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    <h1 class="page-title">Source: mat2d.js</h1>

    
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            <pre class="prettyprint source linenums"><code>import * as glMatrix from "./common.js";

/**
 * 2x3 Matrix
 * @module mat2d
 *
 * @description
 * A mat2d contains six elements defined as:
 * &lt;pre>
 * [a, c, tx,
 *  b, d, ty]
 * &lt;/pre>
 * This is a short form for the 3x3 matrix:
 * &lt;pre>
 * [a, c, tx,
 *  b, d, ty,
 *  0, 0, 1]
 * &lt;/pre>
 * The last row is ignored so the array is shorter and operations are faster.
 */

/**
 * Creates a new identity mat2d
 *
 * @returns {mat2d} a new 2x3 matrix
 */
export function create() {
  let out = new glMatrix.ARRAY_TYPE(6);
  if(glMatrix.ARRAY_TYPE != Float32Array) {
    out[1] = 0;
    out[2] = 0;
    out[4] = 0;
    out[5] = 0;
  }
  out[0] = 1;
  out[3] = 1;
  return out;
}

/**
 * Creates a new mat2d initialized with values from an existing matrix
 *
 * @param {mat2d} a matrix to clone
 * @returns {mat2d} a new 2x3 matrix
 */
export function clone(a) {
  let out = new glMatrix.ARRAY_TYPE(6);
  out[0] = a[0];
  out[1] = a[1];
  out[2] = a[2];
  out[3] = a[3];
  out[4] = a[4];
  out[5] = a[5];
  return out;
}

/**
 * Copy the values from one mat2d to another
 *
 * @param {mat2d} out the receiving matrix
 * @param {mat2d} a the source matrix
 * @returns {mat2d} out
 */
export function copy(out, a) {
  out[0] = a[0];
  out[1] = a[1];
  out[2] = a[2];
  out[3] = a[3];
  out[4] = a[4];
  out[5] = a[5];
  return out;
}

/**
 * Set a mat2d to the identity matrix
 *
 * @param {mat2d} out the receiving matrix
 * @returns {mat2d} out
 */
export function identity(out) {
  out[0] = 1;
  out[1] = 0;
  out[2] = 0;
  out[3] = 1;
  out[4] = 0;
  out[5] = 0;
  return out;
}

/**
 * Create a new mat2d with the given values
 *
 * @param {Number} a Component A (index 0)
 * @param {Number} b Component B (index 1)
 * @param {Number} c Component C (index 2)
 * @param {Number} d Component D (index 3)
 * @param {Number} tx Component TX (index 4)
 * @param {Number} ty Component TY (index 5)
 * @returns {mat2d} A new mat2d
 */
export function fromValues(a, b, c, d, tx, ty) {
  let out = new glMatrix.ARRAY_TYPE(6);
  out[0] = a;
  out[1] = b;
  out[2] = c;
  out[3] = d;
  out[4] = tx;
  out[5] = ty;
  return out;
}

/**
 * Set the components of a mat2d to the given values
 *
 * @param {mat2d} out the receiving matrix
 * @param {Number} a Component A (index 0)
 * @param {Number} b Component B (index 1)
 * @param {Number} c Component C (index 2)
 * @param {Number} d Component D (index 3)
 * @param {Number} tx Component TX (index 4)
 * @param {Number} ty Component TY (index 5)
 * @returns {mat2d} out
 */
export function set(out, a, b, c, d, tx, ty) {
  out[0] = a;
  out[1] = b;
  out[2] = c;
  out[3] = d;
  out[4] = tx;
  out[5] = ty;
  return out;
}

/**
 * Inverts a mat2d
 *
 * @param {mat2d} out the receiving matrix
 * @param {mat2d} a the source matrix
 * @returns {mat2d} out
 */
export function invert(out, a) {
  let aa = a[0], ab = a[1], ac = a[2], ad = a[3];
  let atx = a[4], aty = a[5];

  let det = aa * ad - ab * ac;
  if(!det){
    return null;
  }
  det = 1.0 / det;

  out[0] = ad * det;
  out[1] = -ab * det;
  out[2] = -ac * det;
  out[3] = aa * det;
  out[4] = (ac * aty - ad * atx) * det;
  out[5] = (ab * atx - aa * aty) * det;
  return out;
}

/**
 * Calculates the determinant of a mat2d
 *
 * @param {mat2d} a the source matrix
 * @returns {Number} determinant of a
 */
export function determinant(a) {
  return a[0] * a[3] - a[1] * a[2];
}

/**
 * Multiplies two mat2d's
 *
 * @param {mat2d} out the receiving matrix
 * @param {mat2d} a the first operand
 * @param {mat2d} b the second operand
 * @returns {mat2d} out
 */
export function multiply(out, a, b) {
  let a0 = a[0], a1 = a[1], a2 = a[2], a3 = a[3], a4 = a[4], a5 = a[5];
  let b0 = b[0], b1 = b[1], b2 = b[2], b3 = b[3], b4 = b[4], b5 = b[5];
  out[0] = a0 * b0 + a2 * b1;
  out[1] = a1 * b0 + a3 * b1;
  out[2] = a0 * b2 + a2 * b3;
  out[3] = a1 * b2 + a3 * b3;
  out[4] = a0 * b4 + a2 * b5 + a4;
  out[5] = a1 * b4 + a3 * b5 + a5;
  return out;
}

/**
 * Rotates a mat2d by the given angle
 *
 * @param {mat2d} out the receiving matrix
 * @param {mat2d} a the matrix to rotate
 * @param {Number} rad the angle to rotate the matrix by
 * @returns {mat2d} out
 */
export function rotate(out, a, rad) {
  let a0 = a[0], a1 = a[1], a2 = a[2], a3 = a[3], a4 = a[4], a5 = a[5];
  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;
  out[4] = a4;
  out[5] = a5;
  return out;
}

/**
 * Scales the mat2d by the dimensions in the given vec2
 *
 * @param {mat2d} out the receiving matrix
 * @param {mat2d} a the matrix to translate
 * @param {vec2} v the vec2 to scale the matrix by
 * @returns {mat2d} out
 **/
export function scale(out, a, v) {
  let a0 = a[0], a1 = a[1], a2 = a[2], a3 = a[3], a4 = a[4], a5 = a[5];
  let v0 = v[0], v1 = v[1];
  out[0] = a0 * v0;
  out[1] = a1 * v0;
  out[2] = a2 * v1;
  out[3] = a3 * v1;
  out[4] = a4;
  out[5] = a5;
  return out;
}

/**
 * Translates the mat2d by the dimensions in the given vec2
 *
 * @param {mat2d} out the receiving matrix
 * @param {mat2d} a the matrix to translate
 * @param {vec2} v the vec2 to translate the matrix by
 * @returns {mat2d} out
 **/
export function translate(out, a, v) {
  let a0 = a[0], a1 = a[1], a2 = a[2], a3 = a[3], a4 = a[4], a5 = a[5];
  let v0 = v[0], v1 = v[1];
  out[0] = a0;
  out[1] = a1;
  out[2] = a2;
  out[3] = a3;
  out[4] = a0 * v0 + a2 * v1 + a4;
  out[5] = a1 * v0 + a3 * v1 + a5;
  return out;
}

/**
 * Creates a matrix from a given angle
 * This is equivalent to (but much faster than):
 *
 *     mat2d.identity(dest);
 *     mat2d.rotate(dest, dest, rad);
 *
 * @param {mat2d} out mat2d receiving operation result
 * @param {Number} rad the angle to rotate the matrix by
 * @returns {mat2d} out
 */
export function fromRotation(out, rad) {
  let s = Math.sin(rad), c = Math.cos(rad);
  out[0] = c;
  out[1] = s;
  out[2] = -s;
  out[3] = c;
  out[4] = 0;
  out[5] = 0;
  return out;
}

/**
 * Creates a matrix from a vector scaling
 * This is equivalent to (but much faster than):
 *
 *     mat2d.identity(dest);
 *     mat2d.scale(dest, dest, vec);
 *
 * @param {mat2d} out mat2d receiving operation result
 * @param {vec2} v Scaling vector
 * @returns {mat2d} out
 */
export function fromScaling(out, v) {
  out[0] = v[0];
  out[1] = 0;
  out[2] = 0;
  out[3] = v[1];
  out[4] = 0;
  out[5] = 0;
  return out;
}

/**
 * Creates a matrix from a vector translation
 * This is equivalent to (but much faster than):
 *
 *     mat2d.identity(dest);
 *     mat2d.translate(dest, dest, vec);
 *
 * @param {mat2d} out mat2d receiving operation result
 * @param {vec2} v Translation vector
 * @returns {mat2d} out
 */
export function fromTranslation(out, v) {
  out[0] = 1;
  out[1] = 0;
  out[2] = 0;
  out[3] = 1;
  out[4] = v[0];
  out[5] = v[1];
  return out;
}

/**
 * Returns a string representation of a mat2d
 *
 * @param {mat2d} a matrix to represent as a string
 * @returns {String} string representation of the matrix
 */
export function str(a) {
  return 'mat2d(' + a[0] + ', ' + a[1] + ', ' + a[2] + ', ' +
          a[3] + ', ' + a[4] + ', ' + a[5] + ')';
}

/**
 * Returns Frobenius norm of a mat2d
 *
 * @param {mat2d} 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) + Math.pow(a[4], 2) + Math.pow(a[5], 2) + 1))
}

/**
 * Adds two mat2d's
 *
 * @param {mat2d} out the receiving matrix
 * @param {mat2d} a the first operand
 * @param {mat2d} b the second operand
 * @returns {mat2d} 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];
  out[4] = a[4] + b[4];
  out[5] = a[5] + b[5];
  return out;
}

/**
 * Subtracts matrix b from matrix a
 *
 * @param {mat2d} out the receiving matrix
 * @param {mat2d} a the first operand
 * @param {mat2d} b the second operand
 * @returns {mat2d} 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];
  out[4] = a[4] - b[4];
  out[5] = a[5] - b[5];
  return out;
}

/**
 * Multiply each element of the matrix by a scalar.
 *
 * @param {mat2d} out the receiving matrix
 * @param {mat2d} a the matrix to scale
 * @param {Number} b amount to scale the matrix's elements by
 * @returns {mat2d} 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;
  out[4] = a[4] * b;
  out[5] = a[5] * b;
  return out;
}

/**
 * Adds two mat2d's after multiplying each element of the second operand by a scalar value.
 *
 * @param {mat2d} out the receiving vector
 * @param {mat2d} a the first operand
 * @param {mat2d} b the second operand
 * @param {Number} scale the amount to scale b's elements by before adding
 * @returns {mat2d} 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);
  out[4] = a[4] + (b[4] * scale);
  out[5] = a[5] + (b[5] * scale);
  return out;
}

/**
 * Returns whether or not the matrices have exactly the same elements in the same position (when compared with ===)
 *
 * @param {mat2d} a The first matrix.
 * @param {mat2d} b The second matrix.
 * @returns {Boolean} True if the matrices are equal, false otherwise.
 */
export function exactEquals(a, b) {
  return a[0] === b[0] &amp;&amp; a[1] === b[1] &amp;&amp; a[2] === b[2] &amp;&amp; a[3] === b[3] &amp;&amp; a[4] === b[4] &amp;&amp; a[5] === b[5];
}

/**
 * Returns whether or not the matrices have approximately the same elements in the same position.
 *
 * @param {mat2d} a The first matrix.
 * @param {mat2d} 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], a4 = a[4], a5 = a[5];
  let b0 = b[0], b1 = b[1], b2 = b[2], b3 = b[3], b4 = b[4], b5 = b[5];
  return (Math.abs(a0 - b0) &lt;= glMatrix.EPSILON*Math.max(1.0, Math.abs(a0), Math.abs(b0)) &amp;&amp;
          Math.abs(a1 - b1) &lt;= glMatrix.EPSILON*Math.max(1.0, Math.abs(a1), Math.abs(b1)) &amp;&amp;
          Math.abs(a2 - b2) &lt;= glMatrix.EPSILON*Math.max(1.0, Math.abs(a2), Math.abs(b2)) &amp;&amp;
          Math.abs(a3 - b3) &lt;= glMatrix.EPSILON*Math.max(1.0, Math.abs(a3), Math.abs(b3)) &amp;&amp;
          Math.abs(a4 - b4) &lt;= glMatrix.EPSILON*Math.max(1.0, Math.abs(a4), Math.abs(b4)) &amp;&amp;
          Math.abs(a5 - b5) &lt;= glMatrix.EPSILON*Math.max(1.0, Math.abs(a5), Math.abs(b5)));
}

/**
 * Alias for {@link mat2d.multiply}
 * @function
 */
export const mul = multiply;

/**
 * Alias for {@link mat2d.subtract}
 * @function
 */
export const sub = subtract;
</code></pre>
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