@turbox3d/math
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Large-scale graphics application math library
835 lines (653 loc) • 23.3 kB
text/typescript
/* eslint-disable function-call-argument-newline */
import { MathUtils } from '../MathUtils';
import { Euler } from './Euler';
import { Matrix3 } from './Matrix3';
import { Quaternion } from './Quaternion';
import { Vector3 } from './Vector3';
const _v1 = new Vector3();
const _zero = new Vector3(0, 0, 0);
const _one = new Vector3(1, 1, 1);
const _x = new Vector3();
const _y = new Vector3();
const _z = new Vector3();
class Matrix4 {
readonly isMatrix4: boolean;
elements: number[];
constructor() {
this.isMatrix4 = true;
this.elements = [
1, 0, 0, 0,
0, 1, 0, 0,
0, 0, 1, 0,
0, 0, 0, 1,
];
if (arguments.length > 0) {
console.error('THREE.Matrix4: the constructor no longer reads arguments. use .set() instead.');
}
}
set(n11: number, n12: number, n13: number, n14: number, n21: number, n22: number, n23: number, n24: number, n31: number, n32: number, n33: number, n34: number, n41: number, n42: number, n43: number, n44: number) {
const te = this.elements;
te[0] = n11; te[4] = n12; te[8] = n13; te[12] = n14;
te[1] = n21; te[5] = n22; te[9] = n23; te[13] = n24;
te[2] = n31; te[6] = n32; te[10] = n33; te[14] = n34;
te[3] = n41; te[7] = n42; te[11] = n43; te[15] = n44;
return this;
}
identity() {
this.set(
1, 0, 0, 0,
0, 1, 0, 0,
0, 0, 1, 0,
0, 0, 0, 1,
);
return this;
}
clone() {
return new Matrix4().fromArray(this.elements);
}
copy(m: Matrix4) {
const te = this.elements;
const me = m.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;
}
copyPosition(m: Matrix4) {
const te = this.elements; const
me = m.elements;
te[12] = me[12];
te[13] = me[13];
te[14] = me[14];
return this;
}
setFromMatrix3(m: Matrix3) {
const me = m.elements;
this.set(
me[0], me[3], me[6], 0,
me[1], me[4], me[7], 0,
me[2], me[5], me[8], 0,
0, 0, 0, 1
);
return this;
}
extractBasis(xAxis: Vector3, yAxis: Vector3, zAxis: Vector3) {
xAxis.setFromMatrixColumn(this, 0);
yAxis.setFromMatrixColumn(this, 1);
zAxis.setFromMatrixColumn(this, 2);
return this;
}
makeBasis(xAxis: Vector3, yAxis: Vector3, zAxis: Vector3) {
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;
}
extractRotation(m: Matrix4) {
// this method does not support reflection matrices
const te = this.elements;
const me = m.elements;
const scaleX = 1 / _v1.setFromMatrixColumn(m, 0).length;
const scaleY = 1 / _v1.setFromMatrixColumn(m, 1).length;
const scaleZ = 1 / _v1.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;
}
makeRotationFromEuler(euler: Euler) {
const te = this.elements;
const x = euler.x; const y = euler.y; const
z = euler.z;
const a = Math.cos(x); const
b = Math.sin(x);
const c = Math.cos(y); const
d = Math.sin(y);
const e = Math.cos(z); const
f = Math.sin(z);
if (euler.order === 'XYZ') {
const ae = a * e; const af = a * f; const be = b * e; const
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;
} else if (euler.order === 'YXZ') {
const ce = c * e; const cf = c * f; const de = d * e; const
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;
} else if (euler.order === 'ZXY') {
const ce = c * e; const cf = c * f; const de = d * e; const
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;
} else if (euler.order === 'ZYX') {
const ae = a * e; const af = a * f; const be = b * e; const
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;
} else if (euler.order === 'YZX') {
const ac = a * c; const ad = a * d; const bc = b * c; const
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;
} else if (euler.order === 'XZY') {
const ac = a * c; const ad = a * d; const bc = b * c; const
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;
}
// 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;
}
makeRotationFromQuaternion(q: Quaternion) {
return this.compose(_zero, q, _one);
}
lookAt(eye: Vector3, target: Vector3, up: Vector3) {
const te = this.elements;
_z.subVectors(eye, target);
if (_z.lengthSq === 0) {
// eye and target are in the same position
_z.z = 1;
}
_z.normalize();
_x.crossVectors(up, _z);
if (_x.lengthSq === 0) {
// up and z are parallel
if (Math.abs(up.z) === 1) {
_z.x += 0.0001;
} else {
_z.z += 0.0001;
}
_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;
}
multiply(m: Matrix4) {
return this.multiplyMatrices(this, m);
}
multiplied(m: Matrix4) {
return new Matrix4().multiplyMatrices(this, m);
}
premultiply(m: Matrix4) {
return this.multiplyMatrices(m, this);
}
premultiplied(m: Matrix4): Matrix4 {
return new Matrix4().multiplyMatrices(m, this);
}
multiplyMatrices(a: Matrix4, b: Matrix4) {
const ae = a.elements;
const be = b.elements;
const te = this.elements;
const a11 = ae[0]; const a12 = ae[4]; const a13 = ae[8]; const
a14 = ae[12];
const a21 = ae[1]; const a22 = ae[5]; const a23 = ae[9]; const
a24 = ae[13];
const a31 = ae[2]; const a32 = ae[6]; const a33 = ae[10]; const
a34 = ae[14];
const a41 = ae[3]; const a42 = ae[7]; const a43 = ae[11]; const
a44 = ae[15];
const b11 = be[0]; const b12 = be[4]; const b13 = be[8]; const
b14 = be[12];
const b21 = be[1]; const b22 = be[5]; const b23 = be[9]; const
b24 = be[13];
const b31 = be[2]; const b32 = be[6]; const b33 = be[10]; const
b34 = be[14];
const b41 = be[3]; const b42 = be[7]; const b43 = be[11]; const
b44 = be[15];
te[0] = a11 * b11 + a12 * b21 + a13 * b31 + a14 * b41;
te[4] = a11 * b12 + a12 * b22 + a13 * b32 + a14 * b42;
te[8] = a11 * b13 + a12 * b23 + a13 * b33 + a14 * b43;
te[12] = a11 * b14 + a12 * b24 + a13 * b34 + a14 * b44;
te[1] = a21 * b11 + a22 * b21 + a23 * b31 + a24 * b41;
te[5] = a21 * b12 + a22 * b22 + a23 * b32 + a24 * b42;
te[9] = a21 * b13 + a22 * b23 + a23 * b33 + a24 * b43;
te[13] = a21 * b14 + a22 * b24 + a23 * b34 + a24 * b44;
te[2] = a31 * b11 + a32 * b21 + a33 * b31 + a34 * b41;
te[6] = a31 * b12 + a32 * b22 + a33 * b32 + a34 * b42;
te[10] = a31 * b13 + a32 * b23 + a33 * b33 + a34 * b43;
te[14] = a31 * b14 + a32 * b24 + a33 * b34 + a34 * b44;
te[3] = a41 * b11 + a42 * b21 + a43 * b31 + a44 * b41;
te[7] = a41 * b12 + a42 * b22 + a43 * b32 + a44 * b42;
te[11] = a41 * b13 + a42 * b23 + a43 * b33 + a44 * b43;
te[15] = a41 * b14 + a42 * b24 + a43 * b34 + a44 * b44;
return this;
}
multiplyScalar(s: number) {
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;
}
determinant() {
const te = this.elements;
const n11 = te[0]; const n12 = te[4]; const n13 = te[8]; const
n14 = te[12];
const n21 = te[1]; const n22 = te[5]; const n23 = te[9]; const
n24 = te[13];
const n31 = te[2]; const n32 = te[6]; const n33 = te[10]; const
n34 = te[14];
const n41 = te[3]; const n42 = te[7]; const n43 = te[11]; const
n44 = te[15];
// TODO: make this more efficient
// ( based on http://www.euclideanspace.com/maths/algebra/matrix/functions/inverse/fourD/index.htm )
return (
n41 * (
+n14 * n23 * n32
- n13 * n24 * n32
- n14 * n22 * n33
+ n12 * n24 * n33
+ n13 * n22 * n34
- n12 * n23 * n34
) +
n42 * (
+n11 * n23 * n34
- n11 * n24 * n33
+ n14 * n21 * n33
- n13 * n21 * n34
+ n13 * n24 * n31
- n14 * n23 * n31
) +
n43 * (
+n11 * n24 * n32
- n11 * n22 * n34
- n14 * n21 * n32
+ n12 * n21 * n34
+ n14 * n22 * n31
- n12 * n24 * n31
) +
n44 * (
-n13 * n22 * n31
- n11 * n23 * n32
+ n11 * n22 * n33
+ n13 * n21 * n32
- n12 * n21 * n33
+ n12 * n23 * n31
)
);
}
transpose() {
const te = this.elements;
let tmp: number;
tmp = te[1]; te[1] = te[4]; te[4] = tmp;
tmp = te[2]; te[2] = te[8]; te[8] = tmp;
tmp = te[6]; te[6] = te[9]; te[9] = tmp;
tmp = te[3]; te[3] = te[12]; te[12] = tmp;
tmp = te[7]; te[7] = te[13]; te[13] = tmp;
tmp = te[11]; te[11] = te[14]; te[14] = tmp;
return this;
}
setPosition(x = 0, y = 0, z = 0) {
const te = this.elements;
te[12] = x;
te[13] = y;
te[14] = z;
return this;
}
invert() {
// based on http://www.euclideanspace.com/maths/algebra/matrix/functions/inverse/fourD/index.htm
const te = this.elements;
const n11 = te[0]; const n21 = te[1]; const n31 = te[2]; const n41 = te[3];
const n12 = te[4]; const n22 = te[5]; const n32 = te[6]; const n42 = te[7];
const n13 = te[8]; const n23 = te[9]; const n33 = te[10]; const n43 = te[11];
const n14 = te[12]; const n24 = te[13]; const n34 = te[14]; const n44 = te[15];
const t11 = n23 * n34 * n42 - n24 * n33 * n42 + n24 * n32 * n43 - n22 * n34 * n43 - n23 * n32 * n44 + n22 * n33 * n44;
const t12 = n14 * n33 * n42 - n13 * n34 * n42 - n14 * n32 * n43 + n12 * n34 * n43 + n13 * n32 * n44 - n12 * n33 * n44;
const t13 = n13 * n24 * n42 - n14 * n23 * n42 + n14 * n22 * n43 - n12 * n24 * n43 - n13 * n22 * n44 + n12 * n23 * n44;
const t14 = n14 * n23 * n32 - n13 * n24 * n32 - n14 * n22 * n33 + n12 * n24 * n33 + n13 * n22 * n34 - n12 * n23 * n34;
const det = n11 * t11 + n21 * t12 + n31 * t13 + n41 * t14;
if (det === 0) return this.set(0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0);
const detInv = 1 / det;
te[0] = t11 * detInv;
te[1] = (n24 * n33 * n41 - n23 * n34 * n41 - n24 * n31 * n43 + n21 * n34 * n43 + n23 * n31 * n44 - n21 * n33 * n44) * detInv;
te[2] = (n22 * n34 * n41 - n24 * n32 * n41 + n24 * n31 * n42 - n21 * n34 * n42 - n22 * n31 * n44 + n21 * n32 * n44) * detInv;
te[3] = (n23 * n32 * n41 - n22 * n33 * n41 - n23 * n31 * n42 + n21 * n33 * n42 + n22 * n31 * n43 - n21 * n32 * n43) * detInv;
te[4] = t12 * detInv;
te[5] = (n13 * n34 * n41 - n14 * n33 * n41 + n14 * n31 * n43 - n11 * n34 * n43 - n13 * n31 * n44 + n11 * n33 * n44) * detInv;
te[6] = (n14 * n32 * n41 - n12 * n34 * n41 - n14 * n31 * n42 + n11 * n34 * n42 + n12 * n31 * n44 - n11 * n32 * n44) * detInv;
te[7] = (n12 * n33 * n41 - n13 * n32 * n41 + n13 * n31 * n42 - n11 * n33 * n42 - n12 * n31 * n43 + n11 * n32 * n43) * detInv;
te[8] = t13 * detInv;
te[9] = (n14 * n23 * n41 - n13 * n24 * n41 - n14 * n21 * n43 + n11 * n24 * n43 + n13 * n21 * n44 - n11 * n23 * n44) * detInv;
te[10] = (n12 * n24 * n41 - n14 * n22 * n41 + n14 * n21 * n42 - n11 * n24 * n42 - n12 * n21 * n44 + n11 * n22 * n44) * detInv;
te[11] = (n13 * n22 * n41 - n12 * n23 * n41 - n13 * n21 * n42 + n11 * n23 * n42 + n12 * n21 * n43 - n11 * n22 * n43) * detInv;
te[12] = t14 * detInv;
te[13] = (n13 * n24 * n31 - n14 * n23 * n31 + n14 * n21 * n33 - n11 * n24 * n33 - n13 * n21 * n34 + n11 * n23 * n34) * detInv;
te[14] = (n14 * n22 * n31 - n12 * n24 * n31 - n14 * n21 * n32 + n11 * n24 * n32 + n12 * n21 * n34 - n11 * n22 * n34) * detInv;
te[15] = (n12 * n23 * n31 - n13 * n22 * n31 + n13 * n21 * n32 - n11 * n23 * n32 - n12 * n21 * n33 + n11 * n22 * n33) * detInv;
return this;
}
inverted() {
const te = this.elements;
const n11 = te[0]; const n21 = te[1]; const n31 = te[2]; const n41 = te[3];
const n12 = te[4]; const n22 = te[5]; const n32 = te[6]; const n42 = te[7];
const n13 = te[8]; const n23 = te[9]; const n33 = te[10]; const n43 = te[11];
const n14 = te[12]; const n24 = te[13]; const n34 = te[14]; const n44 = te[15];
const t11 = n23 * n34 * n42 - n24 * n33 * n42 + n24 * n32 * n43 - n22 * n34 * n43 - n23 * n32 * n44 + n22 * n33 * n44;
const t12 = n14 * n33 * n42 - n13 * n34 * n42 - n14 * n32 * n43 + n12 * n34 * n43 + n13 * n32 * n44 - n12 * n33 * n44;
const t13 = n13 * n24 * n42 - n14 * n23 * n42 + n14 * n22 * n43 - n12 * n24 * n43 - n13 * n22 * n44 + n12 * n23 * n44;
const t14 = n14 * n23 * n32 - n13 * n24 * n32 - n14 * n22 * n33 + n12 * n24 * n33 + n13 * n22 * n34 - n12 * n23 * n34;
const det = n11 * t11 + n21 * t12 + n31 * t13 + n41 * t14;
if (det === 0) return new Matrix4();
const detInv = 1 / det;
const ne = new Array<number>(16);
ne[0] = t11 * detInv;
ne[1] = (n24 * n33 * n41 - n23 * n34 * n41 - n24 * n31 * n43 + n21 * n34 * n43 + n23 * n31 * n44 - n21 * n33 * n44) * detInv;
ne[2] = (n22 * n34 * n41 - n24 * n32 * n41 + n24 * n31 * n42 - n21 * n34 * n42 - n22 * n31 * n44 + n21 * n32 * n44) * detInv;
ne[3] = (n23 * n32 * n41 - n22 * n33 * n41 - n23 * n31 * n42 + n21 * n33 * n42 + n22 * n31 * n43 - n21 * n32 * n43) * detInv;
ne[4] = t12 * detInv;
ne[5] = (n13 * n34 * n41 - n14 * n33 * n41 + n14 * n31 * n43 - n11 * n34 * n43 - n13 * n31 * n44 + n11 * n33 * n44) * detInv;
ne[6] = (n14 * n32 * n41 - n12 * n34 * n41 - n14 * n31 * n42 + n11 * n34 * n42 + n12 * n31 * n44 - n11 * n32 * n44) * detInv;
ne[7] = (n12 * n33 * n41 - n13 * n32 * n41 + n13 * n31 * n42 - n11 * n33 * n42 - n12 * n31 * n43 + n11 * n32 * n43) * detInv;
ne[8] = t13 * detInv;
ne[9] = (n14 * n23 * n41 - n13 * n24 * n41 - n14 * n21 * n43 + n11 * n24 * n43 + n13 * n21 * n44 - n11 * n23 * n44) * detInv;
ne[10] = (n12 * n24 * n41 - n14 * n22 * n41 + n14 * n21 * n42 - n11 * n24 * n42 - n12 * n21 * n44 + n11 * n22 * n44) * detInv;
ne[11] = (n13 * n22 * n41 - n12 * n23 * n41 - n13 * n21 * n42 + n11 * n23 * n42 + n12 * n21 * n43 - n11 * n22 * n43) * detInv;
ne[12] = t14 * detInv;
ne[13] = (n13 * n24 * n31 - n14 * n23 * n31 + n14 * n21 * n33 - n11 * n24 * n33 - n13 * n21 * n34 + n11 * n23 * n34) * detInv;
ne[14] = (n14 * n22 * n31 - n12 * n24 * n31 - n14 * n21 * n32 + n11 * n24 * n32 + n12 * n21 * n34 - n11 * n22 * n34) * detInv;
ne[15] = (n12 * n23 * n31 - n13 * n22 * n31 + n13 * n21 * n32 - n11 * n23 * n32 - n12 * n21 * n33 + n11 * n22 * n33) * detInv;
const result = new Matrix4();
result.elements = ne;
return result;
}
scale(v: Vector3) {
const te = this.elements;
const x = v.x; const y = v.y; const
z = v.z;
te[0] *= x; te[4] *= y; te[8] *= z;
te[1] *= x; te[5] *= y; te[9] *= z;
te[2] *= x; te[6] *= y; te[10] *= z;
te[3] *= x; te[7] *= y; te[11] *= z;
return this;
}
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));
}
makeTranslation(x: number, y: number, z: number) {
this.set(
1, 0, 0, x,
0, 1, 0, y,
0, 0, 1, z,
0, 0, 0, 1,
);
return this;
}
makeRotationX(theta: number) {
const c = Math.cos(theta); const
s = Math.sin(theta);
this.set(
1, 0, 0, 0,
0, c, -s, 0,
0, s, c, 0,
0, 0, 0, 1,
);
return this;
}
makeRotationY(theta: number) {
const c = Math.cos(theta); const
s = Math.sin(theta);
this.set(
c, 0, s, 0,
0, 1, 0, 0,
-s, 0, c, 0,
0, 0, 0, 1,
);
return this;
}
makeRotationZ(theta: number) {
const c = Math.cos(theta); const
s = Math.sin(theta);
this.set(
c, -s, 0, 0,
s, c, 0, 0,
0, 0, 1, 0,
0, 0, 0, 1,
);
return this;
}
makeRotationAxis(axis: Vector3, angle: number) {
// Based on http://www.gamedev.net/reference/articles/article1199.asp
const c = Math.cos(angle);
const s = Math.sin(angle);
const t = 1 - c;
const x = axis.x; const y = axis.y; const
z = axis.z;
const tx = t * x; const
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;
}
makeScale(x: number, y: number, z: number) {
this.set(
x, 0, 0, 0,
0, y, 0, 0,
0, 0, z, 0,
0, 0, 0, 1,
);
return this;
}
makeShear(x: number, y: number, z: number) {
this.set(
1, y, z, 0,
x, 1, z, 0,
x, y, 1, 0,
0, 0, 0, 1,
);
return this;
}
compose(position: Vector3, quaternion: Quaternion, scale: Vector3) {
const te = this.elements;
const x = quaternion._x; const y = quaternion._y; const z = quaternion._z; const
w = quaternion._w;
const x2 = x + x; const y2 = y + y; const
z2 = z + z;
const xx = x * x2; const xy = x * y2; const
xz = x * z2;
const yy = y * y2; const yz = y * z2; const
zz = z * z2;
const wx = w * x2; const wy = w * y2; const
wz = w * z2;
const sx = scale.x; const sy = scale.y; const
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;
}
decompose(position: Vector3, quaternion: Quaternion, scale: Vector3) {
const te = this.elements;
let sx = _v1.set(te[0], te[1], te[2]).length;
const sy = _v1.set(te[4], te[5], te[6]).length;
const sz = _v1.set(te[8], te[9], te[10]).length;
// if determine is negative, we need to invert one scale
const det = this.determinant();
if (det < 0) sx = -sx;
position.x = te[12];
position.y = te[13];
position.z = te[14];
// scale the rotation part
_m1.copy(this);
const invSX = 1 / sx;
const invSY = 1 / sy;
const invSZ = 1 / sz;
_m1.elements[0] *= invSX;
_m1.elements[1] *= invSX;
_m1.elements[2] *= invSX;
_m1.elements[4] *= invSY;
_m1.elements[5] *= invSY;
_m1.elements[6] *= invSY;
_m1.elements[8] *= invSZ;
_m1.elements[9] *= invSZ;
_m1.elements[10] *= invSZ;
quaternion.setFromRotationMatrix(_m1);
scale.x = sx;
scale.y = sy;
scale.z = sz;
return this;
}
makePerspective(left: number, right: number, top: number, bottom: number, near: number, far: number) {
if (far === undefined) {
console.warn('THREE.Matrix4: .makePerspective() has been redefined and has a new signature. Please check the docs.');
}
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;
}
makeOrthographic(left: number, right: number, top: number, bottom: number, near: number, far: number) {
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;
}
equals(matrix: Matrix4) {
const te = this.elements;
const me = matrix.elements;
for (let i = 0; i < 16; i++) {
if (!(MathUtils.isEqual(te[i], me[i]))) {
return false;
}
}
return true;
}
fromArray(array: number[] | ArrayLike<number>, offset = 0) {
for (let i = 0; i < 16; i++) {
this.elements[i] = array[i + offset];
}
return this;
}
toArray(array: number[] = [], offset = 0) {
const te = this.elements;
array[offset] = te[0];
array[offset + 1] = te[1];
array[offset + 2] = te[2];
array[offset + 3] = te[3];
array[offset + 4] = te[4];
array[offset + 5] = te[5];
array[offset + 6] = te[6];
array[offset + 7] = te[7];
array[offset + 8] = te[8];
array[offset + 9] = te[9];
array[offset + 10] = te[10];
array[offset + 11] = te[11];
array[offset + 12] = te[12];
array[offset + 13] = te[13];
array[offset + 14] = te[14];
array[offset + 15] = te[15];
return array;
}
}
const _m1 = new Matrix4();
export { Matrix4 };