@xtor/cga.js/src/math/Mat4.ts

Xtor Compute Geometry Algorithm Libary 计算几何算法库

import { Vec3, v3 } from './Vec3';
import { Euler } from './Euler';

export class Mat4 {
  elements: number[] = [1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1];
  isMat4: boolean = true;
  constructor() {
    if (arguments.length > 0) {
      console.error(
        " Mat4: 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
  ) {
    var 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;
  }

  static get Identity() {
    return new Mat4();
  }

  identity() {
    this.set(1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1);

    return this;
  }

  clone() {
    return new Mat4().fromArray(this.elements);
  }

  copy(m: Mat4) {
    var te = this.elements;
    var 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: { elements: any; }) {
    var te = this.elements,
      me = m.elements;

    te[12] = me[12];
    te[13] = me[13];
    te[14] = me[14];

    return this;
  }

  extractBasis(xAxis: Vec3, yAxis: Vec3, zAxis: Vec3) {
    xAxis.setFromMatrixColumn(this, 0);
    yAxis.setFromMatrixColumn(this, 1);
    zAxis.setFromMatrixColumn(this, 2);

    return this;
  }

  makeBasis(xAxis: Vec3, yAxis: Vec3, zAxis: Vec3) {
    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: Mat4) {
    // this method does not support reflection matrices

    var te = this.elements;
    var me = m.elements;

    var scaleX = 1 / _v1.setFromMatrixColumn(m, 0).length();
    var scaleY = 1 / _v1.setFromMatrixColumn(m, 1).length();
    var 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) {
    if (!(euler && euler.isEuler)) {
      console.error(
        " Mat4: .makeRotationFromEuler() now expects a Euler rotation rather than a Vec3 and order."
      );
    }

    var te = this.elements;

    var x = euler.x,
      y = euler.y,
      z = euler.z;
    var a = Math.cos(x),
      b = Math.sin(x);
    var c = Math.cos(y),
      d = Math.sin(y);
    var e = Math.cos(z),
      f = Math.sin(z);

    if (euler.order === "XYZ") {
      var 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;
    } else if (euler.order === "YXZ") {
      var 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;
    } else if (euler.order === "ZXY") {
      var 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;
    } else if (euler.order === "ZYX") {
      var 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;
    } else if (euler.order === "YZX") {
      var 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;
    } else if (euler.order === "XZY") {
      var 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;
    }

    // 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;
  }

  makeRotationFromQuat(q: any) {
    return this.compose(_zero, q, _one);
  }

  lookAt(eye: Vec3, target: Vec3, up: Vec3) {
    var te = this.elements;

    _z.subVecs(eye, target);

    if (_z.lengthSq() === 0) {
      // eye and target are in the same position

      _z.z = 1;
    }

    _z.normalize();
    _x.crossVecs(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.crossVecs(up, _z);
    }

    _x.normalize();
    _y.crossVecs(_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: Mat4, n: Mat4) {
    if (n !== undefined) {
      return this.multiplyMatrices(m, n);
    }

    return this.multiplyMatrices(this, m);
  }

  premultiply(m: Mat4) {
    return this.multiplyMatrices(m, this);
  }

  multiplyMatrices(a: Mat4, b: Mat4) {
    var ae = a.elements;
    var be = b.elements;
    var te = this.elements;

    var a11 = ae[0],
      a12 = ae[4],
      a13 = ae[8],
      a14 = ae[12];
    var a21 = ae[1],
      a22 = ae[5],
      a23 = ae[9],
      a24 = ae[13];
    var a31 = ae[2],
      a32 = ae[6],
      a33 = ae[10],
      a34 = ae[14];
    var a41 = ae[3],
      a42 = ae[7],
      a43 = ae[11],
      a44 = ae[15];

    var b11 = be[0],
      b12 = be[4],
      b13 = be[8],
      b14 = be[12];
    var b21 = be[1],
      b22 = be[5],
      b23 = be[9],
      b24 = be[13];
    var b31 = be[2],
      b32 = be[6],
      b33 = be[10],
      b34 = be[14];
    var b41 = be[3],
      b42 = be[7],
      b43 = be[11],
      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) {
    var 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;
  }

  applyToBufferAttribute(attribute: { count: any; getX: (arg0: number) => number; getY: (arg0: number) => number; getZ: (arg0: number) => number; setXYZ: (arg0: number, arg1: number, arg2: number, arg3: number) => void; }) {
    for (var i = 0, l = attribute.count; i < l; i++) {
      _v1.x = attribute.getX(i);
      _v1.y = attribute.getY(i);
      _v1.z = attribute.getZ(i);

      _v1.applyMat4(this);

      attribute.setXYZ(i, _v1.x, _v1.y, _v1.z);
    }

    return attribute;
  }

  determinant() {
    var te = this.elements;

    var n11 = te[0],
      n12 = te[4],
      n13 = te[8],
      n14 = te[12];
    var n21 = te[1],
      n22 = te[5],
      n23 = te[9],
      n24 = te[13];
    var n31 = te[2],
      n32 = te[6],
      n33 = te[10],
      n34 = te[14];
    var n41 = te[3],
      n42 = te[7],
      n43 = te[11],
      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() {
    var te = this.elements;
    var tmp;

    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: number | Vec3 | any, y: number, z: number) {
    var te = this.elements;

    if (x.isVec3) {
      te[12] = x.x;
      te[13] = x.y;
      te[14] = x.z;
    } else {
      te[12] = x;
      te[13] = y;
      te[14] = z;
    }

    return this;
  }

  getInverse(m: { elements: any; }, throwOnDegenerate: boolean) {
    // based on http://www.euclideanspace.com/maths/algebra/matrix/functions/inverse/fourD/index.htm
    var te = this.elements,
      me = m.elements,
      n11 = me[0],
      n21 = me[1],
      n31 = me[2],
      n41 = me[3],
      n12 = me[4],
      n22 = me[5],
      n32 = me[6],
      n42 = me[7],
      n13 = me[8],
      n23 = me[9],
      n33 = me[10],
      n43 = me[11],
      n14 = me[12],
      n24 = me[13],
      n34 = me[14],
      n44 = me[15],
      t11 =
        n23 * n34 * n42 -
        n24 * n33 * n42 +
        n24 * n32 * n43 -
        n22 * n34 * n43 -
        n23 * n32 * n44 +
        n22 * n33 * n44,
      t12 =
        n14 * n33 * n42 -
        n13 * n34 * n42 -
        n14 * n32 * n43 +
        n12 * n34 * n43 +
        n13 * n32 * n44 -
        n12 * n33 * n44,
      t13 =
        n13 * n24 * n42 -
        n14 * n23 * n42 +
        n14 * n22 * n43 -
        n12 * n24 * n43 -
        n13 * n22 * n44 +
        n12 * n23 * n44,
      t14 =
        n14 * n23 * n32 -
        n13 * n24 * n32 -
        n14 * n22 * n33 +
        n12 * n24 * n33 +
        n13 * n22 * n34 -
        n12 * n23 * n34;

    var det = n11 * t11 + n21 * t12 + n31 * t13 + n41 * t14;

    if (det === 0) {
      var msg = " Mat4: .getInverse() can't invert matrix, determinant is 0";

      if (throwOnDegenerate === true) {
        throw new Error(msg);
      } else {
        console.warn(msg);
      }

      return this.identity();
    }

    var 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;
  }

  scale(v: { x: any; y: any; z: any; }) {
    var te = this.elements;
    var x = v.x,
      y = v.y,
      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() {
    var te = this.elements;

    var scaleXSq = te[0] * te[0] + te[1] * te[1] + te[2] * te[2];
    var scaleYSq = te[4] * te[4] + te[5] * te[5] + te[6] * te[6];
    var 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) {
    var 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;
  }

  makeRotationY(theta: number) {
    var 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;
  }

  makeRotationZ(theta: number) {
    var 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;
  }

  makeRotationAxis(axis: { x: any; y: any; z: any; }, angle: number) {
    // Based on http://www.gamedev.net/reference/articles/article1199.asp

    var c = Math.cos(angle);
    var s = Math.sin(angle);
    var t = 1 - c;
    var x = axis.x,
      y = axis.y,
      z = axis.z;
    var 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;
  }

  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: Vec3, Quat: { _x: any; _y: any; _z: any; _w: any; }, scale: Euler|Vec3) {
    var te = this.elements;

    var x = Quat._x,
      y = Quat._y,
      z = Quat._z,
      w = Quat._w;
    var x2 = x + x,
      y2 = y + y,
      z2 = z + z;
    var xx = x * x2,
      xy = x * y2,
      xz = x * z2;
    var yy = y * y2,
      yz = y * z2,
      zz = z * z2;
    var wx = w * x2,
      wy = w * y2,
      wz = w * z2;

    var 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;
  }

  decompose(position: Vec3, Quat: { setFromRotationMatrix: (arg0: Mat4) => void; }, scale: Vec3) {
    var te = this.elements;

    var sx = _v1.set(te[0], te[1], te[2]).length();
    var sy = _v1.set(te[4], te[5], te[6]).length();
    var sz = _v1.set(te[8], te[9], te[10]).length();

    // if determine is negative, we need to invert one scale
    var 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);

    var invSX = 1 / sx;
    var invSY = 1 / sy;
    var 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;

    Quat.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(
        " Mat4: .makePerspective() has been redefined and has a new signature. Please check the docs."
      );
    }

    var te = this.elements;
    var x = (2 * near) / (right - left);
    var y = (2 * near) / (top - bottom);

    var a = (right + left) / (right - left);
    var b = (top + bottom) / (top - bottom);
    var c = -(far + near) / (far - near);
    var 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) {
    var te = this.elements;
    var w = 1.0 / (right - left);
    var h = 1.0 / (top - bottom);
    var p = 1.0 / (far - near);

    var x = (right + left) * w;
    var y = (top + bottom) * h;
    var 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: { elements: any; }) {
    var te = this.elements;
    var me = matrix.elements;

    for (var i = 0; i < 16; i++) {
      if (te[i] !== me[i]) return false;
    }

    return true;
  }

  fromArray(array: number[], offset: number = 0) {
    for (var i = 0; i < 16; i++) {
      this.elements[i] = array[i + offset];
    }

    return this;
  }

  toArray(array: number[] = [], offset: number = 0) {
    var 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 _v1 = v3();
const _m1 = m4();
const _zero = v3(0, 0, 0);
const _one = v3(1, 1, 1);
const _x = v3();
const _y = v3();
const _z = v3();

export function m4() {
  return new Mat4();
}