Source: ui/gl_matrix/matrix_4x4.js

/*! @license
 * glMatrix: https://github.com/toji/gl-matrix/
 * Copyright 2015-2021, Brandon Jones, Colin MacKenzie IV
 * SPDX-License-Identifier: MIT
 */
goog.provide('shaka.ui.Matrix4x4');
/**
 * 4x4 Matrix
 * Format: column-major, when typed out it looks like row-major
 * The matrices are being post multiplied.
 */
shaka.ui.Matrix4x4 = class {
  /**
   * Creates a new identity 4x4 Matrix
   *
   * @return {!Float32Array} a new 4x4 matrix
   */
  static create() {
    const out = new Float32Array(16);
    out[0] = 1;
    out[5] = 1;
    out[10] = 1;
    out[15] = 1;
    return out;
  }
  /**
   * Generates a look-at matrix with the given eye position, focal point, and
   * up axis.
   *
   * @param {!Float32Array} out 4x4 matrix frustum matrix will be written into
   * @param {!Array<number>} eye Position of the viewer
   * @param {!Array<number>} center Point the viewer is looking at
   * @param {!Array<number>} up Vector pointing up
   * @return {!Float32Array}
   */
  static lookAt(out, eye, center, up) {
    let x0;
    let x1;
    let x2;
    let y0;
    let y1;
    let y2;
    let z0;
    let z1;
    let z2;
    let len;
    const eyex = eye[0];
    const eyey = eye[1];
    const eyez = eye[2];
    const upx = up[0];
    const upy = up[1];
    const upz = up[2];
    const centerx = center[0];
    const centery = center[1];
    const centerz = center[2];
    if (Math.abs(eyex - centerx) < shaka.ui.Matrix4x4.EPSILON_ &&
      Math.abs(eyey - centery) < shaka.ui.Matrix4x4.EPSILON_ &&
      Math.abs(eyez - centerz) < shaka.ui.Matrix4x4.EPSILON_) {
      return shaka.ui.Matrix4x4.identity_(out);
    }
    z0 = eyex - centerx;
    z1 = eyey - centery;
    z2 = eyez - centerz;
    len = 1 / Math.sqrt(z0 * z0 + z1 * z1 + z2 * z2);
    z0 *= len;
    z1 *= len;
    z2 *= len;
    x0 = upy * z2 - upz * z1;
    x1 = upz * z0 - upx * z2;
    x2 = upx * z1 - upy * z0;
    len = Math.sqrt(x0 * x0 + x1 * x1 + x2 * x2);
    if (!len) {
      x0 = 0;
      x1 = 0;
      x2 = 0;
    } else {
      len = 1 / len;
      x0 *= len;
      x1 *= len;
      x2 *= len;
    }
    y0 = z1 * x2 - z2 * x1;
    y1 = z2 * x0 - z0 * x2;
    y2 = z0 * x1 - z1 * x0;
    len = Math.sqrt(y0 * y0 + y1 * y1 + y2 * y2);
    if (!len) {
      y0 = 0;
      y1 = 0;
      y2 = 0;
    } else {
      len = 1 / len;
      y0 *= len;
      y1 *= len;
      y2 *= len;
    }
    out[0] = x0;
    out[1] = y0;
    out[2] = z0;
    out[3] = 0;
    out[4] = x1;
    out[5] = y1;
    out[6] = z1;
    out[7] = 0;
    out[8] = x2;
    out[9] = y2;
    out[10] = z2;
    out[11] = 0;
    out[12] = -(x0 * eyex + x1 * eyey + x2 * eyez);
    out[13] = -(y0 * eyex + y1 * eyey + y2 * eyez);
    out[14] = -(z0 * eyex + z1 * eyey + z2 * eyez);
    out[15] = 1;
    return out;
  }
  /**
   * Scales the 4x4 matrix by the dimensions in the given vector not using
   * vectorization
   *
   * @param {!Float32Array} out the receiving matrix
   * @param {!Float32Array} a the matrix to scale
   * @param {!Array<number>} v the vector to scale the matrix by
   */
  static scale(out, a, v) {
    const x = v[0];
    const y = v[1];
    const z = v[2];
    out[0] = a[0] * x;
    out[1] = a[1] * x;
    out[2] = a[2] * x;
    out[3] = a[3] * x;
    out[4] = a[4] * y;
    out[5] = a[5] * y;
    out[6] = a[6] * y;
    out[7] = a[7] * y;
    out[8] = a[8] * z;
    out[9] = a[9] * z;
    out[10] = a[10] * z;
    out[11] = a[11] * z;
    out[12] = a[12];
    out[13] = a[13];
    out[14] = a[14];
    out[15] = a[15];
  }
  /**
   * Generates a perspective projection matrix with the given bounds.
   * The near/far clip planes correspond to a normalized device coordinate Z
   * range of [-1, 1], which matches WebGL's clip volume.
   * Passing null/undefined/no value for far will generate infinite projection
   * matrix.
   *
   * @param {!Float32Array} out 4x4 matrix frustum matrix will be written into
   * @param {number} fovy Vertical field of view in radians
   * @param {number} aspect Aspect ratio. typically viewport width/height
   * @param {number} near Near bound of the frustum
   * @param {number} far Far bound of the frustum, can be null or Infinity
   * @return {!Float32Array}
   */
  static perspective(out, fovy, aspect, near, far) {
    const f = 1.0 / Math.tan(fovy / 2);
    out[0] = f / aspect;
    out[1] = 0;
    out[2] = 0;
    out[3] = 0;
    out[4] = 0;
    out[5] = f;
    out[6] = 0;
    out[7] = 0;
    out[8] = 0;
    out[9] = 0;
    out[11] = -1;
    out[12] = 0;
    out[13] = 0;
    out[15] = 0;
    if (far != null && far !== Infinity) {
      const nf = 1 / (near - far);
      out[10] = (far + near) * nf;
      out[14] = 2 * far * near * nf;
    } else {
      out[10] = -1;
      out[14] = -2 * near;
    }
    return out;
  }
  /**
   * Multiplies two 4x4 matrix
   *
   * @param {!Float32Array} out the receiving matrix
   * @param {!Float32Array} a the first operand
   * @param {!Float32Array} b the second operand
   */
  static multiply(out, a, b) {
    const a00 = a[0];
    const a01 = a[1];
    const a02 = a[2];
    const a03 = a[3];
    const a10 = a[4];
    const a11 = a[5];
    const a12 = a[6];
    const a13 = a[7];
    const a20 = a[8];
    const a21 = a[9];
    const a22 = a[10];
    const a23 = a[11];
    const a30 = a[12];
    const a31 = a[13];
    const a32 = a[14];
    const a33 = a[15];
    // Cache only the current line of the second matrix
    let b0 = b[0];
    let b1 = b[1];
    let b2 = b[2];
    let b3 = b[3];
    out[0] = b0 * a00 + b1 * a10 + b2 * a20 + b3 * a30;
    out[1] = b0 * a01 + b1 * a11 + b2 * a21 + b3 * a31;
    out[2] = b0 * a02 + b1 * a12 + b2 * a22 + b3 * a32;
    out[3] = b0 * a03 + b1 * a13 + b2 * a23 + b3 * a33;
    b0 = b[4];
    b1 = b[5];
    b2 = b[6];
    b3 = b[7];
    out[4] = b0 * a00 + b1 * a10 + b2 * a20 + b3 * a30;
    out[5] = b0 * a01 + b1 * a11 + b2 * a21 + b3 * a31;
    out[6] = b0 * a02 + b1 * a12 + b2 * a22 + b3 * a32;
    out[7] = b0 * a03 + b1 * a13 + b2 * a23 + b3 * a33;
    b0 = b[8];
    b1 = b[9];
    b2 = b[10];
    b3 = b[11];
    out[8] = b0 * a00 + b1 * a10 + b2 * a20 + b3 * a30;
    out[9] = b0 * a01 + b1 * a11 + b2 * a21 + b3 * a31;
    out[10] = b0 * a02 + b1 * a12 + b2 * a22 + b3 * a32;
    out[11] = b0 * a03 + b1 * a13 + b2 * a23 + b3 * a33;
    b0 = b[12];
    b1 = b[13];
    b2 = b[14];
    b3 = b[15];
    out[12] = b0 * a00 + b1 * a10 + b2 * a20 + b3 * a30;
    out[13] = b0 * a01 + b1 * a11 + b2 * a21 + b3 * a31;
    out[14] = b0 * a02 + b1 * a12 + b2 * a22 + b3 * a32;
    out[15] = b0 * a03 + b1 * a13 + b2 * a23 + b3 * a33;
  }
  /**
   * Generates a frustum matrix with the given bounds
   *
   * @param {!Float32Array} out 4x4 matrix frustum matrix will be written into
   * @param {number} left Left bound of the frustum
   * @param {number} right Right bound of the frustum
   * @param {number} bottom Bottom bound of the frustum
   * @param {number} top Top bound of the frustum
   * @param {number} near Near bound of the frustum
   * @param {number} far Far bound of the frustum
   * @return {!Float32Array}
   */
  static frustum(out, left, right, bottom, top, near, far) {
    const rl = 1 / (right - left);
    const tb = 1 / (top - bottom);
    const nf = 1 / (near - far);
    out[0] = near * 2 * rl;
    out[1] = 0;
    out[2] = 0;
    out[3] = 0;
    out[4] = 0;
    out[5] = near * 2 * tb;
    out[6] = 0;
    out[7] = 0;
    out[8] = (right + left) * rl;
    out[9] = (top + bottom) * tb;
    out[10] = (far + near) * nf;
    out[11] = -1;
    out[12] = 0;
    out[13] = 0;
    out[14] = far * near * 2 * nf;
    out[15] = 0;
    return out;
  }
  /**
   * Rotates a matrix by the given angle around the X axis
   *
   * @param {!Float32Array} out the receiving matrix
   * @param {!Float32Array} a the matrix to rotate
   * @param {number} rad the angle to rotate the matrix by
   */
  static rotateX(out, a, rad) {
    const s = Math.sin(rad);
    const c = Math.cos(rad);
    const a10 = a[4];
    const a11 = a[5];
    const a12 = a[6];
    const a13 = a[7];
    const a20 = a[8];
    const a21 = a[9];
    const a22 = a[10];
    const a23 = a[11];
    if (a !== out) {
      // If the source and destination differ, copy the unchanged rows
      out[0] = a[0];
      out[1] = a[1];
      out[2] = a[2];
      out[3] = a[3];
      out[12] = a[12];
      out[13] = a[13];
      out[14] = a[14];
      out[15] = a[15];
    }
    // Perform axis-specific matrix multiplication
    out[4] = a10 * c + a20 * s;
    out[5] = a11 * c + a21 * s;
    out[6] = a12 * c + a22 * s;
    out[7] = a13 * c + a23 * s;
    out[8] = a20 * c - a10 * s;
    out[9] = a21 * c - a11 * s;
    out[10] = a22 * c - a12 * s;
    out[11] = a23 * c - a13 * s;
  }
  /**
   * Rotates a matrix by the given angle around the Y axis
   *
   * @param {!Float32Array} out the receiving matrix
   * @param {!Float32Array} a the matrix to rotate
   * @param {number} rad the angle to rotate the matrix by
   */
  static rotateY(out, a, rad) {
    const s = Math.sin(rad);
    const c = Math.cos(rad);
    const a00 = a[0];
    const a01 = a[1];
    const a02 = a[2];
    const a03 = a[3];
    const a20 = a[8];
    const a21 = a[9];
    const a22 = a[10];
    const a23 = a[11];
    if (a !== out) {
      // If the source and destination differ, copy the unchanged rows
      out[4] = a[4];
      out[5] = a[5];
      out[6] = a[6];
      out[7] = a[7];
      out[12] = a[12];
      out[13] = a[13];
      out[14] = a[14];
      out[15] = a[15];
    }
    // Perform axis-specific matrix multiplication
    out[0] = a00 * c - a20 * s;
    out[1] = a01 * c - a21 * s;
    out[2] = a02 * c - a22 * s;
    out[3] = a03 * c - a23 * s;
    out[8] = a00 * s + a20 * c;
    out[9] = a01 * s + a21 * c;
    out[10] = a02 * s + a22 * c;
    out[11] = a03 * s + a23 * c;
  }
  /**
   * Rotates a matrix by the given angle around the Z axis
   *
   * @param {!Float32Array} out the receiving matrix
   * @param {!Float32Array} a the matrix to rotate
   * @param {number} rad the angle to rotate the matrix by
   */
  static rotateZ(out, a, rad) {
    const s = Math.sin(rad);
    const c = Math.cos(rad);
    const a00 = a[0];
    const a01 = a[1];
    const a02 = a[2];
    const a03 = a[3];
    const a10 = a[4];
    const a11 = a[5];
    const a12 = a[6];
    const a13 = a[7];
    if (a !== out) {
      // If the source and destination differ, copy the unchanged last row
      out[8] = a[8];
      out[9] = a[9];
      out[10] = a[10];
      out[11] = a[11];
      out[12] = a[12];
      out[13] = a[13];
      out[14] = a[14];
      out[15] = a[15];
    }
    // Perform axis-specific matrix multiplication
    out[0] = a00 * c + a10 * s;
    out[1] = a01 * c + a11 * s;
    out[2] = a02 * c + a12 * s;
    out[3] = a03 * c + a13 * s;
    out[4] = a10 * c - a00 * s;
    out[5] = a11 * c - a01 * s;
    out[6] = a12 * c - a02 * s;
    out[7] = a13 * c - a03 * s;
  }
  /**
   * Returns a quaternion representing the rotational component
   * of a transformation matrix. If a matrix is built with
   * fromRotationTranslation, the returned quaternion will be the
   * same as the quaternion originally supplied.
   * @param {!Float32Array} out Quaternion to receive the rotation component
   * @param {!Float32Array} mat Matrix to be decomposed (input)
   * @return {!Float32Array}
   */
  static getRotation(out, mat) {
    const scaling = new Float32Array(3);
    shaka.ui.Matrix4x4.getScaling_(scaling, mat);
    const is1 = 1 / scaling[0];
    const is2 = 1 / scaling[1];
    const is3 = 1 / scaling[2];
    const sm11 = mat[0] * is1;
    const sm12 = mat[1] * is2;
    const sm13 = mat[2] * is3;
    const sm21 = mat[4] * is1;
    const sm22 = mat[5] * is2;
    const sm23 = mat[6] * is3;
    const sm31 = mat[8] * is1;
    const sm32 = mat[9] * is2;
    const sm33 = mat[10] * is3;
    const trace = sm11 + sm22 + sm33;
    let S = 0;
    if (trace > 0) {
      S = Math.sqrt(trace + 1.0) * 2;
      out[3] = 0.25 * S;
      out[0] = (sm23 - sm32) / S;
      out[1] = (sm31 - sm13) / S;
      out[2] = (sm12 - sm21) / S;
    } else if (sm11 > sm22 && sm11 > sm33) {
      S = Math.sqrt(1.0 + sm11 - sm22 - sm33) * 2;
      out[3] = (sm23 - sm32) / S;
      out[0] = 0.25 * S;
      out[1] = (sm12 + sm21) / S;
      out[2] = (sm31 + sm13) / S;
    } else if (sm22 > sm33) {
      S = Math.sqrt(1.0 + sm22 - sm11 - sm33) * 2;
      out[3] = (sm31 - sm13) / S;
      out[0] = (sm12 + sm21) / S;
      out[1] = 0.25 * S;
      out[2] = (sm23 + sm32) / S;
    } else {
      S = Math.sqrt(1.0 + sm33 - sm11 - sm22) * 2;
      out[3] = (sm12 - sm21) / S;
      out[0] = (sm31 + sm13) / S;
      out[1] = (sm23 + sm32) / S;
      out[2] = 0.25 * S;
    }
    return out;
  }
  /**
   * Calculates a 4x4 matrix from the given quaternion
   *
   * @param {!Float32Array} out 4x4 matrix receiving operation result
   * @param {!Float32Array} q Quaternion to create matrix from
   */
  static fromQuat(out, q) {
    const x = q[0];
    const y = q[1];
    const z = q[2];
    const w = q[3];
    const x2 = x + x;
    const y2 = y + y;
    const z2 = z + z;
    const xx = x * x2;
    const yx = y * x2;
    const yy = y * y2;
    const zx = z * x2;
    const zy = z * y2;
    const zz = z * z2;
    const wx = w * x2;
    const wy = w * y2;
    const wz = w * z2;
    out[0] = 1 - yy - zz;
    out[1] = yx + wz;
    out[2] = zx - wy;
    out[3] = 0;
    out[4] = yx - wz;
    out[5] = 1 - xx - zz;
    out[6] = zy + wx;
    out[7] = 0;
    out[8] = zx + wy;
    out[9] = zy - wx;
    out[10] = 1 - xx - yy;
    out[11] = 0;
    out[12] = 0;
    out[13] = 0;
    out[14] = 0;
    out[15] = 1;
  }
  /**
   * Set a 4x4 matrix to the identity matrix
   *
   * @param {!Float32Array} out the receiving matrix
   * @return {!Float32Array}
   * @private
   */
  static identity_(out) {
    for (let i = 0; i < 16; i++) {
      out[i] = (i % 5) == 0 ? 1 : 0;
    }
    return out;
  }
  /**
   * Returns the scaling factor component of a transformation
   * matrix. If a matrix is built with fromRotationTranslationScale
   * with a normalized Quaternion parameter, the returned vector will be
   * the same as the scaling vector
   * originally supplied.
   * @param  {!Float32Array} out Vector to receive scaling factor component
   * @param  {!Float32Array} mat Matrix to be decomposed (input)
   * @private
   */
  static getScaling_(out, mat) {
    const m11 = mat[0];
    const m12 = mat[1];
    const m13 = mat[2];
    const m21 = mat[4];
    const m22 = mat[5];
    const m23 = mat[6];
    const m31 = mat[8];
    const m32 = mat[9];
    const m33 = mat[10];
    out[0] = Math.sqrt(m11 * m11 + m12 * m12 + m13 * m13);
    out[1] = Math.sqrt(m21 * m21 + m22 * m22 + m23 * m23);
    out[2] = Math.sqrt(m31 * m31 + m32 * m32 + m33 * m33);
  }
};
/**
 * @const {number}
 * @private
 */
shaka.ui.Matrix4x4.EPSILON_ = 0.000001;