JSDoc: Source: mat3.js

# Source: mat3.js

    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] && a[1] === b[1] && a[2] === b[2] &&
             a[3] === b[3] && a[4] === b[4] && a[5] === b[5] &&
             a[6] === b[6] && a[7] === b[7] && 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) <= 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)) &&
              Math.abs(a4 - b4) <= glMatrix.EPSILON*Math.max(1.0, Math.abs(a4), Math.abs(b4)) &&
              Math.abs(a5 - b5) <= glMatrix.EPSILON*Math.max(1.0, Math.abs(a5), Math.abs(b5)) &&
              Math.abs(a6 - b6) <= glMatrix.EPSILON*Math.max(1.0, Math.abs(a6), Math.abs(b6)) &&
              Math.abs(a7 - b7) <= glMatrix.EPSILON*Math.max(1.0, Math.abs(a7), Math.abs(b7)) &&
              Math.abs(a8 - b8) <= 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;