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    <h1 class="page-title">Source: mat3.js</h1>

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

/**
 * 3x3 Matrix
 * @module mat3
 */

/**
 * Creates a new identity mat3
 *
 * @returns {mat3} a new 3x3 matrix
 */
export function create() {
  let out = new glMatrix.ARRAY_TYPE(9);
  if(glMatrix.ARRAY_TYPE != Float32Array) {
    out[1] = 0;
    out[2] = 0;
    out[3] = 0;
    out[5] = 0;
    out[6] = 0;
    out[7] = 0;
  }
  out[0] = 1;
  out[4] = 1;
  out[8] = 1;
  return out;
}

/**
 * Copies the upper-left 3x3 values into the given mat3.
 *
 * @param {mat3} out the receiving 3x3 matrix
 * @param {mat4} a   the source 4x4 matrix
 * @returns {mat3} out
 */
export function fromMat4(out, a) {
  out[0] = a[0];
  out[1] = a[1];
  out[2] = a[2];
  out[3] = a[4];
  out[4] = a[5];
  out[5] = a[6];
  out[6] = a[8];
  out[7] = a[9];
  out[8] = a[10];
  return out;
}

/**
 * Creates a new mat3 initialized with values from an existing matrix
 *
 * @param {mat3} a matrix to clone
 * @returns {mat3} a new 3x3 matrix
 */
export function clone(a) {
  let out = new glMatrix.ARRAY_TYPE(9);
  out[0] = a[0];
  out[1] = a[1];
  out[2] = a[2];
  out[3] = a[3];
  out[4] = a[4];
  out[5] = a[5];
  out[6] = a[6];
  out[7] = a[7];
  out[8] = a[8];
  return out;
}

/**
 * Copy the values from one mat3 to another
 *
 * @param {mat3} out the receiving matrix
 * @param {mat3} a the source matrix
 * @returns {mat3} 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];
  out[6] = a[6];
  out[7] = a[7];
  out[8] = a[8];
  return out;
}

/**
 * Create a new mat3 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} m02 Component in column 0, row 2 position (index 2)
 * @param {Number} m10 Component in column 1, row 0 position (index 3)
 * @param {Number} m11 Component in column 1, row 1 position (index 4)
 * @param {Number} m12 Component in column 1, row 2 position (index 5)
 * @param {Number} m20 Component in column 2, row 0 position (index 6)
 * @param {Number} m21 Component in column 2, row 1 position (index 7)
 * @param {Number} m22 Component in column 2, row 2 position (index 8)
 * @returns {mat3} A new mat3
 */
export function fromValues(m00, m01, m02, m10, m11, m12, m20, m21, m22) {
  let out = new glMatrix.ARRAY_TYPE(9);
  out[0] = m00;
  out[1] = m01;
  out[2] = m02;
  out[3] = m10;
  out[4] = m11;
  out[5] = m12;
  out[6] = m20;
  out[7] = m21;
  out[8] = m22;
  return out;
}

/**
 * Set the components of a mat3 to the given values
 *
 * @param {mat3} 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} m02 Component in column 0, row 2 position (index 2)
 * @param {Number} m10 Component in column 1, row 0 position (index 3)
 * @param {Number} m11 Component in column 1, row 1 position (index 4)
 * @param {Number} m12 Component in column 1, row 2 position (index 5)
 * @param {Number} m20 Component in column 2, row 0 position (index 6)
 * @param {Number} m21 Component in column 2, row 1 position (index 7)
 * @param {Number} m22 Component in column 2, row 2 position (index 8)
 * @returns {mat3} out
 */
export function set(out, m00, m01, m02, m10, m11, m12, m20, m21, m22) {
  out[0] = m00;
  out[1] = m01;
  out[2] = m02;
  out[3] = m10;
  out[4] = m11;
  out[5] = m12;
  out[6] = m20;
  out[7] = m21;
  out[8] = m22;
  return out;
}

/**
 * Set a mat3 to the identity matrix
 *
 * @param {mat3} out the receiving matrix
 * @returns {mat3} out
 */
export function identity(out) {
  out[0] = 1;
  out[1] = 0;
  out[2] = 0;
  out[3] = 0;
  out[4] = 1;
  out[5] = 0;
  out[6] = 0;
  out[7] = 0;
  out[8] = 1;
  return out;
}

/**
 * Transpose the values of a mat3
 *
 * @param {mat3} out the receiving matrix
 * @param {mat3} a the source matrix
 * @returns {mat3} 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 a01 = a[1], a02 = a[2], a12 = a[5];
    out[1] = a[3];
    out[2] = a[6];
    out[3] = a01;
    out[5] = a[7];
    out[6] = a02;
    out[7] = a12;
  } else {
    out[0] = a[0];
    out[1] = a[3];
    out[2] = a[6];
    out[3] = a[1];
    out[4] = a[4];
    out[5] = a[7];
    out[6] = a[2];
    out[7] = a[5];
    out[8] = a[8];
  }

  return out;
}

/**
 * Inverts a mat3
 *
 * @param {mat3} out the receiving matrix
 * @param {mat3} a the source matrix
 * @returns {mat3} out
 */
export function invert(out, a) {
  let a00 = a[0], a01 = a[1], a02 = a[2];
  let a10 = a[3], a11 = a[4], a12 = a[5];
  let a20 = a[6], a21 = a[7], a22 = a[8];

  let b01 = a22 * a11 - a12 * a21;
  let b11 = -a22 * a10 + a12 * a20;
  let b21 = a21 * a10 - a11 * a20;

  // Calculate the determinant
  let det = a00 * b01 + a01 * b11 + a02 * b21;

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

  out[0] = b01 * det;
  out[1] = (-a22 * a01 + a02 * a21) * det;
  out[2] = (a12 * a01 - a02 * a11) * det;
  out[3] = b11 * det;
  out[4] = (a22 * a00 - a02 * a20) * det;
  out[5] = (-a12 * a00 + a02 * a10) * det;
  out[6] = b21 * det;
  out[7] = (-a21 * a00 + a01 * a20) * det;
  out[8] = (a11 * a00 - a01 * a10) * det;
  return out;
}

/**
 * Calculates the adjugate of a mat3
 *
 * @param {mat3} out the receiving matrix
 * @param {mat3} a the source matrix
 * @returns {mat3} out
 */
export function adjoint(out, a) {
  let a00 = a[0], a01 = a[1], a02 = a[2];
  let a10 = a[3], a11 = a[4], a12 = a[5];
  let a20 = a[6], a21 = a[7], a22 = a[8];

  out[0] = (a11 * a22 - a12 * a21);
  out[1] = (a02 * a21 - a01 * a22);
  out[2] = (a01 * a12 - a02 * a11);
  out[3] = (a12 * a20 - a10 * a22);
  out[4] = (a00 * a22 - a02 * a20);
  out[5] = (a02 * a10 - a00 * a12);
  out[6] = (a10 * a21 - a11 * a20);
  out[7] = (a01 * a20 - a00 * a21);
  out[8] = (a00 * a11 - a01 * a10);
  return out;
}

/**
 * Calculates the determinant of a mat3
 *
 * @param {mat3} a the source matrix
 * @returns {Number} determinant of a
 */
export function determinant(a) {
  let a00 = a[0], a01 = a[1], a02 = a[2];
  let a10 = a[3], a11 = a[4], a12 = a[5];
  let a20 = a[6], a21 = a[7], a22 = a[8];

  return a00 * (a22 * a11 - a12 * a21) + a01 * (-a22 * a10 + a12 * a20) + a02 * (a21 * a10 - a11 * a20);
}

/**
 * Multiplies two mat3's
 *
 * @param {mat3} out the receiving matrix
 * @param {mat3} a the first operand
 * @param {mat3} b the second operand
 * @returns {mat3} out
 */
export function multiply(out, a, b) {
  let a00 = a[0], a01 = a[1], a02 = a[2];
  let a10 = a[3], a11 = a[4], a12 = a[5];
  let a20 = a[6], a21 = a[7], a22 = a[8];

  let b00 = b[0], b01 = b[1], b02 = b[2];
  let b10 = b[3], b11 = b[4], b12 = b[5];
  let b20 = b[6], b21 = b[7], b22 = b[8];

  out[0] = b00 * a00 + b01 * a10 + b02 * a20;
  out[1] = b00 * a01 + b01 * a11 + b02 * a21;
  out[2] = b00 * a02 + b01 * a12 + b02 * a22;

  out[3] = b10 * a00 + b11 * a10 + b12 * a20;
  out[4] = b10 * a01 + b11 * a11 + b12 * a21;
  out[5] = b10 * a02 + b11 * a12 + b12 * a22;

  out[6] = b20 * a00 + b21 * a10 + b22 * a20;
  out[7] = b20 * a01 + b21 * a11 + b22 * a21;
  out[8] = b20 * a02 + b21 * a12 + b22 * a22;
  return out;
}

/**
 * Translate a mat3 by the given vector
 *
 * @param {mat3} out the receiving matrix
 * @param {mat3} a the matrix to translate
 * @param {vec2} v vector to translate by
 * @returns {mat3} out
 */
export function translate(out, a, v) {
  let a00 = a[0], a01 = a[1], a02 = a[2],
    a10 = a[3], a11 = a[4], a12 = a[5],
    a20 = a[6], a21 = a[7], a22 = a[8],
    x = v[0], y = v[1];

  out[0] = a00;
  out[1] = a01;
  out[2] = a02;

  out[3] = a10;
  out[4] = a11;
  out[5] = a12;

  out[6] = x * a00 + y * a10 + a20;
  out[7] = x * a01 + y * a11 + a21;
  out[8] = x * a02 + y * a12 + a22;
  return out;
}

/**
 * Rotates a mat3 by the given angle
 *
 * @param {mat3} out the receiving matrix
 * @param {mat3} a the matrix to rotate
 * @param {Number} rad the angle to rotate the matrix by
 * @returns {mat3} out
 */
export function rotate(out, a, rad) {
  let a00 = a[0], a01 = a[1], a02 = a[2],
    a10 = a[3], a11 = a[4], a12 = a[5],
    a20 = a[6], a21 = a[7], a22 = a[8],

    s = Math.sin(rad),
    c = Math.cos(rad);

  out[0] = c * a00 + s * a10;
  out[1] = c * a01 + s * a11;
  out[2] = c * a02 + s * a12;

  out[3] = c * a10 - s * a00;
  out[4] = c * a11 - s * a01;
  out[5] = c * a12 - s * a02;

  out[6] = a20;
  out[7] = a21;
  out[8] = a22;
  return out;
};

/**
 * Scales the mat3 by the dimensions in the given vec2
 *
 * @param {mat3} out the receiving matrix
 * @param {mat3} a the matrix to rotate
 * @param {vec2} v the vec2 to scale the matrix by
 * @returns {mat3} out
 **/
export function scale(out, a, v) {
  let x = v[0], y = v[1];

  out[0] = x * a[0];
  out[1] = x * a[1];
  out[2] = x * a[2];

  out[3] = y * a[3];
  out[4] = y * a[4];
  out[5] = y * a[5];

  out[6] = a[6];
  out[7] = a[7];
  out[8] = a[8];
  return out;
}

/**
 * Creates a matrix from a vector translation
 * This is equivalent to (but much faster than):
 *
 *     mat3.identity(dest);
 *     mat3.translate(dest, dest, vec);
 *
 * @param {mat3} out mat3 receiving operation result
 * @param {vec2} v Translation vector
 * @returns {mat3} out
 */
export function fromTranslation(out, v) {
  out[0] = 1;
  out[1] = 0;
  out[2] = 0;
  out[3] = 0;
  out[4] = 1;
  out[5] = 0;
  out[6] = v[0];
  out[7] = v[1];
  out[8] = 1;
  return out;
}

/**
 * Creates a matrix from a given angle
 * This is equivalent to (but much faster than):
 *
 *     mat3.identity(dest);
 *     mat3.rotate(dest, dest, rad);
 *
 * @param {mat3} out mat3 receiving operation result
 * @param {Number} rad the angle to rotate the matrix by
 * @returns {mat3} out
 */
export function fromRotation(out, rad) {
  let s = Math.sin(rad), c = Math.cos(rad);

  out[0] = c;
  out[1] = s;
  out[2] = 0;

  out[3] = -s;
  out[4] = c;
  out[5] = 0;

  out[6] = 0;
  out[7] = 0;
  out[8] = 1;
  return out;
}

/**
 * Creates a matrix from a vector scaling
 * This is equivalent to (but much faster than):
 *
 *     mat3.identity(dest);
 *     mat3.scale(dest, dest, vec);
 *
 * @param {mat3} out mat3 receiving operation result
 * @param {vec2} v Scaling vector
 * @returns {mat3} out
 */
export function fromScaling(out, v) {
  out[0] = v[0];
  out[1] = 0;
  out[2] = 0;

  out[3] = 0;
  out[4] = v[1];
  out[5] = 0;

  out[6] = 0;
  out[7] = 0;
  out[8] = 1;
  return out;
}

/**
 * Copies the values from a mat2d into a mat3
 *
 * @param {mat3} out the receiving matrix
 * @param {mat2d} a the matrix to copy
 * @returns {mat3} out
 **/
export function fromMat2d(out, a) {
  out[0] = a[0];
  out[1] = a[1];
  out[2] = 0;

  out[3] = a[2];
  out[4] = a[3];
  out[5] = 0;

  out[6] = a[4];
  out[7] = a[5];
  out[8] = 1;
  return out;
}

/**
* Calculates a 3x3 matrix from the given quaternion
*
* @param {mat3} out mat3 receiving operation result
* @param {quat} q Quaternion to create matrix from
*
* @returns {mat3} out
*/
export function fromQuat(out, q) {
  let x = q[0], y = q[1], z = q[2], w = q[3];
  let x2 = x + x;
  let y2 = y + y;
  let z2 = z + z;

  let xx = x * x2;
  let yx = y * x2;
  let yy = y * y2;
  let zx = z * x2;
  let zy = z * y2;
  let zz = z * z2;
  let wx = w * x2;
  let wy = w * y2;
  let wz = w * z2;

  out[0] = 1 - yy - zz;
  out[3] = yx - wz;
  out[6] = zx + wy;

  out[1] = yx + wz;
  out[4] = 1 - xx - zz;
  out[7] = zy - wx;

  out[2] = zx - wy;
  out[5] = zy + wx;
  out[8] = 1 - xx - yy;

  return out;
}

/**
* Calculates a 3x3 normal matrix (transpose inverse) from the 4x4 matrix
*
* @param {mat3} out mat3 receiving operation result
* @param {mat4} a Mat4 to derive the normal matrix from
*
* @returns {mat3} out
*/
export function normalFromMat4(out, a) {
  let a00 = a[0], a01 = a[1], a02 = a[2], a03 = a[3];
  let a10 = a[4], a11 = a[5], a12 = a[6], a13 = a[7];
  let a20 = a[8], a21 = a[9], a22 = a[10], a23 = a[11];
  let a30 = a[12], a31 = a[13], a32 = a[14], a33 = a[15];

  let b00 = a00 * a11 - a01 * a10;
  let b01 = a00 * a12 - a02 * a10;
  let b02 = a00 * a13 - a03 * a10;
  let b03 = a01 * a12 - a02 * a11;
  let b04 = a01 * a13 - a03 * a11;
  let b05 = a02 * a13 - a03 * a12;
  let b06 = a20 * a31 - a21 * a30;
  let b07 = a20 * a32 - a22 * a30;
  let b08 = a20 * a33 - a23 * a30;
  let b09 = a21 * a32 - a22 * a31;
  let b10 = a21 * a33 - a23 * a31;
  let b11 = a22 * a33 - a23 * a32;

  // Calculate the determinant
  let det = b00 * b11 - b01 * b10 + b02 * b09 + b03 * b08 - b04 * b07 + b05 * b06;

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

  out[0] = (a11 * b11 - a12 * b10 + a13 * b09) * det;
  out[1] = (a12 * b08 - a10 * b11 - a13 * b07) * det;
  out[2] = (a10 * b10 - a11 * b08 + a13 * b06) * det;

  out[3] = (a02 * b10 - a01 * b11 - a03 * b09) * det;
  out[4] = (a00 * b11 - a02 * b08 + a03 * b07) * det;
  out[5] = (a01 * b08 - a00 * b10 - a03 * b06) * det;

  out[6] = (a31 * b05 - a32 * b04 + a33 * b03) * det;
  out[7] = (a32 * b02 - a30 * b05 - a33 * b01) * det;
  out[8] = (a30 * b04 - a31 * b02 + a33 * b00) * det;

  return out;
}

/**
 * Generates a 2D projection matrix with the given bounds
 *
 * @param {mat3} out mat3 frustum matrix will be written into
 * @param {number} width Width of your gl context
 * @param {number} height Height of gl context
 * @returns {mat3} out
 */
export function projection(out, width, height) {
    out[0] = 2 / width;
    out[1] = 0;
    out[2] = 0;
    out[3] = 0;
    out[4] = -2 / height;
    out[5] = 0;
    out[6] = -1;
    out[7] = 1;
    out[8] = 1;
    return out;
}

/**
 * Returns a string representation of a mat3
 *
 * @param {mat3} a matrix to represent as a string
 * @returns {String} string representation of the matrix
 */
export function str(a) {
  return 'mat3(' + a[0] + ', ' + a[1] + ', ' + a[2] + ', ' +
          a[3] + ', ' + a[4] + ', ' + a[5] + ', ' +
          a[6] + ', ' + a[7] + ', ' + a[8] + ')';
}

/**
 * Returns Frobenius norm of a mat3
 *
 * @param {mat3} 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) + Math.pow(a[6], 2) + Math.pow(a[7], 2) + Math.pow(a[8], 2)))
}

/**
 * Adds two mat3's
 *
 * @param {mat3} out the receiving matrix
 * @param {mat3} a the first operand
 * @param {mat3} b the second operand
 * @returns {mat3} 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];
  out[6] = a[6] + b[6];
  out[7] = a[7] + b[7];
  out[8] = a[8] + b[8];
  return out;
}

/**
 * Subtracts matrix b from matrix a
 *
 * @param {mat3} out the receiving matrix
 * @param {mat3} a the first operand
 * @param {mat3} b the second operand
 * @returns {mat3} 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];
  out[6] = a[6] - b[6];
  out[7] = a[7] - b[7];
  out[8] = a[8] - b[8];
  return out;
}


/**
 * Multiply each element of the matrix by a scalar.
 *
 * @param {mat3} out the receiving matrix
 * @param {mat3} a the matrix to scale
 * @param {Number} b amount to scale the matrix's elements by
 * @returns {mat3} 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;
  out[6] = a[6] * b;
  out[7] = a[7] * b;
  out[8] = a[8] * b;
  return out;
}

/**
 * Adds two mat3's after multiplying each element of the second operand by a scalar value.
 *
 * @param {mat3} out the receiving vector
 * @param {mat3} a the first operand
 * @param {mat3} b the second operand
 * @param {Number} scale the amount to scale b's elements by before adding
 * @returns {mat3} 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);
  out[6] = a[6] + (b[6] * scale);
  out[7] = a[7] + (b[7] * scale);
  out[8] = a[8] + (b[8] * scale);
  return out;
}

/**
 * Returns whether or not the matrices have exactly the same elements in the same position (when compared with ===)
 *
 * @param {mat3} a The first matrix.
 * @param {mat3} 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] &amp;&amp;
         a[6] === b[6] &amp;&amp; a[7] === b[7] &amp;&amp; a[8] === b[8];
}

/**
 * Returns whether or not the matrices have approximately the same elements in the same position.
 *
 * @param {mat3} a The first matrix.
 * @param {mat3} 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], a6 = a[6], a7 = a[7], a8 = a[8];
  let b0 = b[0], b1 = b[1], b2 = b[2], b3 = b[3], b4 = b[4], b5 = b[5], b6 = b[6], b7 = b[7], b8 = b[8];
  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)) &amp;&amp;
          Math.abs(a6 - b6) &lt;= glMatrix.EPSILON*Math.max(1.0, Math.abs(a6), Math.abs(b6)) &amp;&amp;
          Math.abs(a7 - b7) &lt;= glMatrix.EPSILON*Math.max(1.0, Math.abs(a7), Math.abs(b7)) &amp;&amp;
          Math.abs(a8 - b8) &lt;= glMatrix.EPSILON*Math.max(1.0, Math.abs(a8), Math.abs(b8)));
}

/**
 * Alias for {@link mat3.multiply}
 * @function
 */
export const mul = multiply;

/**
 * Alias for {@link mat3.subtract}
 * @function
 */
export const sub = subtract;
</code></pre>
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