sawine@2: /*
sawine@2:     CanvasMatrix4 class
sawine@2:     
sawine@2:     This class implements a 4x4 matrix. It has functions which
sawine@2:     duplicate the functionality of the OpenGL matrix stack and
sawine@2:     glut functions.
sawine@2:     
sawine@2:     IDL:
sawine@2:     
sawine@2:     [
sawine@2:         Constructor(in CanvasMatrix4 matrix),           // copy passed matrix into new CanvasMatrix4
sawine@2:         Constructor(in sequence<float> array)           // create new CanvasMatrix4 with 16 floats (row major)
sawine@2:         Constructor()                                   // create new CanvasMatrix4 with identity matrix
sawine@2:     ]
sawine@2:     interface CanvasMatrix4 {
sawine@2:         attribute float m11;
sawine@2:         attribute float m12;
sawine@2:         attribute float m13;
sawine@2:         attribute float m14;
sawine@2:         attribute float m21;
sawine@2:         attribute float m22;
sawine@2:         attribute float m23;
sawine@2:         attribute float m24;
sawine@2:         attribute float m31;
sawine@2:         attribute float m32;
sawine@2:         attribute float m33;
sawine@2:         attribute float m34;
sawine@2:         attribute float m41;
sawine@2:         attribute float m42;
sawine@2:         attribute float m43;
sawine@2:         attribute float m44;
sawine@2: 
sawine@2:         void load(in CanvasMatrix4 matrix);                 // copy the values from the passed matrix
sawine@2:         void load(in sequence<float> array);                // copy 16 floats into the matrix
sawine@2:         sequence<float> getAsArray();                       // return the matrix as an array of 16 floats
sawine@2:         WebGLFloatArray getAsCanvasFloatArray();           // return the matrix as a WebGLFloatArray with 16 values
sawine@2:         void makeIdentity();                                // replace the matrix with identity
sawine@2:         void transpose();                                   // replace the matrix with its transpose
sawine@2:         void invert();                                      // replace the matrix with its inverse
sawine@2:         
sawine@2:         void translate(in float x, in float y, in float z); // multiply the matrix by passed translation values on the right
sawine@2:         void scale(in float x, in float y, in float z);     // multiply the matrix by passed scale values on the right
sawine@2:         void rotate(in float angle,                         // multiply the matrix by passed rotation values on the right
sawine@2:                     in float x, in float y, in float z);    // (angle is in degrees)
sawine@2:         void multRight(in CanvasMatrix matrix);             // multiply the matrix by the passed matrix on the right
sawine@2:         void multLeft(in CanvasMatrix matrix);              // multiply the matrix by the passed matrix on the left
sawine@2:         void ortho(in float left, in float right,           // multiply the matrix by the passed ortho values on the right
sawine@2:                    in float bottom, in float top, 
sawine@2:                    in float near, in float far);
sawine@2:         void frustum(in float left, in float right,         // multiply the matrix by the passed frustum values on the right
sawine@2:                      in float bottom, in float top, 
sawine@2:                      in float near, in float far);
sawine@2:         void perspective(in float fovy, in float aspect,    // multiply the matrix by the passed perspective values on the right
sawine@2:                          in float zNear, in float zFar);
sawine@2:         void lookat(in float eyex, in float eyey, in float eyez,    // multiply the matrix by the passed lookat 
sawine@2:                     in float ctrx, in float ctry, in float ctrz,    // values on the right
sawine@2:                     in float upx, in float upy, in float upz);
sawine@2:     }
sawine@2: */
sawine@2: 
sawine@2: CanvasMatrix4 = function(m)
sawine@2: {
sawine@2:     if (typeof m == 'object') {
sawine@2:         if ("length" in m && m.length >= 16) {
sawine@2:             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]);
sawine@2:             return;
sawine@2:         }
sawine@2:         else if (m instanceof CanvasMatrix4) {
sawine@2:             this.load(m);
sawine@2:             return;
sawine@2:         }
sawine@2:     }
sawine@2:     this.makeIdentity();
sawine@2: }
sawine@2: 
sawine@2: CanvasMatrix4.prototype.load = function()
sawine@2: {
sawine@2:     if (arguments.length == 1 && typeof arguments[0] == 'object') {
sawine@2:         var matrix = arguments[0];
sawine@2:         
sawine@2:         if ("length" in matrix && matrix.length == 16) {
sawine@2:             this.m11 = matrix[0];
sawine@2:             this.m12 = matrix[1];
sawine@2:             this.m13 = matrix[2];
sawine@2:             this.m14 = matrix[3];
sawine@2: 
sawine@2:             this.m21 = matrix[4];
sawine@2:             this.m22 = matrix[5];
sawine@2:             this.m23 = matrix[6];
sawine@2:             this.m24 = matrix[7];
sawine@2: 
sawine@2:             this.m31 = matrix[8];
sawine@2:             this.m32 = matrix[9];
sawine@2:             this.m33 = matrix[10];
sawine@2:             this.m34 = matrix[11];
sawine@2: 
sawine@2:             this.m41 = matrix[12];
sawine@2:             this.m42 = matrix[13];
sawine@2:             this.m43 = matrix[14];
sawine@2:             this.m44 = matrix[15];
sawine@2:             return;
sawine@2:         }
sawine@2:             
sawine@2:         if (arguments[0] instanceof CanvasMatrix4) {
sawine@2:         
sawine@2:             this.m11 = matrix.m11;
sawine@2:             this.m12 = matrix.m12;
sawine@2:             this.m13 = matrix.m13;
sawine@2:             this.m14 = matrix.m14;
sawine@2: 
sawine@2:             this.m21 = matrix.m21;
sawine@2:             this.m22 = matrix.m22;
sawine@2:             this.m23 = matrix.m23;
sawine@2:             this.m24 = matrix.m24;
sawine@2: 
sawine@2:             this.m31 = matrix.m31;
sawine@2:             this.m32 = matrix.m32;
sawine@2:             this.m33 = matrix.m33;
sawine@2:             this.m34 = matrix.m34;
sawine@2: 
sawine@2:             this.m41 = matrix.m41;
sawine@2:             this.m42 = matrix.m42;
sawine@2:             this.m43 = matrix.m43;
sawine@2:             this.m44 = matrix.m44;
sawine@2:             return;
sawine@2:         }
sawine@2:     }
sawine@2:     
sawine@2:     this.makeIdentity();
sawine@2: }
sawine@2: 
sawine@2: CanvasMatrix4.prototype.getAsArray = function()
sawine@2: {
sawine@2:     return [
sawine@2:         this.m11, this.m12, this.m13, this.m14, 
sawine@2:         this.m21, this.m22, this.m23, this.m24, 
sawine@2:         this.m31, this.m32, this.m33, this.m34, 
sawine@2:         this.m41, this.m42, this.m43, this.m44
sawine@2:     ];
sawine@2: }
sawine@2: 
sawine@2: CanvasMatrix4.prototype.getAsCanvasFloatArray = function()
sawine@2: {
sawine@2:     return new WebGLFloatArray(this.getAsArray());
sawine@2: }
sawine@2: 
sawine@2: CanvasMatrix4.prototype.makeIdentity = function()
sawine@2: {
sawine@2:     this.m11 = 1;
sawine@2:     this.m12 = 0;
sawine@2:     this.m13 = 0;
sawine@2:     this.m14 = 0;
sawine@2:     
sawine@2:     this.m21 = 0;
sawine@2:     this.m22 = 1;
sawine@2:     this.m23 = 0;
sawine@2:     this.m24 = 0;
sawine@2:     
sawine@2:     this.m31 = 0;
sawine@2:     this.m32 = 0;
sawine@2:     this.m33 = 1;
sawine@2:     this.m34 = 0;
sawine@2:     
sawine@2:     this.m41 = 0;
sawine@2:     this.m42 = 0;
sawine@2:     this.m43 = 0;
sawine@2:     this.m44 = 1;
sawine@2: }
sawine@2: 
sawine@2: CanvasMatrix4.prototype.transpose = function()
sawine@2: {
sawine@2:     var tmp = this.m12;
sawine@2:     this.m12 = this.m21;
sawine@2:     this.m21 = tmp;
sawine@2:     
sawine@2:     tmp = this.m13;
sawine@2:     this.m13 = this.m31;
sawine@2:     this.m31 = tmp;
sawine@2:     
sawine@2:     tmp = this.m14;
sawine@2:     this.m14 = this.m41;
sawine@2:     this.m41 = tmp;
sawine@2:     
sawine@2:     tmp = this.m23;
sawine@2:     this.m23 = this.m32;
sawine@2:     this.m32 = tmp;
sawine@2:     
sawine@2:     tmp = this.m24;
sawine@2:     this.m24 = this.m42;
sawine@2:     this.m42 = tmp;
sawine@2:     
sawine@2:     tmp = this.m34;
sawine@2:     this.m34 = this.m43;
sawine@2:     this.m43 = tmp;
sawine@2: }
sawine@2: 
sawine@2: CanvasMatrix4.prototype.invert = function()
sawine@2: {
sawine@2:     // Calculate the 4x4 determinant
sawine@2:     // If the determinant is zero, 
sawine@2:     // then the inverse matrix is not unique.
sawine@2:     var det = this._determinant4x4();
sawine@2: 
sawine@2:     if (Math.abs(det) < 1e-8)
sawine@2:         return null;
sawine@2: 
sawine@2:     this._makeAdjoint();
sawine@2: 
sawine@2:     // Scale the adjoint matrix to get the inverse
sawine@2:     this.m11 /= det;
sawine@2:     this.m12 /= det;
sawine@2:     this.m13 /= det;
sawine@2:     this.m14 /= det;
sawine@2:     
sawine@2:     this.m21 /= det;
sawine@2:     this.m22 /= det;
sawine@2:     this.m23 /= det;
sawine@2:     this.m24 /= det;
sawine@2:     
sawine@2:     this.m31 /= det;
sawine@2:     this.m32 /= det;
sawine@2:     this.m33 /= det;
sawine@2:     this.m34 /= det;
sawine@2:     
sawine@2:     this.m41 /= det;
sawine@2:     this.m42 /= det;
sawine@2:     this.m43 /= det;
sawine@2:     this.m44 /= det;
sawine@2: }
sawine@2: 
sawine@2: CanvasMatrix4.prototype.translate = function(x,y,z)
sawine@2: {
sawine@2:     if (x == undefined)
sawine@2:         x = 0;
sawine@2:         if (y == undefined)
sawine@2:             y = 0;
sawine@2:     if (z == undefined)
sawine@2:         z = 0;
sawine@2:     
sawine@2:     var matrix = new CanvasMatrix4();
sawine@2:     matrix.m41 = x;
sawine@2:     matrix.m42 = y;
sawine@2:     matrix.m43 = z;
sawine@2: 
sawine@2:     this.multRight(matrix);
sawine@2: }
sawine@2: 
sawine@2: CanvasMatrix4.prototype.scale = function(x,y,z)
sawine@2: {
sawine@2:     if (x == undefined)
sawine@2:         x = 1;
sawine@2:     if (z == undefined) {
sawine@2:         if (y == undefined) {
sawine@2:             y = x;
sawine@2:             z = x;
sawine@2:         }
sawine@2:         else
sawine@2:             z = 1;
sawine@2:     }
sawine@2:     else if (y == undefined)
sawine@2:         y = x;
sawine@2:     
sawine@2:     var matrix = new CanvasMatrix4();
sawine@2:     matrix.m11 = x;
sawine@2:     matrix.m22 = y;
sawine@2:     matrix.m33 = z;
sawine@2:     
sawine@2:     this.multRight(matrix);
sawine@2: }
sawine@2: 
sawine@2: CanvasMatrix4.prototype.rotate = function(angle,x,y,z)
sawine@2: {
sawine@2:     // angles are in degrees. Switch to radians
sawine@2:     angle = angle / 180 * Math.PI;
sawine@2:     
sawine@2:     angle /= 2;
sawine@2:     var sinA = Math.sin(angle);
sawine@2:     var cosA = Math.cos(angle);
sawine@2:     var sinA2 = sinA * sinA;
sawine@2:     
sawine@2:     // normalize
sawine@2:     var length = Math.sqrt(x * x + y * y + z * z);
sawine@2:     if (length == 0) {
sawine@2:         // bad vector, just use something reasonable
sawine@2:         x = 0;
sawine@2:         y = 0;
sawine@2:         z = 1;
sawine@2:     } else if (length != 1) {
sawine@2:         x /= length;
sawine@2:         y /= length;
sawine@2:         z /= length;
sawine@2:     }
sawine@2:     
sawine@2:     var mat = new CanvasMatrix4();
sawine@2: 
sawine@2:     // optimize case where axis is along major axis
sawine@2:     if (x == 1 && y == 0 && z == 0) {
sawine@2:         mat.m11 = 1;
sawine@2:         mat.m12 = 0;
sawine@2:         mat.m13 = 0;
sawine@2:         mat.m21 = 0;
sawine@2:         mat.m22 = 1 - 2 * sinA2;
sawine@2:         mat.m23 = 2 * sinA * cosA;
sawine@2:         mat.m31 = 0;
sawine@2:         mat.m32 = -2 * sinA * cosA;
sawine@2:         mat.m33 = 1 - 2 * sinA2;
sawine@2:         mat.m14 = mat.m24 = mat.m34 = 0;
sawine@2:         mat.m41 = mat.m42 = mat.m43 = 0;
sawine@2:         mat.m44 = 1;
sawine@2:     } else if (x == 0 && y == 1 && z == 0) {
sawine@2:         mat.m11 = 1 - 2 * sinA2;
sawine@2:         mat.m12 = 0;
sawine@2:         mat.m13 = -2 * sinA * cosA;
sawine@2:         mat.m21 = 0;
sawine@2:         mat.m22 = 1;
sawine@2:         mat.m23 = 0;
sawine@2:         mat.m31 = 2 * sinA * cosA;
sawine@2:         mat.m32 = 0;
sawine@2:         mat.m33 = 1 - 2 * sinA2;
sawine@2:         mat.m14 = mat.m24 = mat.m34 = 0;
sawine@2:         mat.m41 = mat.m42 = mat.m43 = 0;
sawine@2:         mat.m44 = 1;
sawine@2:     } else if (x == 0 && y == 0 && z == 1) {
sawine@2:         mat.m11 = 1 - 2 * sinA2;
sawine@2:         mat.m12 = 2 * sinA * cosA;
sawine@2:         mat.m13 = 0;
sawine@2:         mat.m21 = -2 * sinA * cosA;
sawine@2:         mat.m22 = 1 - 2 * sinA2;
sawine@2:         mat.m23 = 0;
sawine@2:         mat.m31 = 0;
sawine@2:         mat.m32 = 0;
sawine@2:         mat.m33 = 1;
sawine@2:         mat.m14 = mat.m24 = mat.m34 = 0;
sawine@2:         mat.m41 = mat.m42 = mat.m43 = 0;
sawine@2:         mat.m44 = 1;
sawine@2:     } else {
sawine@2:         var x2 = x*x;
sawine@2:         var y2 = y*y;
sawine@2:         var z2 = z*z;
sawine@2:     
sawine@2:         mat.m11 = 1 - 2 * (y2 + z2) * sinA2;
sawine@2:         mat.m12 = 2 * (x * y * sinA2 + z * sinA * cosA);
sawine@2:         mat.m13 = 2 * (x * z * sinA2 - y * sinA * cosA);
sawine@2:         mat.m21 = 2 * (y * x * sinA2 - z * sinA * cosA);
sawine@2:         mat.m22 = 1 - 2 * (z2 + x2) * sinA2;
sawine@2:         mat.m23 = 2 * (y * z * sinA2 + x * sinA * cosA);
sawine@2:         mat.m31 = 2 * (z * x * sinA2 + y * sinA * cosA);
sawine@2:         mat.m32 = 2 * (z * y * sinA2 - x * sinA * cosA);
sawine@2:         mat.m33 = 1 - 2 * (x2 + y2) * sinA2;
sawine@2:         mat.m14 = mat.m24 = mat.m34 = 0;
sawine@2:         mat.m41 = mat.m42 = mat.m43 = 0;
sawine@2:         mat.m44 = 1;
sawine@2:     }
sawine@2:     this.multRight(mat);
sawine@2: }
sawine@2: 
sawine@2: CanvasMatrix4.prototype.multRight = function(mat)
sawine@2: {
sawine@2:     var m11 = (this.m11 * mat.m11 + this.m12 * mat.m21
sawine@2:                + this.m13 * mat.m31 + this.m14 * mat.m41);
sawine@2:     var m12 = (this.m11 * mat.m12 + this.m12 * mat.m22
sawine@2:                + this.m13 * mat.m32 + this.m14 * mat.m42);
sawine@2:     var m13 = (this.m11 * mat.m13 + this.m12 * mat.m23
sawine@2:                + this.m13 * mat.m33 + this.m14 * mat.m43);
sawine@2:     var m14 = (this.m11 * mat.m14 + this.m12 * mat.m24
sawine@2:                + this.m13 * mat.m34 + this.m14 * mat.m44);
sawine@2: 
sawine@2:     var m21 = (this.m21 * mat.m11 + this.m22 * mat.m21
sawine@2:                + this.m23 * mat.m31 + this.m24 * mat.m41);
sawine@2:     var m22 = (this.m21 * mat.m12 + this.m22 * mat.m22
sawine@2:                + this.m23 * mat.m32 + this.m24 * mat.m42);
sawine@2:     var m23 = (this.m21 * mat.m13 + this.m22 * mat.m23
sawine@2:                + this.m23 * mat.m33 + this.m24 * mat.m43);
sawine@2:     var m24 = (this.m21 * mat.m14 + this.m22 * mat.m24
sawine@2:                + this.m23 * mat.m34 + this.m24 * mat.m44);
sawine@2: 
sawine@2:     var m31 = (this.m31 * mat.m11 + this.m32 * mat.m21
sawine@2:                + this.m33 * mat.m31 + this.m34 * mat.m41);
sawine@2:     var m32 = (this.m31 * mat.m12 + this.m32 * mat.m22
sawine@2:                + this.m33 * mat.m32 + this.m34 * mat.m42);
sawine@2:     var m33 = (this.m31 * mat.m13 + this.m32 * mat.m23
sawine@2:                + this.m33 * mat.m33 + this.m34 * mat.m43);
sawine@2:     var m34 = (this.m31 * mat.m14 + this.m32 * mat.m24
sawine@2:                + this.m33 * mat.m34 + this.m34 * mat.m44);
sawine@2: 
sawine@2:     var m41 = (this.m41 * mat.m11 + this.m42 * mat.m21
sawine@2:                + this.m43 * mat.m31 + this.m44 * mat.m41);
sawine@2:     var m42 = (this.m41 * mat.m12 + this.m42 * mat.m22
sawine@2:                + this.m43 * mat.m32 + this.m44 * mat.m42);
sawine@2:     var m43 = (this.m41 * mat.m13 + this.m42 * mat.m23
sawine@2:                + this.m43 * mat.m33 + this.m44 * mat.m43);
sawine@2:     var m44 = (this.m41 * mat.m14 + this.m42 * mat.m24
sawine@2:                + this.m43 * mat.m34 + this.m44 * mat.m44);
sawine@2:     
sawine@2:     this.m11 = m11;
sawine@2:     this.m12 = m12;
sawine@2:     this.m13 = m13;
sawine@2:     this.m14 = m14;
sawine@2:     
sawine@2:     this.m21 = m21;
sawine@2:     this.m22 = m22;
sawine@2:     this.m23 = m23;
sawine@2:     this.m24 = m24;
sawine@2:     
sawine@2:     this.m31 = m31;
sawine@2:     this.m32 = m32;
sawine@2:     this.m33 = m33;
sawine@2:     this.m34 = m34;
sawine@2:     
sawine@2:     this.m41 = m41;
sawine@2:     this.m42 = m42;
sawine@2:     this.m43 = m43;
sawine@2:     this.m44 = m44;
sawine@2: }
sawine@2: 
sawine@2: CanvasMatrix4.prototype.multLeft = function(mat)
sawine@2: {
sawine@2:     var m11 = (mat.m11 * this.m11 + mat.m12 * this.m21
sawine@2:                + mat.m13 * this.m31 + mat.m14 * this.m41);
sawine@2:     var m12 = (mat.m11 * this.m12 + mat.m12 * this.m22
sawine@2:                + mat.m13 * this.m32 + mat.m14 * this.m42);
sawine@2:     var m13 = (mat.m11 * this.m13 + mat.m12 * this.m23
sawine@2:                + mat.m13 * this.m33 + mat.m14 * this.m43);
sawine@2:     var m14 = (mat.m11 * this.m14 + mat.m12 * this.m24
sawine@2:                + mat.m13 * this.m34 + mat.m14 * this.m44);
sawine@2: 
sawine@2:     var m21 = (mat.m21 * this.m11 + mat.m22 * this.m21
sawine@2:                + mat.m23 * this.m31 + mat.m24 * this.m41);
sawine@2:     var m22 = (mat.m21 * this.m12 + mat.m22 * this.m22
sawine@2:                + mat.m23 * this.m32 + mat.m24 * this.m42);
sawine@2:     var m23 = (mat.m21 * this.m13 + mat.m22 * this.m23
sawine@2:                + mat.m23 * this.m33 + mat.m24 * this.m43);
sawine@2:     var m24 = (mat.m21 * this.m14 + mat.m22 * this.m24
sawine@2:                + mat.m23 * this.m34 + mat.m24 * this.m44);
sawine@2: 
sawine@2:     var m31 = (mat.m31 * this.m11 + mat.m32 * this.m21
sawine@2:                + mat.m33 * this.m31 + mat.m34 * this.m41);
sawine@2:     var m32 = (mat.m31 * this.m12 + mat.m32 * this.m22
sawine@2:                + mat.m33 * this.m32 + mat.m34 * this.m42);
sawine@2:     var m33 = (mat.m31 * this.m13 + mat.m32 * this.m23
sawine@2:                + mat.m33 * this.m33 + mat.m34 * this.m43);
sawine@2:     var m34 = (mat.m31 * this.m14 + mat.m32 * this.m24
sawine@2:                + mat.m33 * this.m34 + mat.m34 * this.m44);
sawine@2: 
sawine@2:     var m41 = (mat.m41 * this.m11 + mat.m42 * this.m21
sawine@2:                + mat.m43 * this.m31 + mat.m44 * this.m41);
sawine@2:     var m42 = (mat.m41 * this.m12 + mat.m42 * this.m22
sawine@2:                + mat.m43 * this.m32 + mat.m44 * this.m42);
sawine@2:     var m43 = (mat.m41 * this.m13 + mat.m42 * this.m23
sawine@2:                + mat.m43 * this.m33 + mat.m44 * this.m43);
sawine@2:     var m44 = (mat.m41 * this.m14 + mat.m42 * this.m24
sawine@2:                + mat.m43 * this.m34 + mat.m44 * this.m44);
sawine@2:     
sawine@2:     this.m11 = m11;
sawine@2:     this.m12 = m12;
sawine@2:     this.m13 = m13;
sawine@2:     this.m14 = m14;
sawine@2: 
sawine@2:     this.m21 = m21;
sawine@2:     this.m22 = m22;
sawine@2:     this.m23 = m23;
sawine@2:     this.m24 = m24;
sawine@2: 
sawine@2:     this.m31 = m31;
sawine@2:     this.m32 = m32;
sawine@2:     this.m33 = m33;
sawine@2:     this.m34 = m34;
sawine@2: 
sawine@2:     this.m41 = m41;
sawine@2:     this.m42 = m42;
sawine@2:     this.m43 = m43;
sawine@2:     this.m44 = m44;
sawine@2: }
sawine@2: 
sawine@2: CanvasMatrix4.prototype.ortho = function(left, right, bottom, top, near, far)
sawine@2: {
sawine@2:     var tx = (left + right) / (left - right);
sawine@2:     var ty = (top + bottom) / (top - bottom);
sawine@2:     var tz = (far + near) / (far - near);
sawine@2:     
sawine@2:     var matrix = new CanvasMatrix4();
sawine@2:     matrix.m11 = 2 / (left - right);
sawine@2:     matrix.m12 = 0;
sawine@2:     matrix.m13 = 0;
sawine@2:     matrix.m14 = 0;
sawine@2:     matrix.m21 = 0;
sawine@2:     matrix.m22 = 2 / (top - bottom);
sawine@2:     matrix.m23 = 0;
sawine@2:     matrix.m24 = 0;
sawine@2:     matrix.m31 = 0;
sawine@2:     matrix.m32 = 0;
sawine@2:     matrix.m33 = -2 / (far - near);
sawine@2:     matrix.m34 = 0;
sawine@2:     matrix.m41 = tx;
sawine@2:     matrix.m42 = ty;
sawine@2:     matrix.m43 = tz;
sawine@2:     matrix.m44 = 1;
sawine@2:     
sawine@2:     this.multRight(matrix);
sawine@2: }
sawine@2: 
sawine@2: CanvasMatrix4.prototype.frustum = function(left, right, bottom, top, near, far)
sawine@2: {
sawine@2:     var matrix = new CanvasMatrix4();
sawine@2:     var A = (right + left) / (right - left);
sawine@2:     var B = (top + bottom) / (top - bottom);
sawine@2:     var C = -(far + near) / (far - near);
sawine@2:     var D = -(2 * far * near) / (far - near);
sawine@2:     
sawine@2:     matrix.m11 = (2 * near) / (right - left);
sawine@2:     matrix.m12 = 0;
sawine@2:     matrix.m13 = 0;
sawine@2:     matrix.m14 = 0;
sawine@2:     
sawine@2:     matrix.m21 = 0;
sawine@2:     matrix.m22 = 2 * near / (top - bottom);
sawine@2:     matrix.m23 = 0;
sawine@2:     matrix.m24 = 0;
sawine@2:     
sawine@2:     matrix.m31 = A;
sawine@2:     matrix.m32 = B;
sawine@2:     matrix.m33 = C;
sawine@2:     matrix.m34 = -1;
sawine@2:     
sawine@2:     matrix.m41 = 0;
sawine@2:     matrix.m42 = 0;
sawine@2:     matrix.m43 = D;
sawine@2:     matrix.m44 = 0;
sawine@2:     
sawine@2:     this.multRight(matrix);
sawine@2: }
sawine@2: 
sawine@2: CanvasMatrix4.prototype.perspective = function(fovy, aspect, zNear, zFar)
sawine@2: {
sawine@2:     var top = Math.tan(fovy * Math.PI / 360) * zNear;
sawine@2:     var bottom = -top;
sawine@2:     var left = aspect * bottom;
sawine@2:     var right = aspect * top;
sawine@2:     this.frustum(left, right, bottom, top, zNear, zFar);
sawine@2: }
sawine@2: 
sawine@2: CanvasMatrix4.prototype.lookat = function(eyex, eyey, eyez, centerx, centery, centerz, upx, upy, upz)
sawine@2: {
sawine@2:     var matrix = new CanvasMatrix4();
sawine@2:     
sawine@2:     // Make rotation matrix
sawine@2: 
sawine@2:     // Z vector
sawine@2:     var zx = eyex - centerx;
sawine@2:     var zy = eyey - centery;
sawine@2:     var zz = eyez - centerz;
sawine@2:     var mag = Math.sqrt(zx * zx + zy * zy + zz * zz);
sawine@2:     if (mag) {
sawine@2:         zx /= mag;
sawine@2:         zy /= mag;
sawine@2:         zz /= mag;
sawine@2:     }
sawine@2: 
sawine@2:     // Y vector
sawine@2:     var yx = upx;
sawine@2:     var yy = upy;
sawine@2:     var yz = upz;
sawine@2: 
sawine@2:     // X vector = Y cross Z
sawine@2:     xx =  yy * zz - yz * zy;
sawine@2:     xy = -yx * zz + yz * zx;
sawine@2:     xz =  yx * zy - yy * zx;
sawine@2: 
sawine@2:     // Recompute Y = Z cross X
sawine@2:     yx = zy * xz - zz * xy;
sawine@2:     yy = -zx * xz + zz * xx;
sawine@2:     yx = zx * xy - zy * xx;
sawine@2: 
sawine@2:     // cross product gives area of parallelogram, which is < 1.0 for
sawine@2:     // non-perpendicular unit-length vectors; so normalize x, y here
sawine@2: 
sawine@2:     mag = Math.sqrt(xx * xx + xy * xy + xz * xz);
sawine@2:     if (mag) {
sawine@2:         xx /= mag;
sawine@2:         xy /= mag;
sawine@2:         xz /= mag;
sawine@2:     }
sawine@2: 
sawine@2:     mag = Math.sqrt(yx * yx + yy * yy + yz * yz);
sawine@2:     if (mag) {
sawine@2:         yx /= mag;
sawine@2:         yy /= mag;
sawine@2:         yz /= mag;
sawine@2:     }
sawine@2: 
sawine@2:     matrix.m11 = xx;
sawine@2:     matrix.m12 = xy;
sawine@2:     matrix.m13 = xz;
sawine@2:     matrix.m14 = 0;
sawine@2:     
sawine@2:     matrix.m21 = yx;
sawine@2:     matrix.m22 = yy;
sawine@2:     matrix.m23 = yz;
sawine@2:     matrix.m24 = 0;
sawine@2:     
sawine@2:     matrix.m31 = zx;
sawine@2:     matrix.m32 = zy;
sawine@2:     matrix.m33 = zz;
sawine@2:     matrix.m34 = 0;
sawine@2:     
sawine@2:     matrix.m41 = 0;
sawine@2:     matrix.m42 = 0;
sawine@2:     matrix.m43 = 0;
sawine@2:     matrix.m44 = 1;
sawine@2:     matrix.translate(-eyex, -eyey, -eyez);
sawine@2:     
sawine@2:     this.multRight(matrix);
sawine@2: }
sawine@2: 
sawine@2: // Support functions
sawine@2: CanvasMatrix4.prototype._determinant2x2 = function(a, b, c, d)
sawine@2: {
sawine@2:     return a * d - b * c;
sawine@2: }
sawine@2: 
sawine@2: CanvasMatrix4.prototype._determinant3x3 = function(a1, a2, a3, b1, b2, b3, c1, c2, c3)
sawine@2: {
sawine@2:     return a1 * this._determinant2x2(b2, b3, c2, c3)
sawine@2:          - b1 * this._determinant2x2(a2, a3, c2, c3)
sawine@2:          + c1 * this._determinant2x2(a2, a3, b2, b3);
sawine@2: }
sawine@2: 
sawine@2: CanvasMatrix4.prototype._determinant4x4 = function()
sawine@2: {
sawine@2:     var a1 = this.m11;
sawine@2:     var b1 = this.m12; 
sawine@2:     var c1 = this.m13;
sawine@2:     var d1 = this.m14;
sawine@2: 
sawine@2:     var a2 = this.m21;
sawine@2:     var b2 = this.m22; 
sawine@2:     var c2 = this.m23;
sawine@2:     var d2 = this.m24;
sawine@2: 
sawine@2:     var a3 = this.m31;
sawine@2:     var b3 = this.m32; 
sawine@2:     var c3 = this.m33;
sawine@2:     var d3 = this.m34;
sawine@2: 
sawine@2:     var a4 = this.m41;
sawine@2:     var b4 = this.m42; 
sawine@2:     var c4 = this.m43;
sawine@2:     var d4 = this.m44;
sawine@2: 
sawine@2:     return a1 * this._determinant3x3(b2, b3, b4, c2, c3, c4, d2, d3, d4)
sawine@2:          - b1 * this._determinant3x3(a2, a3, a4, c2, c3, c4, d2, d3, d4)
sawine@2:          + c1 * this._determinant3x3(a2, a3, a4, b2, b3, b4, d2, d3, d4)
sawine@2:          - d1 * this._determinant3x3(a2, a3, a4, b2, b3, b4, c2, c3, c4);
sawine@2: }
sawine@2: 
sawine@2: CanvasMatrix4.prototype._makeAdjoint = function()
sawine@2: {
sawine@2:     var a1 = this.m11;
sawine@2:     var b1 = this.m12; 
sawine@2:     var c1 = this.m13;
sawine@2:     var d1 = this.m14;
sawine@2: 
sawine@2:     var a2 = this.m21;
sawine@2:     var b2 = this.m22; 
sawine@2:     var c2 = this.m23;
sawine@2:     var d2 = this.m24;
sawine@2: 
sawine@2:     var a3 = this.m31;
sawine@2:     var b3 = this.m32; 
sawine@2:     var c3 = this.m33;
sawine@2:     var d3 = this.m34;
sawine@2: 
sawine@2:     var a4 = this.m41;
sawine@2:     var b4 = this.m42; 
sawine@2:     var c4 = this.m43;
sawine@2:     var d4 = this.m44;
sawine@2: 
sawine@2:     // Row column labeling reversed since we transpose rows & columns
sawine@2:     this.m11  =   this._determinant3x3(b2, b3, b4, c2, c3, c4, d2, d3, d4);
sawine@2:     this.m21  = - this._determinant3x3(a2, a3, a4, c2, c3, c4, d2, d3, d4);
sawine@2:     this.m31  =   this._determinant3x3(a2, a3, a4, b2, b3, b4, d2, d3, d4);
sawine@2:     this.m41  = - this._determinant3x3(a2, a3, a4, b2, b3, b4, c2, c3, c4);
sawine@2:         
sawine@2:     this.m12  = - this._determinant3x3(b1, b3, b4, c1, c3, c4, d1, d3, d4);
sawine@2:     this.m22  =   this._determinant3x3(a1, a3, a4, c1, c3, c4, d1, d3, d4);
sawine@2:     this.m32  = - this._determinant3x3(a1, a3, a4, b1, b3, b4, d1, d3, d4);
sawine@2:     this.m42  =   this._determinant3x3(a1, a3, a4, b1, b3, b4, c1, c3, c4);
sawine@2:         
sawine@2:     this.m13  =   this._determinant3x3(b1, b2, b4, c1, c2, c4, d1, d2, d4);
sawine@2:     this.m23  = - this._determinant3x3(a1, a2, a4, c1, c2, c4, d1, d2, d4);
sawine@2:     this.m33  =   this._determinant3x3(a1, a2, a4, b1, b2, b4, d1, d2, d4);
sawine@2:     this.m43  = - this._determinant3x3(a1, a2, a4, b1, b2, b4, c1, c2, c4);
sawine@2:         
sawine@2:     this.m14  = - this._determinant3x3(b1, b2, b3, c1, c2, c3, d1, d2, d3);
sawine@2:     this.m24  =   this._determinant3x3(a1, a2, a3, c1, c2, c3, d1, d2, d3);
sawine@2:     this.m34  = - this._determinant3x3(a1, a2, a3, b1, b2, b3, d1, d2, d3);
sawine@2:     this.m44  =   this._determinant3x3(a1, a2, a3, b1, b2, b3, c1, c2, c3);
sawine@2: }