
/*
 * Copyright (C) 2009 Apple Inc. All Rights Reserved.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions
 * are met:
 * 1. Redistributions of source code must retain the above copyright
 *    notice, this list of conditions and the following disclaimer.
 * 2. Redistributions in binary form must reproduce the above copyright
 *    notice, this list of conditions and the following disclaimer in the
 *    documentation and/or other materials provided with the distribution.
 *
 * THIS SOFTWARE IS PROVIDED BY APPLE INC. ``AS IS'' AND ANY
 * EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
 * PURPOSE ARE DISCLAIMED.  IN NO EVENT SHALL APPLE INC. OR
 * CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
 * EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
 * PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
 * PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY
 * OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
 * OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. 
 */
/*
    CanvasMatrix4 class
    
    This class implements a 4x4 matrix. It has functions which
    duplicate the functionality of the OpenGL matrix stack and
    glut functions.
    
    IDL:
    
    [
        Constructor(in CanvasMatrix4 matrix),           // copy passed matrix into new CanvasMatrix4
        Constructor(in sequence<float> array)           // create new CanvasMatrix4 with 16 floats (row major)
        Constructor()                                   // create new CanvasMatrix4 with identity matrix
    ]
    interface CanvasMatrix4 {
        attribute float m11;
        attribute float m12;
        attribute float m13;
        attribute float m14;
        attribute float m21;
        attribute float m22;
        attribute float m23;
        attribute float m24;
        attribute float m31;
        attribute float m32;
        attribute float m33;
        attribute float m34;
        attribute float m41;
        attribute float m42;
        attribute float m43;
        attribute float m44;

        void load(in CanvasMatrix4 matrix);                 // copy the values from the passed matrix
        void load(in sequence<float> array);                // copy 16 floats into the matrix
        sequence<float> getAsArray();                       // return the matrix as an array of 16 floats
        WebGLFloatArray getAsCanvasFloatArray();           // return the matrix as a WebGLFloatArray with 16 values
        void makeIdentity();                                // replace the matrix with identity
        void transpose();                                   // replace the matrix with its transpose
        void invert();                                      // replace the matrix with its inverse
        
        void translate(in float x, in float y, in float z); // multiply the matrix by passed translation values on the right
        void scale(in float x, in float y, in float z);     // multiply the matrix by passed scale values on the right
        void rotate(in float angle,                         // multiply the matrix by passed rotation values on the right
                    in float x, in float y, in float z);    // (angle is in degrees)
        void multRight(in CanvasMatrix matrix);             // multiply the matrix by the passed matrix on the right
        void multLeft(in CanvasMatrix matrix);              // multiply the matrix by the passed matrix on the left
        void ortho(in float left, in float right,           // multiply the matrix by the passed ortho values on the right
                   in float bottom, in float top, 
                   in float near, in float far);
        void frustum(in float left, in float right,         // multiply the matrix by the passed frustum values on the right
                     in float bottom, in float top, 
                     in float near, in float far);
        void perspective(in float fovy, in float aspect,    // multiply the matrix by the passed perspective values on the right
                         in float zNear, in float zFar);
        void lookat(in float eyex, in float eyey, in float eyez,    // multiply the matrix by the passed lookat 
                    in float ctrx, in float ctry, in float ctrz,    // values on the right
                    in float upx, in float upy, in float upz);
    }
*/

CanvasMatrix4 = function(m)
{
    if (typeof m == 'object') {
        if ("length" in m && m.length >= 16) {
            this.load(m[0], m[1], m[2], m[3], m[4], m[5], m[6], m[7], m[8], m[9], m[10], m[11], m[12], m[13], m[14], m[15]);
            return;
        }
        else if (m instanceof CanvasMatrix4) {
            this.load(m);
            return;
        }
    }
    this.makeIdentity();
}

CanvasMatrix4.prototype.load = function()
{
    if (arguments.length == 1 && typeof arguments[0] == 'object') {
        var matrix = arguments[0];
        
        if ("length" in matrix && matrix.length == 16) {
            this.m11 = matrix[0];
            this.m12 = matrix[1];
            this.m13 = matrix[2];
            this.m14 = matrix[3];

            this.m21 = matrix[4];
            this.m22 = matrix[5];
            this.m23 = matrix[6];
            this.m24 = matrix[7];

            this.m31 = matrix[8];
            this.m32 = matrix[9];
            this.m33 = matrix[10];
            this.m34 = matrix[11];

            this.m41 = matrix[12];
            this.m42 = matrix[13];
            this.m43 = matrix[14];
            this.m44 = matrix[15];
            return;
        }
            
        if (arguments[0] instanceof CanvasMatrix4) {
        
            this.m11 = matrix.m11;
            this.m12 = matrix.m12;
            this.m13 = matrix.m13;
            this.m14 = matrix.m14;

            this.m21 = matrix.m21;
            this.m22 = matrix.m22;
            this.m23 = matrix.m23;
            this.m24 = matrix.m24;

            this.m31 = matrix.m31;
            this.m32 = matrix.m32;
            this.m33 = matrix.m33;
            this.m34 = matrix.m34;

            this.m41 = matrix.m41;
            this.m42 = matrix.m42;
            this.m43 = matrix.m43;
            this.m44 = matrix.m44;
            return;
        }
    }
    
    this.makeIdentity();
}

CanvasMatrix4.prototype.getAsArray = function()
{
    return [
        this.m11, this.m12, this.m13, this.m14, 
        this.m21, this.m22, this.m23, this.m24, 
        this.m31, this.m32, this.m33, this.m34, 
        this.m41, this.m42, this.m43, this.m44
    ];
}

CanvasMatrix4.prototype.getAsWebGLFloatArray = function()
{
    return new WebGLFloatArray(this.getAsArray());
}

CanvasMatrix4.prototype.makeIdentity = function()
{
    this.m11 = 1;
    this.m12 = 0;
    this.m13 = 0;
    this.m14 = 0;
    
    this.m21 = 0;
    this.m22 = 1;
    this.m23 = 0;
    this.m24 = 0;
    
    this.m31 = 0;
    this.m32 = 0;
    this.m33 = 1;
    this.m34 = 0;
    
    this.m41 = 0;
    this.m42 = 0;
    this.m43 = 0;
    this.m44 = 1;
}

CanvasMatrix4.prototype.transpose = function()
{
    var tmp = this.m12;
    this.m12 = this.m21;
    this.m21 = tmp;
    
    tmp = this.m13;
    this.m13 = this.m31;
    this.m31 = tmp;
    
    tmp = this.m14;
    this.m14 = this.m41;
    this.m41 = tmp;
    
    tmp = this.m23;
    this.m23 = this.m32;
    this.m32 = tmp;
    
    tmp = this.m24;
    this.m24 = this.m42;
    this.m42 = tmp;
    
    tmp = this.m34;
    this.m34 = this.m43;
    this.m43 = tmp;
}

CanvasMatrix4.prototype.invert = function()
{
    // Calculate the 4x4 determinant
    // If the determinant is zero, 
    // then the inverse matrix is not unique.
    var det = this._determinant4x4();

    if (Math.abs(det) < 1e-8)
        return null;

    this._makeAdjoint();

    // Scale the adjoint matrix to get the inverse
    this.m11 /= det;
    this.m12 /= det;
    this.m13 /= det;
    this.m14 /= det;
    
    this.m21 /= det;
    this.m22 /= det;
    this.m23 /= det;
    this.m24 /= det;
    
    this.m31 /= det;
    this.m32 /= det;
    this.m33 /= det;
    this.m34 /= det;
    
    this.m41 /= det;
    this.m42 /= det;
    this.m43 /= det;
    this.m44 /= det;
}

CanvasMatrix4.prototype.translate = function(x,y,z)
{
    if (x == undefined)
        x = 0;
        if (y == undefined)
            y = 0;
    if (z == undefined)
        z = 0;
    
    var matrix = new CanvasMatrix4();
    matrix.m41 = x;
    matrix.m42 = y;
    matrix.m43 = z;

    this.multRight(matrix);
}

CanvasMatrix4.prototype.scale = function(x,y,z)
{
    if (x == undefined)
        x = 1;
    if (z == undefined) {
        if (y == undefined) {
            y = x;
            z = x;
        }
        else
            z = 1;
    }
    else if (y == undefined)
        y = x;
    
    var matrix = new CanvasMatrix4();
    matrix.m11 = x;
    matrix.m22 = y;
    matrix.m33 = z;
    
    this.multRight(matrix);
}

CanvasMatrix4.prototype.rotate = function(angle,x,y,z)
{
    // angles are in degrees. Switch to radians
    angle = angle / 180 * Math.PI;
    
    angle /= 2;
    var sinA = Math.sin(angle);
    var cosA = Math.cos(angle);
    var sinA2 = sinA * sinA;
    
    // normalize
    var length = Math.sqrt(x * x + y * y + z * z);
    if (length == 0) {
        // bad vector, just use something reasonable
        x = 0;
        y = 0;
        z = 1;
    } else if (length != 1) {
        x /= length;
        y /= length;
        z /= length;
    }
    
    var mat = new CanvasMatrix4();

    // optimize case where axis is along major axis
    if (x == 1 && y == 0 && z == 0) {
        mat.m11 = 1;
        mat.m12 = 0;
        mat.m13 = 0;
        mat.m21 = 0;
        mat.m22 = 1 - 2 * sinA2;
        mat.m23 = 2 * sinA * cosA;
        mat.m31 = 0;
        mat.m32 = -2 * sinA * cosA;
        mat.m33 = 1 - 2 * sinA2;
        mat.m14 = mat.m24 = mat.m34 = 0;
        mat.m41 = mat.m42 = mat.m43 = 0;
        mat.m44 = 1;
    } else if (x == 0 && y == 1 && z == 0) {
        mat.m11 = 1 - 2 * sinA2;
        mat.m12 = 0;
        mat.m13 = -2 * sinA * cosA;
        mat.m21 = 0;
        mat.m22 = 1;
        mat.m23 = 0;
        mat.m31 = 2 * sinA * cosA;
        mat.m32 = 0;
        mat.m33 = 1 - 2 * sinA2;
        mat.m14 = mat.m24 = mat.m34 = 0;
        mat.m41 = mat.m42 = mat.m43 = 0;
        mat.m44 = 1;
    } else if (x == 0 && y == 0 && z == 1) {
        mat.m11 = 1 - 2 * sinA2;
        mat.m12 = 2 * sinA * cosA;
        mat.m13 = 0;
        mat.m21 = -2 * sinA * cosA;
        mat.m22 = 1 - 2 * sinA2;
        mat.m23 = 0;
        mat.m31 = 0;
        mat.m32 = 0;
        mat.m33 = 1;
        mat.m14 = mat.m24 = mat.m34 = 0;
        mat.m41 = mat.m42 = mat.m43 = 0;
        mat.m44 = 1;
    } else {
        var x2 = x*x;
        var y2 = y*y;
        var z2 = z*z;
    
        mat.m11 = 1 - 2 * (y2 + z2) * sinA2;
        mat.m12 = 2 * (x * y * sinA2 + z * sinA * cosA);
        mat.m13 = 2 * (x * z * sinA2 - y * sinA * cosA);
        mat.m21 = 2 * (y * x * sinA2 - z * sinA * cosA);
        mat.m22 = 1 - 2 * (z2 + x2) * sinA2;
        mat.m23 = 2 * (y * z * sinA2 + x * sinA * cosA);
        mat.m31 = 2 * (z * x * sinA2 + y * sinA * cosA);
        mat.m32 = 2 * (z * y * sinA2 - x * sinA * cosA);
        mat.m33 = 1 - 2 * (x2 + y2) * sinA2;
        mat.m14 = mat.m24 = mat.m34 = 0;
        mat.m41 = mat.m42 = mat.m43 = 0;
        mat.m44 = 1;
    }
    this.multRight(mat);
}

CanvasMatrix4.prototype.multRight = function(mat)
{
    var m11 = (this.m11 * mat.m11 + this.m12 * mat.m21
               + this.m13 * mat.m31 + this.m14 * mat.m41);
    var m12 = (this.m11 * mat.m12 + this.m12 * mat.m22
               + this.m13 * mat.m32 + this.m14 * mat.m42);
    var m13 = (this.m11 * mat.m13 + this.m12 * mat.m23
               + this.m13 * mat.m33 + this.m14 * mat.m43);
    var m14 = (this.m11 * mat.m14 + this.m12 * mat.m24
               + this.m13 * mat.m34 + this.m14 * mat.m44);

    var m21 = (this.m21 * mat.m11 + this.m22 * mat.m21
               + this.m23 * mat.m31 + this.m24 * mat.m41);
    var m22 = (this.m21 * mat.m12 + this.m22 * mat.m22
               + this.m23 * mat.m32 + this.m24 * mat.m42);
    var m23 = (this.m21 * mat.m13 + this.m22 * mat.m23
               + this.m23 * mat.m33 + this.m24 * mat.m43);
    var m24 = (this.m21 * mat.m14 + this.m22 * mat.m24
               + this.m23 * mat.m34 + this.m24 * mat.m44);

    var m31 = (this.m31 * mat.m11 + this.m32 * mat.m21
               + this.m33 * mat.m31 + this.m34 * mat.m41);
    var m32 = (this.m31 * mat.m12 + this.m32 * mat.m22
               + this.m33 * mat.m32 + this.m34 * mat.m42);
    var m33 = (this.m31 * mat.m13 + this.m32 * mat.m23
               + this.m33 * mat.m33 + this.m34 * mat.m43);
    var m34 = (this.m31 * mat.m14 + this.m32 * mat.m24
               + this.m33 * mat.m34 + this.m34 * mat.m44);

    var m41 = (this.m41 * mat.m11 + this.m42 * mat.m21
               + this.m43 * mat.m31 + this.m44 * mat.m41);
    var m42 = (this.m41 * mat.m12 + this.m42 * mat.m22
               + this.m43 * mat.m32 + this.m44 * mat.m42);
    var m43 = (this.m41 * mat.m13 + this.m42 * mat.m23
               + this.m43 * mat.m33 + this.m44 * mat.m43);
    var m44 = (this.m41 * mat.m14 + this.m42 * mat.m24
               + this.m43 * mat.m34 + this.m44 * mat.m44);
    
    this.m11 = m11;
    this.m12 = m12;
    this.m13 = m13;
    this.m14 = m14;
    
    this.m21 = m21;
    this.m22 = m22;
    this.m23 = m23;
    this.m24 = m24;
    
    this.m31 = m31;
    this.m32 = m32;
    this.m33 = m33;
    this.m34 = m34;
    
    this.m41 = m41;
    this.m42 = m42;
    this.m43 = m43;
    this.m44 = m44;
}

CanvasMatrix4.prototype.multLeft = function(mat)
{
    var m11 = (mat.m11 * this.m11 + mat.m12 * this.m21
               + mat.m13 * this.m31 + mat.m14 * this.m41);
    var m12 = (mat.m11 * this.m12 + mat.m12 * this.m22
               + mat.m13 * this.m32 + mat.m14 * this.m42);
    var m13 = (mat.m11 * this.m13 + mat.m12 * this.m23
               + mat.m13 * this.m33 + mat.m14 * this.m43);
    var m14 = (mat.m11 * this.m14 + mat.m12 * this.m24
               + mat.m13 * this.m34 + mat.m14 * this.m44);

    var m21 = (mat.m21 * this.m11 + mat.m22 * this.m21
               + mat.m23 * this.m31 + mat.m24 * this.m41);
    var m22 = (mat.m21 * this.m12 + mat.m22 * this.m22
               + mat.m23 * this.m32 + mat.m24 * this.m42);
    var m23 = (mat.m21 * this.m13 + mat.m22 * this.m23
               + mat.m23 * this.m33 + mat.m24 * this.m43);
    var m24 = (mat.m21 * this.m14 + mat.m22 * this.m24
               + mat.m23 * this.m34 + mat.m24 * this.m44);

    var m31 = (mat.m31 * this.m11 + mat.m32 * this.m21
               + mat.m33 * this.m31 + mat.m34 * this.m41);
    var m32 = (mat.m31 * this.m12 + mat.m32 * this.m22
               + mat.m33 * this.m32 + mat.m34 * this.m42);
    var m33 = (mat.m31 * this.m13 + mat.m32 * this.m23
               + mat.m33 * this.m33 + mat.m34 * this.m43);
    var m34 = (mat.m31 * this.m14 + mat.m32 * this.m24
               + mat.m33 * this.m34 + mat.m34 * this.m44);

    var m41 = (mat.m41 * this.m11 + mat.m42 * this.m21
               + mat.m43 * this.m31 + mat.m44 * this.m41);
    var m42 = (mat.m41 * this.m12 + mat.m42 * this.m22
               + mat.m43 * this.m32 + mat.m44 * this.m42);
    var m43 = (mat.m41 * this.m13 + mat.m42 * this.m23
               + mat.m43 * this.m33 + mat.m44 * this.m43);
    var m44 = (mat.m41 * this.m14 + mat.m42 * this.m24
               + mat.m43 * this.m34 + mat.m44 * this.m44);
    
    this.m11 = m11;
    this.m12 = m12;
    this.m13 = m13;
    this.m14 = m14;

    this.m21 = m21;
    this.m22 = m22;
    this.m23 = m23;
    this.m24 = m24;

    this.m31 = m31;
    this.m32 = m32;
    this.m33 = m33;
    this.m34 = m34;

    this.m41 = m41;
    this.m42 = m42;
    this.m43 = m43;
    this.m44 = m44;
}

CanvasMatrix4.prototype.ortho = function(left, right, bottom, top, near, far)
{
    var tx = (left + right) / (left - right);
    var ty = (top + bottom) / (top - bottom);
    var tz = (far + near) / (far - near);
    
    var matrix = new CanvasMatrix4();
    matrix.m11 = 2 / (left - right);
    matrix.m12 = 0;
    matrix.m13 = 0;
    matrix.m14 = 0;
    matrix.m21 = 0;
    matrix.m22 = 2 / (top - bottom);
    matrix.m23 = 0;
    matrix.m24 = 0;
    matrix.m31 = 0;
    matrix.m32 = 0;
    matrix.m33 = -2 / (far - near);
    matrix.m34 = 0;
    matrix.m41 = tx;
    matrix.m42 = ty;
    matrix.m43 = tz;
    matrix.m44 = 1;
    
    this.multRight(matrix);
}

CanvasMatrix4.prototype.frustum = function(left, right, bottom, top, near, far)
{
    var matrix = new CanvasMatrix4();
    var A = (right + left) / (right - left);
    var B = (top + bottom) / (top - bottom);
    var C = -(far + near) / (far - near);
    var D = -(2 * far * near) / (far - near);
    
    matrix.m11 = (2 * near) / (right - left);
    matrix.m12 = 0;
    matrix.m13 = 0;
    matrix.m14 = 0;
    
    matrix.m21 = 0;
    matrix.m22 = 2 * near / (top - bottom);
    matrix.m23 = 0;
    matrix.m24 = 0;
    
    matrix.m31 = A;
    matrix.m32 = B;
    matrix.m33 = C;
    matrix.m34 = -1;
    
    matrix.m41 = 0;
    matrix.m42 = 0;
    matrix.m43 = D;
    matrix.m44 = 0;
    
    this.multRight(matrix);
}

CanvasMatrix4.prototype.perspective = function(fovy, aspect, zNear, zFar)
{
    var top = Math.tan(fovy * Math.PI / 360) * zNear;
    var bottom = -top;
    var left = aspect * bottom;
    var right = aspect * top;
    this.frustum(left, right, bottom, top, zNear, zFar);
}

CanvasMatrix4.prototype.lookat = function(eyex, eyey, eyez, centerx, centery, centerz, upx, upy, upz)
{
    var matrix = new CanvasMatrix4();
    
    // Make rotation matrix

    // Z vector
    var zx = eyex - centerx;
    var zy = eyey - centery;
    var zz = eyez - centerz;
    var mag = Math.sqrt(zx * zx + zy * zy + zz * zz);
    if (mag) {
        zx /= mag;
        zy /= mag;
        zz /= mag;
    }

    // Y vector
    var yx = upx;
    var yy = upy;
    var yz = upz;

    // X vector = Y cross Z
    xx =  yy * zz - yz * zy;
    xy = -yx * zz + yz * zx;
    xz =  yx * zy - yy * zx;

    // Recompute Y = Z cross X
    yx = zy * xz - zz * xy;
    yy = -zx * xz + zz * xx;
    yx = zx * xy - zy * xx;

    // cross product gives area of parallelogram, which is < 1.0 for
    // non-perpendicular unit-length vectors; so normalize x, y here

    mag = Math.sqrt(xx * xx + xy * xy + xz * xz);
    if (mag) {
        xx /= mag;
        xy /= mag;
        xz /= mag;
    }

    mag = Math.sqrt(yx * yx + yy * yy + yz * yz);
    if (mag) {
        yx /= mag;
        yy /= mag;
        yz /= mag;
    }

    matrix.m11 = xx;
    matrix.m12 = xy;
    matrix.m13 = xz;
    matrix.m14 = 0;
    
    matrix.m21 = yx;
    matrix.m22 = yy;
    matrix.m23 = yz;
    matrix.m24 = 0;
    
    matrix.m31 = zx;
    matrix.m32 = zy;
    matrix.m33 = zz;
    matrix.m34 = 0;
    
    matrix.m41 = 0;
    matrix.m42 = 0;
    matrix.m43 = 0;
    matrix.m44 = 1;
    matrix.translate(-eyex, -eyey, -eyez);
    
    this.multRight(matrix);
}

// Support functions
CanvasMatrix4.prototype._determinant2x2 = function(a, b, c, d)
{
    return a * d - b * c;
}

CanvasMatrix4.prototype._determinant3x3 = function(a1, a2, a3, b1, b2, b3, c1, c2, c3)
{
    return a1 * this._determinant2x2(b2, b3, c2, c3)
         - b1 * this._determinant2x2(a2, a3, c2, c3)
         + c1 * this._determinant2x2(a2, a3, b2, b3);
}

CanvasMatrix4.prototype._determinant4x4 = function()
{
    var a1 = this.m11;
    var b1 = this.m12; 
    var c1 = this.m13;
    var d1 = this.m14;

    var a2 = this.m21;
    var b2 = this.m22; 
    var c2 = this.m23;
    var d2 = this.m24;

    var a3 = this.m31;
    var b3 = this.m32; 
    var c3 = this.m33;
    var d3 = this.m34;

    var a4 = this.m41;
    var b4 = this.m42; 
    var c4 = this.m43;
    var d4 = this.m44;

    return a1 * this._determinant3x3(b2, b3, b4, c2, c3, c4, d2, d3, d4)
         - b1 * this._determinant3x3(a2, a3, a4, c2, c3, c4, d2, d3, d4)
         + c1 * this._determinant3x3(a2, a3, a4, b2, b3, b4, d2, d3, d4)
         - d1 * this._determinant3x3(a2, a3, a4, b2, b3, b4, c2, c3, c4);
}

CanvasMatrix4.prototype._makeAdjoint = function()
{
    var a1 = this.m11;
    var b1 = this.m12; 
    var c1 = this.m13;
    var d1 = this.m14;

    var a2 = this.m21;
    var b2 = this.m22; 
    var c2 = this.m23;
    var d2 = this.m24;

    var a3 = this.m31;
    var b3 = this.m32; 
    var c3 = this.m33;
    var d3 = this.m34;

    var a4 = this.m41;
    var b4 = this.m42; 
    var c4 = this.m43;
    var d4 = this.m44;

    // Row column labeling reversed since we transpose rows & columns
    this.m11  =   this._determinant3x3(b2, b3, b4, c2, c3, c4, d2, d3, d4);
    this.m21  = - this._determinant3x3(a2, a3, a4, c2, c3, c4, d2, d3, d4);
    this.m31  =   this._determinant3x3(a2, a3, a4, b2, b3, b4, d2, d3, d4);
    this.m41  = - this._determinant3x3(a2, a3, a4, b2, b3, b4, c2, c3, c4);
        
    this.m12  = - this._determinant3x3(b1, b3, b4, c1, c3, c4, d1, d3, d4);
    this.m22  =   this._determinant3x3(a1, a3, a4, c1, c3, c4, d1, d3, d4);
    this.m32  = - this._determinant3x3(a1, a3, a4, b1, b3, b4, d1, d3, d4);
    this.m42  =   this._determinant3x3(a1, a3, a4, b1, b3, b4, c1, c3, c4);
        
    this.m13  =   this._determinant3x3(b1, b2, b4, c1, c2, c4, d1, d2, d4);
    this.m23  = - this._determinant3x3(a1, a2, a4, c1, c2, c4, d1, d2, d4);
    this.m33  =   this._determinant3x3(a1, a2, a4, b1, b2, b4, d1, d2, d4);
    this.m43  = - this._determinant3x3(a1, a2, a4, b1, b2, b4, c1, c2, c4);
        
    this.m14  = - this._determinant3x3(b1, b2, b3, c1, c2, c3, d1, d2, d3);
    this.m24  =   this._determinant3x3(a1, a2, a3, c1, c2, c3, d1, d2, d3);
    this.m34  = - this._determinant3x3(a1, a2, a3, b1, b2, b3, d1, d2, d3);
    this.m44  =   this._determinant3x3(a1, a2, a3, b1, b2, b3, c1, c2, c3);
}
