle", angle);
const cosAngle = Math.cos(angle);
const sinAngle = Math.sin(angle);
if (!defined_default(result)) {
return new _Matrix3(
cosAngle,
-sinAngle,
0,
sinAngle,
cosAngle,
0,
0,
0,
1
);
}
result[0] = cosAngle;
result[1] = sinAngle;
result[2] = 0;
result[3] = -sinAngle;
result[4] = cosAngle;
result[5] = 0;
result[6] = 0;
result[7] = 0;
result[8] = 1;
return result;
}
/**
* Creates an Array from the provided Matrix3 instance.
* The array will be in column-major order.
*
* @param {Matrix3} matrix The matrix to use..
* @param {number[]} [result] The Array onto which to store the result.
* @returns {number[]} The modified Array parameter or a new Array instance if one was not provided.
*/
static toArray(matrix, result) {
Check_default.typeOf.object("matrix", matrix);
if (!defined_default(result)) {
return [
matrix[0],
matrix[1],
matrix[2],
matrix[3],
matrix[4],
matrix[5],
matrix[6],
matrix[7],
matrix[8]
];
}
result[0] = matrix[0];
result[1] = matrix[1];
result[2] = matrix[2];
result[3] = matrix[3];
result[4] = matrix[4];
result[5] = matrix[5];
result[6] = matrix[6];
result[7] = matrix[7];
result[8] = matrix[8];
return result;
}
/**
* Computes the array index of the element at the provided row and column.
*
* @param {number} column The zero-based index of the column.
* @param {number} row The zero-based index of the row.
* @returns {number} The index of the element at the provided row and column.
*
* @exception {DeveloperError} row must be 0, 1, or 2.
* @exception {DeveloperError} column must be 0, 1, or 2.
*
* @example
* const myMatrix = new Cesium.Matrix3();
* const column1Row0Index = Cesium.Matrix3.getElementIndex(1, 0);
* const column1Row0 = myMatrix[column1Row0Index]
* myMatrix[column1Row0Index] = 10.0;
*/
static getElementIndex(column, row) {
Check_default.typeOf.number.greaterThanOrEquals("row", row, 0);
Check_default.typeOf.number.lessThanOrEquals("row", row, 2);
Check_default.typeOf.number.greaterThanOrEquals("column", column, 0);
Check_default.typeOf.number.lessThanOrEquals("column", column, 2);
return column * 3 + row;
}
/**
* Retrieves a copy of the matrix column at the provided index as a Cartesian3 instance.
*
* @param {Matrix3} matrix The matrix to use.
* @param {number} index The zero-based index of the column to retrieve.
* @param {Cartesian3} result The object onto which to store the result.
* @returns {Cartesian3} The modified result parameter.
*
* @exception {DeveloperError} index must be 0, 1, or 2.
*/
static getColumn(matrix, index, result) {
Check_default.typeOf.object("matrix", matrix);
Check_default.typeOf.number.greaterThanOrEquals("index", index, 0);
Check_default.typeOf.number.lessThanOrEquals("index", index, 2);
Check_default.typeOf.object("result", result);
const startIndex = index * 3;
const x = matrix[startIndex];
const y = matrix[startIndex + 1];
const z = matrix[startIndex + 2];
result.x = x;
result.y = y;
result.z = z;
return result;
}
/**
* Computes a new matrix that replaces the specified column in the provided matrix with the provided Cartesian3 instance.
*
* @param {Matrix3} matrix The matrix to use.
* @param {number} index The zero-based index of the column to set.
* @param {Cartesian3} cartesian The Cartesian whose values will be assigned to the specified column.
* @param {Matrix3} result The object onto which to store the result.
* @returns {Matrix3} The modified result parameter.
*
* @exception {DeveloperError} index must be 0, 1, or 2.
*/
static setColumn(matrix, index, cartesian, result) {
Check_default.typeOf.object("matrix", matrix);
Check_default.typeOf.number.greaterThanOrEquals("index", index, 0);
Check_default.typeOf.number.lessThanOrEquals("index", index, 2);
Check_default.typeOf.object("cartesian", cartesian);
Check_default.typeOf.object("result", result);
result = _Matrix3.clone(matrix, result);
const startIndex = index * 3;
result[startIndex] = cartesian.x;
result[startIndex + 1] = cartesian.y;
result[startIndex + 2] = cartesian.z;
return result;
}
/**
* Retrieves a copy of the matrix row at the provided index as a Cartesian3 instance.
*
* @param {Matrix3} matrix The matrix to use.
* @param {number} index The zero-based index of the row to retrieve.
* @param {Cartesian3} result The object onto which to store the result.
* @returns {Cartesian3} The modified result parameter.
*
* @exception {DeveloperError} index must be 0, 1, or 2.
*/
static getRow(matrix, index, result) {
Check_default.typeOf.object("matrix", matrix);
Check_default.typeOf.number.greaterThanOrEquals("index", index, 0);
Check_default.typeOf.number.lessThanOrEquals("index", index, 2);
Check_default.typeOf.object("result", result);
const x = matrix[index];
const y = matrix[index + 3];
const z = matrix[index + 6];
result.x = x;
result.y = y;
result.z = z;
return result;
}
/**
* Computes a new matrix that replaces the specified row in the provided matrix with the provided Cartesian3 instance.
*
* @param {Matrix3} matrix The matrix to use.
* @param {number} index The zero-based index of the row to set.
* @param {Cartesian3} cartesian The Cartesian whose values will be assigned to the specified row.
* @param {Matrix3} result The object onto which to store the result.
* @returns {Matrix3} The modified result parameter.
*
* @exception {DeveloperError} index must be 0, 1, or 2.
*/
static setRow(matrix, index, cartesian, result) {
Check_default.typeOf.object("matrix", matrix);
Check_default.typeOf.number.greaterThanOrEquals("index", index, 0);
Check_default.typeOf.number.lessThanOrEquals("index", index, 2);
Check_default.typeOf.object("cartesian", cartesian);
Check_default.typeOf.object("result", result);
result = _Matrix3.clone(matrix, result);
result[index] = cartesian.x;
result[index + 3] = cartesian.y;
result[index + 6] = cartesian.z;
return result;
}
/**
* Computes a new matrix that replaces the scale with the provided scale.
* This assumes the matrix is an affine transformation.
*
* @param {Matrix3} matrix The matrix to use.
* @param {Cartesian3} scale The scale that replaces the scale of the provided matrix.
* @param {Matrix3} result The object onto which to store the result.
* @returns {Matrix3} The modified result parameter.
*
* @see Matrix3.setUniformScale
* @see Matrix3.fromScale
* @see Matrix3.fromUniformScale
* @see Matrix3.multiplyByScale
* @see Matrix3.multiplyByUniformScale
* @see Matrix3.getScale
*/
static setScale(matrix, scale, result) {
Check_default.typeOf.object("matrix", matrix);
Check_default.typeOf.object("scale", scale);
Check_default.typeOf.object("result", result);
const existingScale = _Matrix3.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] * scaleRatioY;
result[4] = matrix[4] * scaleRatioY;
result[5] = matrix[5] * scaleRatioY;
result[6] = matrix[6] * scaleRatioZ;
result[7] = matrix[7] * scaleRatioZ;
result[8] = matrix[8] * scaleRatioZ;
return result;
}
/**
* Computes a new matrix that replaces the scale with the provided uniform scale.
* This assumes the matrix is an affine transformation.
*
* @param {Matrix3} matrix The matrix to use.
* @param {number} scale The uniform scale that replaces the scale of the provided matrix.
* @param {Matrix3} result The object onto which to store the result.
* @returns {Matrix3} The modified result parameter.
*
* @see Matrix3.setScale
* @see Matrix3.fromScale
* @see Matrix3.fromUniformScale
* @see Matrix3.multiplyByScale
* @see Matrix3.multiplyByUniformScale
* @see Matrix3.getScale
*/
static setUniformScale(matrix, scale, result) {
Check_default.typeOf.object("matrix", matrix);
Check_default.typeOf.number("scale", scale);
Check_default.typeOf.object("result", result);
const existingScale = _Matrix3.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] * scaleRatioY;
result[4] = matrix[4] * scaleRatioY;
result[5] = matrix[5] * scaleRatioY;
result[6] = matrix[6] * scaleRatioZ;
result[7] = matrix[7] * scaleRatioZ;
result[8] = matrix[8] * scaleRatioZ;
return result;
}
/**
* Extracts the non-uniform scale assuming the matrix is an affine transformation.
*
* @param {Matrix3} matrix The matrix.
* @param {Cartesian3} result The object onto which to store the result.
* @returns {Cartesian3} The modified result parameter.
*
* @see Matrix3.multiplyByScale
* @see Matrix3.multiplyByUniformScale
* @see Matrix3.fromScale
* @see Matrix3.fromUniformScale
* @see Matrix3.setScale
* @see Matrix3.setUniformScale
*/
static getScale(matrix, result) {
Check_default.typeOf.object("matrix", matrix);
Check_default.typeOf.object("result", result);
result.x = Cartesian3_default.magnitude(
Cartesian3_default.fromElements(matrix[0], matrix[1], matrix[2], scratchColumn)
);
result.y = Cartesian3_default.magnitude(
Cartesian3_default.fromElements(matrix[3], matrix[4], matrix[5], scratchColumn)
);
result.z = Cartesian3_default.magnitude(
Cartesian3_default.fromElements(matrix[6], matrix[7], matrix[8], scratchColumn)
);
return result;
}
/**
* Computes the maximum scale assuming the matrix is an affine transformation.
* The maximum scale is the maximum length of the column vectors.
*
* @param {Matrix3} matrix The matrix.
* @returns {number} The maximum scale.
*/
static getMaximumScale(matrix) {
_Matrix3.getScale(matrix, scaleScratch3);
return Cartesian3_default.maximumComponent(scaleScratch3);
}
/**
* Sets the rotation assuming the matrix is an affine transformation.
*
* @param {Matrix3} matrix The matrix.
* @param {Matrix3} rotation The rotation matrix.
* @param {Matrix3} result The object onto which to store the result.
* @returns {Matrix3} The modified result parameter.
*
* @see Matrix3.getRotation
*/
static setRotation(matrix, rotation, result) {
Check_default.typeOf.object("matrix", matrix);
Check_default.typeOf.object("result", result);
const scale = _Matrix3.getScale(matrix, scaleScratch4);
result[0] = rotation[0] * scale.x;
result[1] = rotation[1] * scale.x;
result[2] = rotation[2] * scale.x;
result[3] = rotation[3] * scale.y;
result[4] = rotation[4] * scale.y;
result[5] = rotation[5] * scale.y;
result[6] = rotation[6] * scale.z;
result[7] = rotation[7] * scale.z;
result[8] = rotation[8] * scale.z;
return result;
}
/**
* Extracts the rotation matrix assuming the matrix is an affine transformation.
*
* @param {Matrix3} matrix The matrix.
* @param {Matrix3} result The object onto which to store the result.
* @returns {Matrix3} The modified result parameter.
*
* @see Matrix3.setRotation
*/
static getRotation(matrix, result) {
Check_default.typeOf.object("matrix", matrix);
Check_default.typeOf.object("result", result);
const scale = _Matrix3.getScale(matrix, scaleScratch5);
result[0] = matrix[0] / scale.x;
result[1] = matrix[1] / scale.x;
result[2] = matrix[2] / scale.x;
result[3] = matrix[3] / scale.y;
result[4] = matrix[4] / scale.y;
result[5] = matrix[5] / scale.y;
result[6] = matrix[6] / scale.z;
result[7] = matrix[7] / scale.z;
result[8] = matrix[8] / scale.z;
return result;
}
/**
* Computes the product of two matrices.
*
* @param {Matrix3} left The first matrix.
* @param {Matrix3} right The second matrix.
* @param {Matrix3} result The object onto which to store the result.
* @returns {Matrix3} The modified result parameter.
*/
static multiply(left, right, result) {
Check_default.typeOf.object("left", left);
Check_default.typeOf.object("right", right);
Check_default.typeOf.object("result", result);
const column0Row0 = left[0] * right[0] + left[3] * right[1] + left[6] * right[2];
const column0Row1 = left[1] * right[0] + left[4] * right[1] + left[7] * right[2];
const column0Row2 = left[2] * right[0] + left[5] * right[1] + left[8] * right[2];
const column1Row0 = left[0] * right[3] + left[3] * right[4] + left[6] * right[5];
const column1Row1 = left[1] * right[3] + left[4] * right[4] + left[7] * right[5];
const column1Row2 = left[2] * right[3] + left[5] * right[4] + left[8] * right[5];
const column2Row0 = left[0] * right[6] + left[3] * right[7] + left[6] * right[8];
const column2Row1 = left[1] * right[6] + left[4] * right[7] + left[7] * right[8];
const column2Row2 = left[2] * right[6] + left[5] * right[7] + left[8] * right[8];
result[0] = column0Row0;
result[1] = column0Row1;
result[2] = column0Row2;
result[3] = column1Row0;
result[4] = column1Row1;
result[5] = column1Row2;
result[6] = column2Row0;
result[7] = column2Row1;
result[8] = column2Row2;
return result;
}
/**
* Computes the sum of two matrices.
*
* @param {Matrix3} left The first matrix.
* @param {Matrix3} right The second matrix.
* @param {Matrix3} result The object onto which to store the result.
* @returns {Matrix3} The modified result parameter.
*/
static add(left, right, result) {
Check_default.typeOf.object("left", left);
Check_default.typeOf.object("right", right);
Check_default.typeOf.object("result", result);
result[0] = left[0] + right[0];
result[1] = left[1] + right[1];
result[2] = left[2] + right[2];
result[3] = left[3] + right[3];
result[4] = left[4] + right[4];
result[5] = left[5] + right[5];
result[6] = left[6] + right[6];
result[7] = left[7] + right[7];
result[8] = left[8] + right[8];
return result;
}
/**
* Computes the difference of two matrices.
*
* @param {Matrix3} left The first matrix.
* @param {Matrix3} right The second matrix.
* @param {Matrix3} result The object onto which to store the result.
* @returns {Matrix3} The modified result parameter.
*/
static subtract(left, right, result) {
Check_default.typeOf.object("left", left);
Check_default.typeOf.object("right", right);
Check_default.typeOf.object("result", result);
result[0] = left[0] - right[0];
result[1] = left[1] - right[1];
result[2] = left[2] - right[2];
result[3] = left[3] - right[3];
result[4] = left[4] - right[4];
result[5] = left[5] - right[5];
result[6] = left[6] - right[6];
result[7] = left[7] - right[7];
result[8] = left[8] - right[8];
return result;
}
/**
* Computes the product of a matrix and a column vector.
*
* @param {Matrix3} matrix The matrix.
* @param {Cartesian3} cartesian The column.
* @param {Cartesian3} result The object onto which to store the result.
* @returns {Cartesian3} The modified result parameter.
*/
static multiplyByVector(matrix, cartesian, result) {
Check_default.typeOf.object("matrix", matrix);
Check_default.typeOf.object("cartesian", cartesian);
Check_default.typeOf.object("result", result);
const vX = cartesian.x;
const vY = cartesian.y;
const vZ = cartesian.z;
const x = matrix[0] * vX + matrix[3] * vY + matrix[6] * vZ;
const y = matrix[1] * vX + matrix[4] * vY + matrix[7] * vZ;
const z = matrix[2] * vX + matrix[5] * vY + matrix[8] * vZ;
result.x = x;
result.y = y;
result.z = z;
return result;
}
/**
* Computes the product of a matrix and a scalar.
*
* @param {Matrix3} matrix The matrix.
* @param {number} scalar The number to multiply by.
* @param {Matrix3} result The object onto which to store the result.
* @returns {Matrix3} The modified result parameter.
*/
static multiplyByScalar(matrix, scalar, result) {
Check_default.typeOf.object("matrix", matrix);
Check_default.typeOf.number("scalar", scalar);
Check_default.typeOf.object("result", result);
result[0] = matrix[0] * scalar;
result[1] = matrix[1] * scalar;
result[2] = matrix[2] * scalar;
result[3] = matrix[3] * scalar;
result[4] = matrix[4] * scalar;
result[5] = matrix[5] * scalar;
result[6] = matrix[6] * scalar;
result[7] = matrix[7] * scalar;
result[8] = matrix[8] * scalar;
return result;
}
/**
* Computes the product of a matrix times a (non-uniform) scale, as if the scale were a scale matrix.
*
* @param {Matrix3} matrix The matrix on the left-hand side.
* @param {Cartesian3} scale The non-uniform scale on the right-hand side.
* @param {Matrix3} result The object onto which to store the result.
* @returns {Matrix3} The modified result parameter.
*
*
* @example
* // Instead of Cesium.Matrix3.multiply(m, Cesium.Matrix3.fromScale(scale), m);
* Cesium.Matrix3.multiplyByScale(m, scale, m);
*
* @see Matrix3.multiplyByUniformScale
* @see Matrix3.fromScale
* @see Matrix3.fromUniformScale
* @see Matrix3.setScale
* @see Matrix3.setUniformScale
* @see Matrix3.getScale
*/
static multiplyByScale(matrix, scale, result) {
Check_default.typeOf.object("matrix", matrix);
Check_default.typeOf.object("scale", scale);
Check_default.typeOf.object("result", result);
result[0] = matrix[0] * scale.x;
result[1] = matrix[1] * scale.x;
result[2] = matrix[2] * scale.x;
result[3] = matrix[3] * scale.y;
result[4] = matrix[4] * scale.y;
result[5] = matrix[5] * scale.y;
result[6] = matrix[6] * scale.z;
result[7] = matrix[7] * scale.z;
result[8] = matrix[8] * scale.z;
return result;
}
/**
* Computes the product of a matrix times a uniform scale, as if the scale were a scale matrix.
*
* @param {Matrix3} matrix The matrix on the left-hand side.
* @param {number} scale The uniform scale on the right-hand side.
* @param {Matrix3} result The object onto which to store the result.
* @returns {Matrix3} The modified result parameter.
*
* @example
* // Instead of Cesium.Matrix3.multiply(m, Cesium.Matrix3.fromUniformScale(scale), m);
* Cesium.Matrix3.multiplyByUniformScale(m, scale, m);
*
* @see Matrix3.multiplyByScale
* @see Matrix3.fromScale
* @see Matrix3.fromUniformScale
* @see Matrix3.setScale
* @see Matrix3.setUniformScale
* @see Matrix3.getScale
*/
static multiplyByUniformScale(matrix, scale, result) {
Check_default.typeOf.object("matrix", matrix);
Check_default.typeOf.number("scale", scale);
Check_default.typeOf.object("result", result);
result[0] = matrix[0] * scale;
result[1] = matrix[1] * scale;
result[2] = matrix[2] * scale;
result[3] = matrix[3] * scale;
result[4] = matrix[4] * scale;
result[5] = matrix[5] * scale;
result[6] = matrix[6] * scale;
result[7] = matrix[7] * scale;
result[8] = matrix[8] * scale;
return result;
}
/**
* Creates a negated copy of the provided matrix.
*
* @param {Matrix3} matrix The matrix to negate.
* @param {Matrix3} result The object onto which to store the result.
* @returns {Matrix3} The modified result parameter.
*/
static negate(matrix, result) {
Check_default.typeOf.object("matrix", matrix);
Check_default.typeOf.object("result", result);
result[0] = -matrix[0];
result[1] = -matrix[1];
result[2] = -matrix[2];
result[3] = -matrix[3];
result[4] = -matrix[4];
result[5] = -matrix[5];
result[6] = -matrix[6];
result[7] = -matrix[7];
result[8] = -matrix[8];
return result;
}
/**
* Computes the transpose of the provided matrix.
*
* @param {Matrix3} matrix The matrix to transpose.
* @param {Matrix3} result The object onto which to store the result.
* @returns {Matrix3} The modified result parameter.
*/
static transpose(matrix, result) {
Check_default.typeOf.object("matrix", matrix);
Check_default.typeOf.object("result", result);
const column0Row0 = matrix[0];
const column0Row1 = matrix[3];
const column0Row2 = matrix[6];
const column1Row0 = matrix[1];
const column1Row1 = matrix[4];
const column1Row2 = matrix[7];
const column2Row0 = matrix[2];
const column2Row1 = matrix[5];
const column2Row2 = matrix[8];
result[0] = column0Row0;
result[1] = column0Row1;
result[2] = column0Row2;
result[3] = column1Row0;
result[4] = column1Row1;
result[5] = column1Row2;
result[6] = column2Row0;
result[7] = column2Row1;
result[8] = column2Row2;
return result;
}
/**
* Computes the eigenvectors and eigenvalues of a symmetric matrix.
*
* Returns a diagonal matrix and unitary matrix such that:
* matrix = unitary matrix * diagonal matrix * transpose(unitary matrix)
*
* The values along the diagonal of the diagonal matrix are the eigenvalues. The columns * of the unitary matrix are the corresponding eigenvectors. *
* * @param {Matrix3} matrix The matrix to decompose into diagonal and unitary matrix. Expected to be symmetric. * @param {EigenDecompositionResult} [result] An object with unitary and diagonal properties which are matrices onto which to store the result. * @returns {EigenDecompositionResult} An object with unitary and diagonal properties which are the unitary and diagonal matrices, respectively. * * @example * const a = //... symetric matrix * const result = { * unitary : new Cesium.Matrix3(), * diagonal : new Cesium.Matrix3() * }; * Cesium.Matrix3.computeEigenDecomposition(a, result); * * const unitaryTranspose = Cesium.Matrix3.transpose(result.unitary, new Cesium.Matrix3()); * const b = Cesium.Matrix3.multiply(result.unitary, result.diagonal, new Cesium.Matrix3()); * Cesium.Matrix3.multiply(b, unitaryTranspose, b); // b is now equal to a * * const lambda = Cesium.Matrix3.getColumn(result.diagonal, 0, new Cesium.Cartesian3()).x; // first eigenvalue * const v = Cesium.Matrix3.getColumn(result.unitary, 0, new Cesium.Cartesian3()); // first eigenvector * const c = Cesium.Cartesian3.multiplyByScalar(v, lambda, new Cesium.Cartesian3()); // equal to Cesium.Matrix3.multiplyByVector(a, v) */ static computeEigenDecomposition(matrix, result) { Check_default.typeOf.object("matrix", matrix); const tolerance = Math_default.EPSILON20; const maxSweeps = 10; let count = 0; let sweep = 0; if (!defined_default(result)) { result = {}; } const unitaryMatrix = result.unitary = _Matrix3.clone( _Matrix3.IDENTITY, result.unitary ); const diagMatrix = result.diagonal = _Matrix3.clone( matrix, result.diagonal ); const epsilon = tolerance * computeFrobeniusNorm(diagMatrix); while (sweep < maxSweeps && offDiagonalFrobeniusNorm(diagMatrix) > epsilon) { shurDecomposition(diagMatrix, jMatrix); _Matrix3.transpose(jMatrix, jMatrixTranspose); _Matrix3.multiply(diagMatrix, jMatrix, diagMatrix); _Matrix3.multiply(jMatrixTranspose, diagMatrix, diagMatrix); _Matrix3.multiply(unitaryMatrix, jMatrix, unitaryMatrix); if (++count > 2) { ++sweep; count = 0; } } return result; } /** * Computes a matrix, which contains the absolute (unsigned) values of the provided matrix's elements. * * @param {Matrix3} matrix The matrix with signed elements. * @param {Matrix3} result The object onto which to store the result. * @returns {Matrix3} The modified result parameter. */ static abs(matrix, result) { Check_default.typeOf.object("matrix", matrix); Check_default.typeOf.object("result", result); result[0] = Math.abs(matrix[0]); result[1] = Math.abs(matrix[1]); result[2] = Math.abs(matrix[2]); result[3] = Math.abs(matrix[3]); result[4] = Math.abs(matrix[4]); result[5] = Math.abs(matrix[5]); result[6] = Math.abs(matrix[6]); result[7] = Math.abs(matrix[7]); result[8] = Math.abs(matrix[8]); return result; } /** * Computes the determinant of the provided matrix. * * @param {Matrix3} matrix The matrix to use. * @returns {number} The value of the determinant of the matrix. */ static determinant(matrix) { Check_default.typeOf.object("matrix", matrix); const m11 = matrix[0]; const m21 = matrix[3]; const m31 = matrix[6]; const m12 = matrix[1]; const m22 = matrix[4]; const m32 = matrix[7]; const m13 = matrix[2]; const m23 = matrix[5]; const m33 = matrix[8]; return m11 * (m22 * m33 - m23 * m32) + m12 * (m23 * m31 - m21 * m33) + m13 * (m21 * m32 - m22 * m31); } /** * Computes the inverse of the provided matrix. * * @param {Matrix3} matrix The matrix to invert. * @param {Matrix3} result The object onto which to store the result. * @returns {Matrix3} The modified result parameter. * * @exception {DeveloperError} matrix is not invertible. */ static inverse(matrix, result) { Check_default.typeOf.object("matrix", matrix); Check_default.typeOf.object("result", result); const m11 = matrix[0]; const m21 = matrix[1]; const m31 = matrix[2]; const m12 = matrix[3]; const m22 = matrix[4]; const m32 = matrix[5]; const m13 = matrix[6]; const m23 = matrix[7]; const m33 = matrix[8]; const determinant = _Matrix3.determinant(matrix); if (Math.abs(determinant) <= Math_default.EPSILON15) { throw new DeveloperError_default("matrix is not invertible"); } result[0] = m22 * m33 - m23 * m32; result[1] = m23 * m31 - m21 * m33; result[2] = m21 * m32 - m22 * m31; result[3] = m13 * m32 - m12 * m33; result[4] = m11 * m33 - m13 * m31; result[5] = m12 * m31 - m11 * m32; result[6] = m12 * m23 - m13 * m22; result[7] = m13 * m21 - m11 * m23; result[8] = m11 * m22 - m12 * m21; const scale = 1 / determinant; return _Matrix3.multiplyByScalar(result, scale, result); } /** * Computes the inverse transpose of a matrix. * * @param {Matrix3} matrix The matrix to transpose and invert. * @param {Matrix3} result The object onto which to store the result. * @returns {Matrix3} The modified result parameter. */ static inverseTranspose(matrix, result) { Check_default.typeOf.object("matrix", matrix); Check_default.typeOf.object("result", result); return _Matrix3.inverse( _Matrix3.transpose(matrix, scratchTransposeMatrix), result ); } /** * Compares the provided matrices componentwise and returns *true if they are equal, false otherwise.
*
* @param {Matrix3} [left] The first matrix.
* @param {Matrix3} [right] The second matrix.
* @returns {boolean} true if left and right are equal, false otherwise.
*/
static equals(left, right) {
return left === right || defined_default(left) && defined_default(right) && left[0] === right[0] && left[1] === right[1] && left[2] === right[2] && left[3] === right[3] && left[4] === right[4] && left[5] === right[5] && left[6] === right[6] && left[7] === right[7] && left[8] === right[8];
}
/**
* Compares the provided matrices componentwise and returns
* true if they are within the provided epsilon,
* false otherwise.
*
* @param {Matrix3} [left] The first matrix.
* @param {Matrix3} [right] The second matrix.
* @param {number} [epsilon=0] The epsilon to use for equality testing.
* @returns {boolean} true if left and right are within the provided epsilon, false otherwise.
*/
static equalsEpsilon(left, right, epsilon) {
epsilon = epsilon ?? 0;
return left === right || defined_default(left) && defined_default(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;
}
/**
* Gets the number of items in the collection.
*
* @type {number}
*/
get length() {
return _Matrix3.packedLength;
}
/**
* Duplicates the provided Matrix3 instance.
*
* @param {Matrix3} [result] The object onto which to store the result.
* @returns {Matrix3} The modified result parameter or a new Matrix3 instance if one was not provided.
*/
clone(result) {
return _Matrix3.clone(this, result);
}
/**
* Compares this matrix to the provided matrix componentwise and returns
* true if they are equal, false otherwise.
*
* @param {Matrix3} [right] The right hand side matrix.
* @returns {boolean} true if they are equal, false otherwise.
*/
equals(right) {
return _Matrix3.equals(this, right);
}
/**
* Compares provided matrix and array, starting from a given array offset.
*
* @param {Matrix3} matrix
* @param {number[]} array
* @param {number} offset
* @ignore
*/
static equalsArray(matrix, array, offset) {
return matrix[0] === array[offset] && matrix[1] === array[offset + 1] && matrix[2] === array[offset + 2] && matrix[3] === array[offset + 3] && matrix[4] === array[offset + 4] && matrix[5] === array[offset + 5] && matrix[6] === array[offset + 6] && matrix[7] === array[offset + 7] && matrix[8] === array[offset + 8];
}
/**
* Compares this matrix to the provided matrix componentwise and returns
* true if they are within the provided epsilon,
* false otherwise.
*
* @param {Matrix3} [right] The right hand side matrix.
* @param {number} [epsilon=0] The epsilon to use for equality testing.
* @returns {boolean} true if they are within the provided epsilon, false otherwise.
*/
equalsEpsilon(right, epsilon) {
return _Matrix3.equalsEpsilon(this, right, epsilon);
}
/**
* Creates a string representing this Matrix with each row being
* on a separate line and in the format '(column0, column1, column2)'.
*
* @returns {string} A string representing the provided Matrix with each row being on a separate line and in the format '(column0, column1, column2)'.
*/
toString() {
return `(${this[0]}, ${this[3]}, ${this[6]})
(${this[1]}, ${this[4]}, ${this[7]})
(${this[2]}, ${this[5]}, ${this[8]})`;
}
};
Matrix3.packedLength = 9;
Matrix3.fromArray = Matrix3.unpack;
Matrix3.IDENTITY = Object.freeze(
new Matrix3(1, 0, 0, 0, 1, 0, 0, 0, 1)
);
Matrix3.ZERO = Object.freeze(
new Matrix3(0, 0, 0, 0, 0, 0, 0, 0, 0)
);
Matrix3.COLUMN0ROW0 = 0;
Matrix3.COLUMN0ROW1 = 1;
Matrix3.COLUMN0ROW2 = 2;
Matrix3.COLUMN1ROW0 = 3;
Matrix3.COLUMN1ROW1 = 4;
Matrix3.COLUMN1ROW2 = 5;
Matrix3.COLUMN2ROW0 = 6;
Matrix3.COLUMN2ROW1 = 7;
Matrix3.COLUMN2ROW2 = 8;
var scaleScratch1 = new Cartesian3_default();
var scaleScratch2 = new Cartesian3_default();
var scratchColumn = new Cartesian3_default();
var scaleScratch3 = new Cartesian3_default();
var scaleScratch4 = new Cartesian3_default();
var scaleScratch5 = new Cartesian3_default();
var jMatrix = new Matrix3();
var jMatrixTranspose = new Matrix3();
var scratchTransposeMatrix = new Matrix3();
function computeFrobeniusNorm(matrix) {
let norm = 0;
for (let i = 0; i < 9; ++i) {
const temp = matrix[i];
norm += temp * temp;
}
return Math.sqrt(norm);
}
var rowVal = [1, 0, 0];
var colVal = [2, 2, 1];
function offDiagonalFrobeniusNorm(matrix) {
let norm = 0;
for (let i = 0; i < 3; ++i) {
const temp = matrix[Matrix3.getElementIndex(colVal[i], rowVal[i])];
norm += 2 * temp * temp;
}
return Math.sqrt(norm);
}
function shurDecomposition(matrix, result) {
const tolerance = Math_default.EPSILON15;
let maxDiagonal = 0;
let rotAxis = 1;
for (let i = 0; i < 3; ++i) {
const temp = Math.abs(
// @ts-expect-error TODO(tsd-jsdoc): Requires index signature support.
matrix[Matrix3.getElementIndex(colVal[i], rowVal[i])]
);
if (temp > maxDiagonal) {
rotAxis = i;
maxDiagonal = temp;
}
}
let c = 1;
let s = 0;
const p = rowVal[rotAxis];
const q = colVal[rotAxis];
if (Math.abs(matrix[Matrix3.getElementIndex(q, p)]) > tolerance) {
const qq = matrix[Matrix3.getElementIndex(q, q)];
const pp = matrix[Matrix3.getElementIndex(p, p)];
const qp = matrix[Matrix3.getElementIndex(q, p)];
const tau = (qq - pp) / 2 / qp;
let t;
if (tau < 0) {
t = -1 / (-tau + Math.sqrt(1 + tau * tau));
} else {
t = 1 / (tau + Math.sqrt(1 + tau * tau));
}
c = 1 / Math.sqrt(1 + t * t);
s = t * c;
}
result = Matrix3.clone(Matrix3.IDENTITY, result);
result[Matrix3.getElementIndex(p, p)] = result[Matrix3.getElementIndex(q, q)] = c;
result[Matrix3.getElementIndex(q, p)] = s;
result[Matrix3.getElementIndex(p, q)] = -s;
return result;
}
var Matrix3_default = Matrix3;
// packages/engine/Source/Core/Frozen.js
var Frozen = {};
Frozen.EMPTY_OBJECT = Object.freeze({});
Frozen.EMPTY_ARRAY = Object.freeze([]);
var Frozen_default = Frozen;
export {
Cartesian3_default,
Matrix3_default,
Frozen_default
};