/*

    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.getAsCanvasFloatArray = 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);

}