src/Matrix4.js
import { RotationOrder } from "./RotationOrder.js";
import { Vector3 } from "./Vector3.js";
/**
* A vector.
*
* @type {Vector3}
* @private
*/
const a = new Vector3();
/**
* A vector.
*
* @type {Vector3}
* @private
*/
const b = new Vector3();
/**
* A vector.
*
* @type {Vector3}
* @private
*/
const c = new Vector3();
/**
* A 4x4 matrix.
*/
export class Matrix4 {
/**
* Constructs a new matrix.
*/
constructor() {
/**
* The matrix elements.
*
* @type {Float32Array}
*/
this.elements = new Float32Array([
1, 0, 0, 0,
0, 1, 0, 0,
0, 0, 1, 0,
0, 0, 0, 1
]);
}
/**
* Sets the values of this matrix.
*
* @param {Number} n00 - The value of the first row, first column.
* @param {Number} n01 - The value of the first row, second column.
* @param {Number} n02 - The value of the first row, third column.
* @param {Number} n03 - The value of the first row, fourth column.
* @param {Number} n10 - The value of the second row, first column.
* @param {Number} n11 - The value of the second row, second column.
* @param {Number} n12 - The value of the second row, third column.
* @param {Number} n13 - The value of the second row, fourth column.
* @param {Number} n20 - The value of the third row, first column.
* @param {Number} n21 - The value of the third row, second column.
* @param {Number} n22 - The value of the third row, third column.
* @param {Number} n23 - The value of the third row, fourth column.
* @param {Number} n30 - The value of the fourth row, first column.
* @param {Number} n31 - The value of the fourth row, second column.
* @param {Number} n32 - The value of the fourth row, third column.
* @param {Number} n33 - The value of the fourth row, fourth column.
* @return {Matrix4} This matrix.
*/
set(n00, n01, n02, n03, n10, n11, n12, n13, n20, n21, n22, n23, n30, n31, n32, n33) {
const te = this.elements;
te[0] = n00; te[4] = n01; te[8] = n02; te[12] = n03;
te[1] = n10; te[5] = n11; te[9] = n12; te[13] = n13;
te[2] = n20; te[6] = n21; te[10] = n22; te[14] = n23;
te[3] = n30; te[7] = n31; te[11] = n32; te[15] = n33;
return this;
}
/**
* Sets this matrix to the identity matrix.
*
* @return {Matrix4} This matrix.
*/
identity() {
this.set(
1, 0, 0, 0,
0, 1, 0, 0,
0, 0, 1, 0,
0, 0, 0, 1
);
return this;
}
/**
* Copies the values of a given matrix.
*
* @param {Matrix4} matrix - A matrix.
* @return {Matrix4} This matrix.
*/
copy(matrix) {
const me = matrix.elements;
const te = this.elements;
te[0] = me[0]; te[1] = me[1]; te[2] = me[2]; te[3] = me[3];
te[4] = me[4]; te[5] = me[5]; te[6] = me[6]; te[7] = me[7];
te[8] = me[8]; te[9] = me[9]; te[10] = me[10]; te[11] = me[11];
te[12] = me[12]; te[13] = me[13]; te[14] = me[14]; te[15] = me[15];
return this;
}
/**
* Clones this matrix.
*
* @return {Matrix4} A clone of this matrix.
*/
clone() {
return new this.constructor().fromArray(this.elements);
}
/**
* Copies the values of a given array.
*
* @param {Number[]} array - An array.
* @param {Number} [offset=0] - An offset into the array.
* @return {Matrix4} This matrix.
*/
fromArray(array, offset = 0) {
const te = this.elements;
let i;
for(i = 0; i < 16; ++i) {
te[i] = array[i + offset];
}
return this;
}
/**
* Stores this matrix in an array.
*
* @param {Number[]} [array] - A target array.
* @param {Number} [offset=0] - An offset into the array.
* @return {Number[]} The array.
*/
toArray(array = [], offset = 0) {
const te = this.elements;
let i;
for(i = 0; i < 16; ++i) {
array[i + offset] = te[i];
}
return array;
}
/**
* Returns the largest scale.
*
* @return {Number} The largest scale of the three axes.
*/
getMaxScaleOnAxis() {
const te = this.elements;
const scaleXSq = te[0] * te[0] + te[1] * te[1] + te[2] * te[2];
const scaleYSq = te[4] * te[4] + te[5] * te[5] + te[6] * te[6];
const scaleZSq = te[8] * te[8] + te[9] * te[9] + te[10] * te[10];
return Math.sqrt(Math.max(scaleXSq, scaleYSq, scaleZSq));
}
/**
* Copies the position values of a given matrix.
*
* @param {Matrix4} matrix - A matrix.
* @return {Matrix4} This matrix.
*/
copyPosition(matrix) {
const te = this.elements;
const me = matrix.elements;
te[12] = me[12];
te[13] = me[13];
te[14] = me[14];
return this;
}
/**
* Sets the position values of this matrix.
*
* @param {Vector3} p - A position.
* @return {Matrix4} This matrix.
*/
setPosition(p) {
const te = this.elements;
te[12] = p.x;
te[13] = p.y;
te[14] = p.z;
return this;
}
/**
* Extracts the basis from this matrix.
*
* @param {Vector3} xAxis - A vector to store the X-axis column in.
* @param {Vector3} yAxis - A vector to store the Y-axis column in.
* @param {Vector3} zAxis - A vector to store the Z-axis column in.
* @return {Matrix4} This matrix.
*/
extractBasis(xAxis, yAxis, zAxis) {
xAxis.setFromMatrixColumn(this, 0);
yAxis.setFromMatrixColumn(this, 1);
zAxis.setFromMatrixColumn(this, 2);
return this;
}
/**
* Sets the basis of this matrix.
*
* @param {Vector3} xAxis - The X-axis.
* @param {Vector3} yAxis - The Y-axis.
* @param {Vector3} zAxis - The Z-axis.
* @return {Matrix4} This matrix.
*/
makeBasis(xAxis, yAxis, zAxis) {
this.set(
xAxis.x, yAxis.x, zAxis.x, 0,
xAxis.y, yAxis.y, zAxis.y, 0,
xAxis.z, yAxis.z, zAxis.z, 0,
0, 0, 0, 1
);
return this;
}
/**
* Extracts the rotation from a given matrix.
*
* This method does not support reflection matrices.
*
* @param {Matrix4} m - A matrix.
* @return {Matrix4} This matrix.
*/
extractRotation(m) {
const te = this.elements;
const me = m.elements;
const scaleX = 1.0 / a.setFromMatrixColumn(m, 0).length();
const scaleY = 1.0 / a.setFromMatrixColumn(m, 1).length();
const scaleZ = 1.0 / a.setFromMatrixColumn(m, 2).length();
te[0] = me[0] * scaleX;
te[1] = me[1] * scaleX;
te[2] = me[2] * scaleX;
te[3] = 0;
te[4] = me[4] * scaleY;
te[5] = me[5] * scaleY;
te[6] = me[6] * scaleY;
te[7] = 0;
te[8] = me[8] * scaleZ;
te[9] = me[9] * scaleZ;
te[10] = me[10] * scaleZ;
te[11] = 0;
te[12] = 0;
te[13] = 0;
te[14] = 0;
te[15] = 1;
return this;
}
/**
* Sets the matrix rotation based on the given Euler angles.
*
* @param {Euler} euler - The euler angles.
* @return {Matrix4} This matrix.
*/
makeRotationFromEuler(euler) {
const te = this.elements;
const x = euler.x;
const y = euler.y;
const z = euler.z;
const a = Math.cos(x), b = Math.sin(x);
const c = Math.cos(y), d = Math.sin(y);
const e = Math.cos(z), f = Math.sin(z);
let ae, af, be, bf;
let ce, cf, de, df;
let ac, ad, bc, bd;
switch(euler.order) {
case RotationOrder.XYZ: {
ae = a * e, af = a * f, be = b * e, bf = b * f;
te[0] = c * e;
te[4] = -c * f;
te[8] = d;
te[1] = af + be * d;
te[5] = ae - bf * d;
te[9] = -b * c;
te[2] = bf - ae * d;
te[6] = be + af * d;
te[10] = a * c;
break;
}
case RotationOrder.YXZ: {
ce = c * e, cf = c * f, de = d * e, df = d * f;
te[0] = ce + df * b;
te[4] = de * b - cf;
te[8] = a * d;
te[1] = a * f;
te[5] = a * e;
te[9] = -b;
te[2] = cf * b - de;
te[6] = df + ce * b;
te[10] = a * c;
break;
}
case RotationOrder.ZXY: {
ce = c * e, cf = c * f, de = d * e, df = d * f;
te[0] = ce - df * b;
te[4] = -a * f;
te[8] = de + cf * b;
te[1] = cf + de * b;
te[5] = a * e;
te[9] = df - ce * b;
te[2] = -a * d;
te[6] = b;
te[10] = a * c;
break;
}
case RotationOrder.ZYX: {
ae = a * e, af = a * f, be = b * e, bf = b * f;
te[0] = c * e;
te[4] = be * d - af;
te[8] = ae * d + bf;
te[1] = c * f;
te[5] = bf * d + ae;
te[9] = af * d - be;
te[2] = -d;
te[6] = b * c;
te[10] = a * c;
break;
}
case RotationOrder.YZX: {
ac = a * c, ad = a * d, bc = b * c, bd = b * d;
te[0] = c * e;
te[4] = bd - ac * f;
te[8] = bc * f + ad;
te[1] = f;
te[5] = a * e;
te[9] = -b * e;
te[2] = -d * e;
te[6] = ad * f + bc;
te[10] = ac - bd * f;
break;
}
case RotationOrder.XZY: {
ac = a * c, ad = a * d, bc = b * c, bd = b * d;
te[0] = c * e;
te[4] = -f;
te[8] = d * e;
te[1] = ac * f + bd;
te[5] = a * e;
te[9] = ad * f - bc;
te[2] = bc * f - ad;
te[6] = b * e;
te[10] = bd * f + ac;
break;
}
}
// Bottom row.
te[3] = 0;
te[7] = 0;
te[11] = 0;
// Last column.
te[12] = 0;
te[13] = 0;
te[14] = 0;
te[15] = 1;
return this;
}
/**
* Sets the matrix rotation based on the given quaternion.
*
* @param {Quaternion} q - The quaternion.
* @return {Matrix4} This matrix.
*/
makeRotationFromQuaternion(q) {
return this.compose(a.set(0, 0, 0), q, b.set(1, 1, 1));
}
/**
* Creates a rotation that looks at the given target.
*
* @param {Vector3} eye - The position of the eye.
* @param {Vector3} target - The target to look at.
* @param {Vector3} up - The up vector.
* @return {Matrix4} This matrix.
*/
lookAt(eye, target, up) {
const te = this.elements;
const x = a, y = b, z = c;
z.subVectors(eye, target);
if(z.lengthSquared() === 0) {
// Eye and target are at the same position.
z.z = 1;
}
z.normalize();
x.crossVectors(up, z);
if(x.lengthSquared() === 0) {
// Up and z are parallel.
if(Math.abs(up.z) === 1) {
z.x += 1e-4;
} else {
z.z += 1e-4;
}
z.normalize();
x.crossVectors(up, z);
}
x.normalize();
y.crossVectors(z, x);
te[0] = x.x; te[4] = y.x; te[8] = z.x;
te[1] = x.y; te[5] = y.y; te[9] = z.y;
te[2] = x.z; te[6] = y.z; te[10] = z.z;
return this;
}
/**
* Sets this matrix to the product of the given matrices.
*
* @param {Matrix4} a - A matrix.
* @param {Matrix4} b - A matrix.
* @return {Matrix4} This matrix.
*/
multiplyMatrices(a, b) {
const te = this.elements;
const ae = a.elements;
const be = b.elements;
const a00 = ae[0], a01 = ae[4], a02 = ae[8], a03 = ae[12];
const a10 = ae[1], a11 = ae[5], a12 = ae[9], a13 = ae[13];
const a20 = ae[2], a21 = ae[6], a22 = ae[10], a23 = ae[14];
const a30 = ae[3], a31 = ae[7], a32 = ae[11], a33 = ae[15];
const b00 = be[0], b01 = be[4], b02 = be[8], b03 = be[12];
const b10 = be[1], b11 = be[5], b12 = be[9], b13 = be[13];
const b20 = be[2], b21 = be[6], b22 = be[10], b23 = be[14];
const b30 = be[3], b31 = be[7], b32 = be[11], b33 = be[15];
te[0] = a00 * b00 + a01 * b10 + a02 * b20 + a03 * b30;
te[4] = a00 * b01 + a01 * b11 + a02 * b21 + a03 * b31;
te[8] = a00 * b02 + a01 * b12 + a02 * b22 + a03 * b32;
te[12] = a00 * b03 + a01 * b13 + a02 * b23 + a03 * b33;
te[1] = a10 * b00 + a11 * b10 + a12 * b20 + a13 * b30;
te[5] = a10 * b01 + a11 * b11 + a12 * b21 + a13 * b31;
te[9] = a10 * b02 + a11 * b12 + a12 * b22 + a13 * b32;
te[13] = a10 * b03 + a11 * b13 + a12 * b23 + a13 * b33;
te[2] = a20 * b00 + a21 * b10 + a22 * b20 + a23 * b30;
te[6] = a20 * b01 + a21 * b11 + a22 * b21 + a23 * b31;
te[10] = a20 * b02 + a21 * b12 + a22 * b22 + a23 * b32;
te[14] = a20 * b03 + a21 * b13 + a22 * b23 + a23 * b33;
te[3] = a30 * b00 + a31 * b10 + a32 * b20 + a33 * b30;
te[7] = a30 * b01 + a31 * b11 + a32 * b21 + a33 * b31;
te[11] = a30 * b02 + a31 * b12 + a32 * b22 + a33 * b32;
te[15] = a30 * b03 + a31 * b13 + a32 * b23 + a33 * b33;
return this;
}
/**
* Multiplies this matrix with the given one.
*
* @param {Matrix4} m - A matrix.
* @return {Matrix4} This matrix.
*/
multiply(m) {
return this.multiplyMatrices(this, m);
}
/**
* Multiplies a given matrix with this one.
*
* @param {Matrix4} m - A matrix.
* @return {Matrix4} This matrix.
*/
premultiply(m) {
return this.multiplyMatrices(m, this);
}
/**
* Multiplies this matrix with a given scalar.
*
* @param {Number} s - A scalar.
* @return {Matrix4} This matrix.
*/
multiplyScalar(s) {
const te = this.elements;
te[0] *= s; te[4] *= s; te[8] *= s; te[12] *= s;
te[1] *= s; te[5] *= s; te[9] *= s; te[13] *= s;
te[2] *= s; te[6] *= s; te[10] *= s; te[14] *= s;
te[3] *= s; te[7] *= s; te[11] *= s; te[15] *= s;
return this;
}
/**
* Calculates the determinant of this matrix.
*
* For more details see:
* http://www.euclideanspace.com/maths/algebra/matrix/functions/inverse/fourD/index.htm
*
* @return {Number} The determinant.
*/
determinant() {
const te = this.elements;
const n00 = te[0], n01 = te[4], n02 = te[8], n03 = te[12];
const n10 = te[1], n11 = te[5], n12 = te[9], n13 = te[13];
const n20 = te[2], n21 = te[6], n22 = te[10], n23 = te[14];
const n30 = te[3], n31 = te[7], n32 = te[11], n33 = te[15];
const n00n11 = n00 * n11, n00n12 = n00 * n12, n00n13 = n00 * n13;
const n01n10 = n01 * n10, n01n12 = n01 * n12, n01n13 = n01 * n13;
const n02n10 = n02 * n10, n02n11 = n02 * n11, n02n13 = n02 * n13;
const n03n10 = n03 * n10, n03n11 = n03 * n11, n03n12 = n03 * n12;
return (
n30 * (
n03n12 * n21 -
n02n13 * n21 -
n03n11 * n22 +
n01n13 * n22 +
n02n11 * n23 -
n01n12 * n23
) +
n31 * (
n00n12 * n23 -
n00n13 * n22 +
n03n10 * n22 -
n02n10 * n23 +
n02n13 * n20 -
n03n12 * n20
) +
n32 * (
n00n13 * n21 -
n00n11 * n23 -
n03n10 * n21 +
n01n10 * n23 +
n03n11 * n20 -
n01n13 * n20
) +
n33 * (
-n02n11 * n20 -
n00n12 * n21 +
n00n11 * n22 +
n02n10 * n21 -
n01n10 * n22 +
n01n12 * n20
)
);
}
/**
* Inverts the given matrix and stores the result in this matrix.
*
* For details see:
* http://www.euclideanspace.com/maths/algebra/matrix/functions/inverse/fourD/index.htm
*
* @param {Matrix4} matrix - The matrix that should be inverted.
* @return {Matrix4} This matrix.
*/
getInverse(matrix) {
const te = this.elements;
const me = matrix.elements;
const n00 = me[0], n10 = me[1], n20 = me[2], n30 = me[3];
const n01 = me[4], n11 = me[5], n21 = me[6], n31 = me[7];
const n02 = me[8], n12 = me[9], n22 = me[10], n32 = me[11];
const n03 = me[12], n13 = me[13], n23 = me[14], n33 = me[15];
const t00 = n12 * n23 * n31 - n13 * n22 * n31 + n13 * n21 * n32 - n11 * n23 * n32 - n12 * n21 * n33 + n11 * n22 * n33;
const t01 = n03 * n22 * n31 - n02 * n23 * n31 - n03 * n21 * n32 + n01 * n23 * n32 + n02 * n21 * n33 - n01 * n22 * n33;
const t02 = n02 * n13 * n31 - n03 * n12 * n31 + n03 * n11 * n32 - n01 * n13 * n32 - n02 * n11 * n33 + n01 * n12 * n33;
const t03 = n03 * n12 * n21 - n02 * n13 * n21 - n03 * n11 * n22 + n01 * n13 * n22 + n02 * n11 * n23 - n01 * n12 * n23;
const det = n00 * t00 + n10 * t01 + n20 * t02 + n30 * t03;
let invDet;
if(det !== 0) {
invDet = 1.0 / det;
te[0] = t00 * invDet;
te[1] = (n13 * n22 * n30 - n12 * n23 * n30 - n13 * n20 * n32 + n10 * n23 * n32 + n12 * n20 * n33 - n10 * n22 * n33) * invDet;
te[2] = (n11 * n23 * n30 - n13 * n21 * n30 + n13 * n20 * n31 - n10 * n23 * n31 - n11 * n20 * n33 + n10 * n21 * n33) * invDet;
te[3] = (n12 * n21 * n30 - n11 * n22 * n30 - n12 * n20 * n31 + n10 * n22 * n31 + n11 * n20 * n32 - n10 * n21 * n32) * invDet;
te[4] = t01 * invDet;
te[5] = (n02 * n23 * n30 - n03 * n22 * n30 + n03 * n20 * n32 - n00 * n23 * n32 - n02 * n20 * n33 + n00 * n22 * n33) * invDet;
te[6] = (n03 * n21 * n30 - n01 * n23 * n30 - n03 * n20 * n31 + n00 * n23 * n31 + n01 * n20 * n33 - n00 * n21 * n33) * invDet;
te[7] = (n01 * n22 * n30 - n02 * n21 * n30 + n02 * n20 * n31 - n00 * n22 * n31 - n01 * n20 * n32 + n00 * n21 * n32) * invDet;
te[8] = t02 * invDet;
te[9] = (n03 * n12 * n30 - n02 * n13 * n30 - n03 * n10 * n32 + n00 * n13 * n32 + n02 * n10 * n33 - n00 * n12 * n33) * invDet;
te[10] = (n01 * n13 * n30 - n03 * n11 * n30 + n03 * n10 * n31 - n00 * n13 * n31 - n01 * n10 * n33 + n00 * n11 * n33) * invDet;
te[11] = (n02 * n11 * n30 - n01 * n12 * n30 - n02 * n10 * n31 + n00 * n12 * n31 + n01 * n10 * n32 - n00 * n11 * n32) * invDet;
te[12] = t03 * invDet;
te[13] = (n02 * n13 * n20 - n03 * n12 * n20 + n03 * n10 * n22 - n00 * n13 * n22 - n02 * n10 * n23 + n00 * n12 * n23) * invDet;
te[14] = (n03 * n11 * n20 - n01 * n13 * n20 - n03 * n10 * n21 + n00 * n13 * n21 + n01 * n10 * n23 - n00 * n11 * n23) * invDet;
te[15] = (n01 * n12 * n20 - n02 * n11 * n20 + n02 * n10 * n21 - n00 * n12 * n21 - n01 * n10 * n22 + n00 * n11 * n22) * invDet;
} else {
this.set(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0);
}
return this;
}
/**
* Transposes this matrix.
*
* @return {Matrix4} This matrix.
*/
transpose() {
const te = this.elements;
let t;
t = te[1]; te[1] = te[4]; te[4] = t;
t = te[2]; te[2] = te[8]; te[8] = t;
t = te[6]; te[6] = te[9]; te[9] = t;
t = te[3]; te[3] = te[12]; te[12] = t;
t = te[7]; te[7] = te[13]; te[13] = t;
t = te[11]; te[11] = te[14]; te[14] = t;
return this;
}
/**
* Scales this matrix.
*
* @param {Number} sx - The X scale.
* @param {Number} sy - The Y scale.
* @param {Number} sz - The Z scale.
* @return {Matrix4} This matrix.
*/
scale(sx, sy, sz) {
const te = this.elements;
te[0] *= sx; te[4] *= sy; te[8] *= sz;
te[1] *= sx; te[5] *= sy; te[9] *= sz;
te[2] *= sx; te[6] *= sy; te[10] *= sz;
te[3] *= sx; te[7] *= sy; te[11] *= sz;
return this;
}
/**
* Makes this matrix a scale matrix.
*
* @param {Number} x - The X scale.
* @param {Number} y - The Y scale.
* @param {Number} z - The Z scale.
* @return {Matrix4} This matrix.
*/
makeScale(x, y, z) {
this.set(
x, 0, 0, 0,
0, y, 0, 0,
0, 0, z, 0,
0, 0, 0, 1
);
return this;
}
/**
* Makes this matrix a translation matrix.
*
* @param {Number} x - The X offset.
* @param {Number} y - The Y offset.
* @param {Number} z - The Z offset.
* @return {Matrix4} This matrix.
*/
makeTranslation(x, y, z) {
this.set(
1, 0, 0, x,
0, 1, 0, y,
0, 0, 1, z,
0, 0, 0, 1
);
return this;
}
/**
* Makes this matrix a rotation matrix.
*
* @param {Number} theta - The angle in radians.
* @return {Matrix4} This matrix.
*/
makeRotationX(theta) {
const c = Math.cos(theta), s = Math.sin(theta);
this.set(
1, 0, 0, 0,
0, c, -s, 0,
0, s, c, 0,
0, 0, 0, 1
);
return this;
}
/**
* Makes this matrix a rotation matrix with respect to the Y-axis.
*
* @param {Number} theta - The angle in radians.
* @return {Matrix4} This matrix.
*/
makeRotationY(theta) {
const c = Math.cos(theta), s = Math.sin(theta);
this.set(
c, 0, s, 0,
0, 1, 0, 0,
-s, 0, c, 0,
0, 0, 0, 1
);
return this;
}
/**
* Makes this matrix a rotation matrix with respect to the Z-axis.
*
* @param {Number} theta - The angle in radians.
* @return {Matrix4} This matrix.
*/
makeRotationZ(theta) {
const c = Math.cos(theta), s = Math.sin(theta);
this.set(
c, -s, 0, 0,
s, c, 0, 0,
0, 0, 1, 0,
0, 0, 0, 1
);
return this;
}
/**
* Makes this matrix a translation matrix with respect to a specific axis.
*
* For mor einformation see:
* http://www.gamedev.net/reference/articles/article1199.asp
*
* @param {Vector3} axis - The axis. Assumed to be normalized.
* @param {Number} angle - The angle in radians.
* @return {Matrix4} This matrix.
*/
makeRotationAxis(axis, angle) {
const c = Math.cos(angle);
const s = Math.sin(angle);
const t = 1.0 - c;
const x = axis.x, y = axis.y, z = axis.z;
const tx = t * x, ty = t * y;
this.set(
tx * x + c, tx * y - s * z, tx * z + s * y, 0,
tx * y + s * z, ty * y + c, ty * z - s * x, 0,
tx * z - s * y, ty * z + s * x, t * z * z + c, 0,
0, 0, 0, 1
);
return this;
}
/**
* Makes this matrix a shear matrix.
*
* @param {Number} x - The X shear value.
* @param {Number} y - The Y shear value.
* @param {Number} z - The Z shear value.
* @return {Matrix4} This matrix.
*/
makeShear(x, y, z) {
this.set(
1, y, z, 0,
x, 1, z, 0,
x, y, 1, 0,
0, 0, 0, 1
);
return this;
}
/**
* Sets this matrix based on the given position, rotation and scale.
*
* @param {Vector3} position - The position.
* @param {Quaternion} quaternion - The rotation.
* @param {Vector3} scale - The scale.
* @return {Matrix4} This matrix.
*/
compose(position, quaternion, scale) {
const te = this.elements;
const x = quaternion.x, y = quaternion.y, z = quaternion.z, w = quaternion.w;
const x2 = x + x, y2 = y + y, z2 = z + z;
const xx = x * x2, xy = x * y2, xz = x * z2;
const yy = y * y2, yz = y * z2, zz = z * z2;
const wx = w * x2, wy = w * y2, wz = w * z2;
const sx = scale.x, sy = scale.y, sz = scale.z;
te[0] = (1 - (yy + zz)) * sx;
te[1] = (xy + wz) * sx;
te[2] = (xz - wy) * sx;
te[3] = 0;
te[4] = (xy - wz) * sy;
te[5] = (1 - (xx + zz)) * sy;
te[6] = (yz + wx) * sy;
te[7] = 0;
te[8] = (xz + wy) * sz;
te[9] = (yz - wx) * sz;
te[10] = (1 - (xx + yy)) * sz;
te[11] = 0;
te[12] = position.x;
te[13] = position.y;
te[14] = position.z;
te[15] = 1;
return this;
}
/**
* Decomposes this matrix into a position, rotation and scale vector.
*
* @param {Vector3} position - The target position.
* @param {Quaternion} quaternion - The target rotation.
* @param {Vector3} scale - The target scale.
* @return {Matrix4} This matrix.
*/
decompose(position, quaternion, scale) {
const te = this.elements;
const n00 = te[0], n10 = te[1], n20 = te[2];
const n01 = te[4], n11 = te[5], n21 = te[6];
const n02 = te[8], n12 = te[9], n22 = te[10];
const det = this.determinant();
// If the determinant is negative, one scale must be inverted.
const sx = a.set(n00, n10, n20).length() * ((det < 0) ? -1 : 1);
const sy = a.set(n01, n11, n21).length();
const sz = a.set(n02, n12, n22).length();
const invSX = 1.0 / sx;
const invSY = 1.0 / sy;
const invSZ = 1.0 / sz;
// Export the position.
position.x = te[12];
position.y = te[13];
position.z = te[14];
// Scale the rotation part.
te[0] *= invSX; te[1] *= invSX; te[2] *= invSX;
te[4] *= invSY; te[5] *= invSY; te[6] *= invSY;
te[8] *= invSZ; te[9] *= invSZ; te[10] *= invSZ;
// Export the rotation.
quaternion.setFromRotationMatrix(this);
// Restore the original values.
te[0] = n00; te[1] = n10; te[2] = n20;
te[4] = n01; te[5] = n11; te[6] = n21;
te[8] = n02; te[9] = n12; te[10] = n22;
// Export the scale.
scale.x = sx;
scale.y = sy;
scale.z = sz;
return this;
}
/**
* Creates a perspective matrix.
*
* @param {Number} left - The distance to the left plane.
* @param {Number} right - The distance to the right plane.
* @param {Number} top - The distance to the top plane.
* @param {Number} bottom - The distance to the bottom plane.
* @param {Number} near - The distance to the near plane.
* @param {Number} far - The distance to the far plane.
* @return {Matrix4} This matrix.
*/
makePerspective(left, right, top, bottom, near, far) {
const te = this.elements;
const x = 2 * near / (right - left);
const y = 2 * near / (top - bottom);
const a = (right + left) / (right - left);
const b = (top + bottom) / (top - bottom);
const c = -(far + near) / (far - near);
const d = -2 * far * near / (far - near);
te[0] = x; te[4] = 0; te[8] = a; te[12] = 0;
te[1] = 0; te[5] = y; te[9] = b; te[13] = 0;
te[2] = 0; te[6] = 0; te[10] = c; te[14] = d;
te[3] = 0; te[7] = 0; te[11] = -1; te[15] = 0;
return this;
}
/**
* Creates an orthographic matrix.
*
* @param {Number} left - The distance to the left plane.
* @param {Number} right - The distance to the right plane.
* @param {Number} top - The distance to the top plane.
* @param {Number} bottom - The distance to the bottom plane.
* @param {Number} near - The distance to the near plane.
* @param {Number} far - The distance to the far plane.
* @return {Matrix4} This matrix.
*/
makeOrthographic(left, right, top, bottom, near, far) {
const te = this.elements;
const w = 1.0 / (right - left);
const h = 1.0 / (top - bottom);
const p = 1.0 / (far - near);
const x = (right + left) * w;
const y = (top + bottom) * h;
const z = (far + near) * p;
te[0] = 2 * w; te[4] = 0; te[8] = 0; te[12] = -x;
te[1] = 0; te[5] = 2 * h; te[9] = 0; te[13] = -y;
te[2] = 0; te[6] = 0; te[10] = -2 * p; te[14] = -z;
te[3] = 0; te[7] = 0; te[11] = 0; te[15] = 1;
return this;
}
/**
* Checks if this matrix equals the given one.
*
* @param {Matrix4} m - A matrix.
* @return {Boolean} Whether the matrix are equal.
*/
equals(m) {
const te = this.elements;
const me = m.elements;
let result = true;
let i;
for(i = 0; result && i < 16; ++i) {
if(te[i] !== me[i]) {
result = false;
}
}
return result;
}
}
