mat2.js

/* Copyright (c) 2015, Brandon Jones, Colin MacKenzie IV.

Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in
all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
THE SOFTWARE. */

import * as glMatrix from "./common.js"

/**
 * 2x2 Matrix
 * @module mat2
 */

/**
 * Creates a new identity mat2
 *
 * @returns {mat2} a new 2x2 matrix
 */
export function create() {
  let out = new glMatrix.ARRAY_TYPE(4);
  out[0] = 1;
  out[1] = 0;
  out[2] = 0;
  out[3] = 1;
  return out;
}

/**
 * Creates a new mat2 initialized with values from an existing matrix
 *
 * @param {mat2} a matrix to clone
 * @returns {mat2} a new 2x2 matrix
 */
export function clone(a) {
  let out = new glMatrix.ARRAY_TYPE(4);
  out[0] = a[0];
  out[1] = a[1];
  out[2] = a[2];
  out[3] = a[3];
  return out;
}

/**
 * Copy the values from one mat2 to another
 *
 * @param {mat2} out the receiving matrix
 * @param {mat2} a the source matrix
 * @returns {mat2} out
 */
export function copy(out, a) {
  out[0] = a[0];
  out[1] = a[1];
  out[2] = a[2];
  out[3] = a[3];
  return out;
}

/**
 * Set a mat2 to the identity matrix
 *
 * @param {mat2} out the receiving matrix
 * @returns {mat2} out
 */
export function identity(out) {
  out[0] = 1;
  out[1] = 0;
  out[2] = 0;
  out[3] = 1;
  return out;
}

/**
 * Create a new mat2 with the given values
 *
 * @param {Number} m00 Component in column 0, row 0 position (index 0)
 * @param {Number} m01 Component in column 0, row 1 position (index 1)
 * @param {Number} m10 Component in column 1, row 0 position (index 2)
 * @param {Number} m11 Component in column 1, row 1 position (index 3)
 * @returns {mat2} out A new 2x2 matrix
 */
export function fromValues(m00, m01, m10, m11) {
  let out = new glMatrix.ARRAY_TYPE(4);
  out[0] = m00;
  out[1] = m01;
  out[2] = m10;
  out[3] = m11;
  return out;
}

/**
 * Set the components of a mat2 to the given values
 *
 * @param {mat2} out the receiving matrix
 * @param {Number} m00 Component in column 0, row 0 position (index 0)
 * @param {Number} m01 Component in column 0, row 1 position (index 1)
 * @param {Number} m10 Component in column 1, row 0 position (index 2)
 * @param {Number} m11 Component in column 1, row 1 position (index 3)
 * @returns {mat2} out
 */
export function set(out, m00, m01, m10, m11) {
  out[0] = m00;
  out[1] = m01;
  out[2] = m10;
  out[3] = m11;
  return out;
}

/**
 * Transpose the values of a mat2
 *
 * @param {mat2} out the receiving matrix
 * @param {mat2} a the source matrix
 * @returns {mat2} out
 */
export function transpose(out, a) {
  // If we are transposing ourselves we can skip a few steps but have to cache
  // some values
  if (out === a) {
    let a1 = a[1];
    out[1] = a[2];
    out[2] = a1;
  } else {
    out[0] = a[0];
    out[1] = a[2];
    out[2] = a[1];
    out[3] = a[3];
  }

  return out;
}

/**
 * Inverts a mat2
 *
 * @param {mat2} out the receiving matrix
 * @param {mat2} a the source matrix
 * @returns {mat2} out
 */
export function invert(out, a) {
  let a0 = a[0], a1 = a[1], a2 = a[2], a3 = a[3];

  // Calculate the determinant
  let det = a0 * a3 - a2 * a1;

  if (!det) {
    return null;
  }
  det = 1.0 / det;

  out[0] =  a3 * det;
  out[1] = -a1 * det;
  out[2] = -a2 * det;
  out[3] =  a0 * det;

  return out;
}

/**
 * Calculates the adjugate of a mat2
 *
 * @param {mat2} out the receiving matrix
 * @param {mat2} a the source matrix
 * @returns {mat2} out
 */
export function adjoint(out, a) {
  // Caching this value is nessecary if out == a
  let a0 = a[0];
  out[0] =  a[3];
  out[1] = -a[1];
  out[2] = -a[2];
  out[3] =  a0;

  return out;
}

/**
 * Calculates the determinant of a mat2
 *
 * @param {mat2} a the source matrix
 * @returns {Number} determinant of a
 */
export function determinant(a) {
  return a[0] * a[3] - a[2] * a[1];
}

/**
 * Multiplies two mat2's
 *
 * @param {mat2} out the receiving matrix
 * @param {mat2} a the first operand
 * @param {mat2} b the second operand
 * @returns {mat2} out
 */
export function multiply(out, a, b) {
  let a0 = a[0], a1 = a[1], a2 = a[2], a3 = a[3];
  let b0 = b[0], b1 = b[1], b2 = b[2], b3 = b[3];
  out[0] = a0 * b0 + a2 * b1;
  out[1] = a1 * b0 + a3 * b1;
  out[2] = a0 * b2 + a2 * b3;
  out[3] = a1 * b2 + a3 * b3;
  return out;
}

/**
 * Rotates a mat2 by the given angle
 *
 * @param {mat2} out the receiving matrix
 * @param {mat2} a the matrix to rotate
 * @param {Number} rad the angle to rotate the matrix by
 * @returns {mat2} out
 */
export function rotate(out, a, rad) {
  let a0 = a[0], a1 = a[1], a2 = a[2], a3 = a[3];
  let s = Math.sin(rad);
  let c = Math.cos(rad);
  out[0] = a0 *  c + a2 * s;
  out[1] = a1 *  c + a3 * s;
  out[2] = a0 * -s + a2 * c;
  out[3] = a1 * -s + a3 * c;
  return out;
}

/**
 * Scales the mat2 by the dimensions in the given vec2
 *
 * @param {mat2} out the receiving matrix
 * @param {mat2} a the matrix to rotate
 * @param {vec2} v the vec2 to scale the matrix by
 * @returns {mat2} out
 **/
export function scale(out, a, v) {
  let a0 = a[0], a1 = a[1], a2 = a[2], a3 = a[3];
  let v0 = v[0], v1 = v[1];
  out[0] = a0 * v0;
  out[1] = a1 * v0;
  out[2] = a2 * v1;
  out[3] = a3 * v1;
  return out;
}

/**
 * Creates a matrix from a given angle
 * This is equivalent to (but much faster than):
 *
 *     mat2.identity(dest);
 *     mat2.rotate(dest, dest, rad);
 *
 * @param {mat2} out mat2 receiving operation result
 * @param {Number} rad the angle to rotate the matrix by
 * @returns {mat2} out
 */
export function fromRotation(out, rad) {
  let s = Math.sin(rad);
  let c = Math.cos(rad);
  out[0] = c;
  out[1] = s;
  out[2] = -s;
  out[3] = c;
  return out;
}

/**
 * Creates a matrix from a vector scaling
 * This is equivalent to (but much faster than):
 *
 *     mat2.identity(dest);
 *     mat2.scale(dest, dest, vec);
 *
 * @param {mat2} out mat2 receiving operation result
 * @param {vec2} v Scaling vector
 * @returns {mat2} out
 */
export function fromScaling(out, v) {
  out[0] = v[0];
  out[1] = 0;
  out[2] = 0;
  out[3] = v[1];
  return out;
}

/**
 * Returns a string representation of a mat2
 *
 * @param {mat2} a matrix to represent as a string
 * @returns {String} string representation of the matrix
 */
export function str(a) {
  return 'mat2(' + a[0] + ', ' + a[1] + ', ' + a[2] + ', ' + a[3] + ')';
}

/**
 * Returns Frobenius norm of a mat2
 *
 * @param {mat2} a the matrix to calculate Frobenius norm of
 * @returns {Number} Frobenius norm
 */
export function frob(a) {
  return(Math.sqrt(Math.pow(a[0], 2) + Math.pow(a[1], 2) + Math.pow(a[2], 2) + Math.pow(a[3], 2)))
}

/**
 * Returns L, D and U matrices (Lower triangular, Diagonal and Upper triangular) by factorizing the input matrix
 * @param {mat2} L the lower triangular matrix
 * @param {mat2} D the diagonal matrix
 * @param {mat2} U the upper triangular matrix
 * @param {mat2} a the input matrix to factorize
 */

export function LDU(L, D, U, a) {
  L[2] = a[2]/a[0];
  U[0] = a[0];
  U[1] = a[1];
  U[3] = a[3] - L[2] * U[1];
  return [L, D, U];
}

/**
 * Adds two mat2's
 *
 * @param {mat2} out the receiving matrix
 * @param {mat2} a the first operand
 * @param {mat2} b the second operand
 * @returns {mat2} out
 */
export function add(out, a, b) {
  out[0] = a[0] + b[0];
  out[1] = a[1] + b[1];
  out[2] = a[2] + b[2];
  out[3] = a[3] + b[3];
  return out;
}

/**
 * Subtracts matrix b from matrix a
 *
 * @param {mat2} out the receiving matrix
 * @param {mat2} a the first operand
 * @param {mat2} b the second operand
 * @returns {mat2} out
 */
export function subtract(out, a, b) {
  out[0] = a[0] - b[0];
  out[1] = a[1] - b[1];
  out[2] = a[2] - b[2];
  out[3] = a[3] - b[3];
  return out;
}

/**
 * Returns whether or not the matrices have exactly the same elements in the same position (when compared with ===)
 *
 * @param {mat2} a The first matrix.
 * @param {mat2} b The second matrix.
 * @returns {Boolean} True if the matrices are equal, false otherwise.
 */
export function exactEquals(a, b) {
  return a[0] === b[0] && a[1] === b[1] && a[2] === b[2] && a[3] === b[3];
}

/**
 * Returns whether or not the matrices have approximately the same elements in the same position.
 *
 * @param {mat2} a The first matrix.
 * @param {mat2} b The second matrix.
 * @returns {Boolean} True if the matrices are equal, false otherwise.
 */
export function equals(a, b) {
  let a0 = a[0], a1 = a[1], a2 = a[2], a3 = a[3];
  let b0 = b[0], b1 = b[1], b2 = b[2], b3 = b[3];
  return (Math.abs(a0 - b0) <= glMatrix.EPSILON*Math.max(1.0, Math.abs(a0), Math.abs(b0)) &&
          Math.abs(a1 - b1) <= glMatrix.EPSILON*Math.max(1.0, Math.abs(a1), Math.abs(b1)) &&
          Math.abs(a2 - b2) <= glMatrix.EPSILON*Math.max(1.0, Math.abs(a2), Math.abs(b2)) &&
          Math.abs(a3 - b3) <= glMatrix.EPSILON*Math.max(1.0, Math.abs(a3), Math.abs(b3)));
}

/**
 * Multiply each element of the matrix by a scalar.
 *
 * @param {mat2} out the receiving matrix
 * @param {mat2} a the matrix to scale
 * @param {Number} b amount to scale the matrix's elements by
 * @returns {mat2} out
 */
export function multiplyScalar(out, a, b) {
  out[0] = a[0] * b;
  out[1] = a[1] * b;
  out[2] = a[2] * b;
  out[3] = a[3] * b;
  return out;
}

/**
 * Adds two mat2's after multiplying each element of the second operand by a scalar value.
 *
 * @param {mat2} out the receiving vector
 * @param {mat2} a the first operand
 * @param {mat2} b the second operand
 * @param {Number} scale the amount to scale b's elements by before adding
 * @returns {mat2} out
 */
export function multiplyScalarAndAdd(out, a, b, scale) {
  out[0] = a[0] + (b[0] * scale);
  out[1] = a[1] + (b[1] * scale);
  out[2] = a[2] + (b[2] * scale);
  out[3] = a[3] + (b[3] * scale);
  return out;
}

/**
 * Alias for {@link mat2.multiply}
 * @function
 */
export const mul = multiply;

/**
 * Alias for {@link mat2.subtract}
 * @function
 */
export const sub = subtract;