--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/webGL/dandy/resources/CanvasMatrix.js	Mon Jun 07 17:58:31 2010 +0900
@@ -0,0 +1,722 @@
+/*
+ * 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);
+}
\ No newline at end of file