source: Dev/trunk/src/client/dojox/gfx/matrix.js

define(["./_base","dojo/_base/lang"], 
  function(g, lang){
        var m = g.matrix = {};

        // candidates for dojox.math:
        var _degToRadCache = {};
        m._degToRad = function(degree){
                return _degToRadCache[degree] || (_degToRadCache[degree] = (Math.PI * degree / 180));
        };
        m._radToDeg = function(radian){ return radian / Math.PI * 180; };

        m.Matrix2D = function(arg){
                // summary:
                //              a 2D matrix object
                // description:
                //              Normalizes a 2D matrix-like object. If arrays is passed,
                //              all objects of the array are normalized and multiplied sequentially.
                // arg: Object
                //              a 2D matrix-like object, a number, or an array of such objects
                if(arg){
                        if(typeof arg == "number"){
                                this.xx = this.yy = arg;
                        }else if(arg instanceof Array){
                                if(arg.length > 0){
                                        var matrix = m.normalize(arg[0]);
                                        // combine matrices
                                        for(var i = 1; i < arg.length; ++i){
                                                var l = matrix, r = m.normalize(arg[i]);
                                                matrix = new m.Matrix2D();
                                                matrix.xx = l.xx * r.xx + l.xy * r.yx;
                                                matrix.xy = l.xx * r.xy + l.xy * r.yy;
                                                matrix.yx = l.yx * r.xx + l.yy * r.yx;
                                                matrix.yy = l.yx * r.xy + l.yy * r.yy;
                                                matrix.dx = l.xx * r.dx + l.xy * r.dy + l.dx;
                                                matrix.dy = l.yx * r.dx + l.yy * r.dy + l.dy;
                                        }
                                        lang.mixin(this, matrix);
                                }
                        }else{
                                lang.mixin(this, arg);
                        }
                }
        };

        // the default (identity) matrix, which is used to fill in missing values
        lang.extend(m.Matrix2D, {xx: 1, xy: 0, yx: 0, yy: 1, dx: 0, dy: 0});

        lang.mixin(m, {
                // summary:
                //              class constants, and methods of dojox/gfx/matrix

                // matrix constants

                // identity: dojox/gfx/matrix.Matrix2D
                //              an identity matrix constant: identity * (x, y) == (x, y)
                identity: new m.Matrix2D(),

                // flipX: dojox/gfx/matrix.Matrix2D
                //              a matrix, which reflects points at x = 0 line: flipX * (x, y) == (-x, y)
                flipX:    new m.Matrix2D({xx: -1}),

                // flipY: dojox/gfx/matrix.Matrix2D
                //              a matrix, which reflects points at y = 0 line: flipY * (x, y) == (x, -y)
                flipY:    new m.Matrix2D({yy: -1}),

                // flipXY: dojox/gfx/matrix.Matrix2D
                //              a matrix, which reflects points at the origin of coordinates: flipXY * (x, y) == (-x, -y)
                flipXY:   new m.Matrix2D({xx: -1, yy: -1}),

                // matrix creators

                translate: function(a, b){
                        // summary:
                        //              forms a translation matrix
                        // description:
                        //              The resulting matrix is used to translate (move) points by specified offsets.
                        // a: Number|dojox/gfx.Point
                        //              an x coordinate value, or a point-like object, which specifies offsets for both dimensions
                        // b: Number?
                        //              a y coordinate value
                        // returns: dojox/gfx/matrix.Matrix2D
                        if(arguments.length > 1){
                                return new m.Matrix2D({dx: a, dy: b}); // dojox/gfx/matrix.Matrix2D
                        }
                        // branch
                        return new m.Matrix2D({dx: a.x, dy: a.y}); // dojox/gfx/matrix.Matrix2D
                },
                scale: function(a, b){
                        // summary:
                        //              forms a scaling matrix
                        // description:
                        //              The resulting matrix is used to scale (magnify) points by specified offsets.
                        // a: Number|dojox/gfx.Point
                        //              a scaling factor used for the x coordinate, or
                        //              a uniform scaling factor used for the both coordinates, or
                        //              a point-like object, which specifies scale factors for both dimensions
                        // b: Number?
                        //              a scaling factor used for the y coordinate
                        // returns: dojox/gfx/matrix.Matrix2D
                        if(arguments.length > 1){
                                return new m.Matrix2D({xx: a, yy: b}); // dojox/gfx/matrix.Matrix2D
                        }
                        if(typeof a == "number"){
                                return new m.Matrix2D({xx: a, yy: a}); // dojox/gfx/matrix.Matrix2D
                        }
                        return new m.Matrix2D({xx: a.x, yy: a.y}); // dojox/gfx/matrix.Matrix2D
                },
                rotate: function(angle){
                        // summary:
                        //              forms a rotating matrix
                        // description:
                        //              The resulting matrix is used to rotate points
                        //              around the origin of coordinates (0, 0) by specified angle.
                        // angle: Number
                        //              an angle of rotation in radians (>0 for CW)
                        // returns: dojox/gfx/matrix.Matrix2D
                        var c = Math.cos(angle);
                        var s = Math.sin(angle);
                        return new m.Matrix2D({xx: c, xy: -s, yx: s, yy: c}); // dojox/gfx/matrix.Matrix2D
                },
                rotateg: function(degree){
                        // summary:
                        //              forms a rotating matrix
                        // description:
                        //              The resulting matrix is used to rotate points
                        //              around the origin of coordinates (0, 0) by specified degree.
                        //              See dojox/gfx/matrix.rotate() for comparison.
                        // degree: Number
                        //              an angle of rotation in degrees (>0 for CW)
                        // returns: dojox/gfx/matrix.Matrix2D
                        return m.rotate(m._degToRad(degree)); // dojox/gfx/matrix.Matrix2D
                },
                skewX: function(angle) {
                        // summary:
                        //              forms an x skewing matrix
                        // description:
                        //              The resulting matrix is used to skew points in the x dimension
                        //              around the origin of coordinates (0, 0) by specified angle.
                        // angle: Number
                        //              a skewing angle in radians
                        // returns: dojox/gfx/matrix.Matrix2D
                        return new m.Matrix2D({xy: Math.tan(angle)}); // dojox/gfx/matrix.Matrix2D
                },
                skewXg: function(degree){
                        // summary:
                        //              forms an x skewing matrix
                        // description:
                        //              The resulting matrix is used to skew points in the x dimension
                        //              around the origin of coordinates (0, 0) by specified degree.
                        //              See dojox/gfx/matrix.skewX() for comparison.
                        // degree: Number
                        //              a skewing angle in degrees
                        // returns: dojox/gfx/matrix.Matrix2D
                        return m.skewX(m._degToRad(degree)); // dojox/gfx/matrix.Matrix2D
                },
                skewY: function(angle){
                        // summary:
                        //              forms a y skewing matrix
                        // description:
                        //              The resulting matrix is used to skew points in the y dimension
                        //              around the origin of coordinates (0, 0) by specified angle.
                        // angle: Number
                        //              a skewing angle in radians
                        // returns: dojox/gfx/matrix.Matrix2D
                        return new m.Matrix2D({yx: Math.tan(angle)}); // dojox/gfx/matrix.Matrix2D
                },
                skewYg: function(degree){
                        // summary:
                        //              forms a y skewing matrix
                        // description:
                        //              The resulting matrix is used to skew points in the y dimension
                        //              around the origin of coordinates (0, 0) by specified degree.
                        //              See dojox/gfx/matrix.skewY() for comparison.
                        // degree: Number
                        //              a skewing angle in degrees
                        // returns: dojox/gfx/matrix.Matrix2D
                        return m.skewY(m._degToRad(degree)); // dojox/gfx/matrix.Matrix2D
                },
                reflect: function(a, b){
                        // summary:
                        //              forms a reflection matrix
                        // description:
                        //              The resulting matrix is used to reflect points around a vector,
                        //              which goes through the origin.
                        // a: dojox/gfx.Point|Number
                        //              a point-like object, which specifies a vector of reflection, or an X value
                        // b: Number?
                        //              a Y value
                        // returns: dojox/gfx/matrix.Matrix2D
                        if(arguments.length == 1){
                                b = a.y;
                                a = a.x;
                        }
                        // make a unit vector
                        var a2 = a * a, b2 = b * b, n2 = a2 + b2, xy = 2 * a * b / n2;
                        return new m.Matrix2D({xx: 2 * a2 / n2 - 1, xy: xy, yx: xy, yy: 2 * b2 / n2 - 1}); // dojox/gfx/matrix.Matrix2D
                },
                project: function(a, b){
                        // summary:
                        //              forms an orthogonal projection matrix
                        // description:
                        //              The resulting matrix is used to project points orthogonally on a vector,
                        //              which goes through the origin.
                        // a: dojox/gfx.Point|Number
                        //              a point-like object, which specifies a vector of projection, or
                        //              an x coordinate value
                        // b: Number?
                        //              a y coordinate value
                        // returns: dojox/gfx/matrix.Matrix2D
                        if(arguments.length == 1){
                                b = a.y;
                                a = a.x;
                        }
                        // make a unit vector
                        var a2 = a * a, b2 = b * b, n2 = a2 + b2, xy = a * b / n2;
                        return new m.Matrix2D({xx: a2 / n2, xy: xy, yx: xy, yy: b2 / n2}); // dojox/gfx/matrix.Matrix2D
                },

                // ensure matrix 2D conformance
                normalize: function(matrix){
                        // summary:
                        //              converts an object to a matrix, if necessary
                        // description:
                        //              Converts any 2D matrix-like object or an array of
                        //              such objects to a valid dojox/gfx/matrix.Matrix2D object.
                        // matrix: Object
                        //              an object, which is converted to a matrix, if necessary
                        // returns: dojox/gfx/matrix.Matrix2D
                        return (matrix instanceof m.Matrix2D) ? matrix : new m.Matrix2D(matrix); // dojox/gfx/matrix.Matrix2D
                },

                // common operations

                isIdentity: function(matrix){
                        // summary:
                        //              returns whether the specified matrix is the identity.
                        // matrix: dojox/gfx/matrix.Matrix2D
                        //              a 2D matrix object to be tested
                        // returns: Boolean
                        return matrix.xx == 1 && matrix.xy == 0 && matrix.yx == 0 && matrix.yy == 1 && matrix.dx == 0 && matrix.dy == 0; // Boolean
                },
                clone: function(matrix){
                        // summary:
                        //              creates a copy of a 2D matrix
                        // matrix: dojox/gfx/matrix.Matrix2D
                        //              a 2D matrix-like object to be cloned
                        // returns: dojox/gfx/matrix.Matrix2D
                        var obj = new m.Matrix2D();
                        for(var i in matrix){
                                if(typeof(matrix[i]) == "number" && typeof(obj[i]) == "number" && obj[i] != matrix[i]) obj[i] = matrix[i];
                        }
                        return obj; // dojox/gfx/matrix.Matrix2D
                },
                invert: function(matrix){
                        // summary:
                        //              inverts a 2D matrix
                        // matrix: dojox/gfx/matrix.Matrix2D
                        //              a 2D matrix-like object to be inverted
                        // returns: dojox/gfx/matrix.Matrix2D
                        var M = m.normalize(matrix),
                                D = M.xx * M.yy - M.xy * M.yx;
                                M = new m.Matrix2D({
                                        xx: M.yy/D, xy: -M.xy/D,
                                        yx: -M.yx/D, yy: M.xx/D,
                                        dx: (M.xy * M.dy - M.yy * M.dx) / D,
                                        dy: (M.yx * M.dx - M.xx * M.dy) / D
                                });
                        return M; // dojox/gfx/matrix.Matrix2D
                },
                _multiplyPoint: function(matrix, x, y){
                        // summary:
                        //              applies a matrix to a point
                        // matrix: dojox/gfx/matrix.Matrix2D
                        //              a 2D matrix object to be applied
                        // x: Number
                        //              an x coordinate of a point
                        // y: Number
                        //              a y coordinate of a point
                        // returns: dojox/gfx.Point
                        return {x: matrix.xx * x + matrix.xy * y + matrix.dx, y: matrix.yx * x + matrix.yy * y + matrix.dy}; // dojox/gfx.Point
                },
                multiplyPoint: function(matrix, /* Number||Point */ a, /* Number? */ b){
                        // summary:
                        //              applies a matrix to a point
                        // matrix: dojox/gfx/matrix.Matrix2D
                        //              a 2D matrix object to be applied
                        // a: Number|dojox/gfx.Point
                        //              an x coordinate of a point, or a point
                        // b: Number?
                        //              a y coordinate of a point
                        // returns: dojox/gfx.Point
                        var M = m.normalize(matrix);
                        if(typeof a == "number" && typeof b == "number"){
                                return m._multiplyPoint(M, a, b); // dojox/gfx.Point
                        }
                        return m._multiplyPoint(M, a.x, a.y); // dojox/gfx.Point
                },
                multiplyRectangle: function(matrix, /*Rectangle*/ rect){
                        // summary:
                        //              Applies a matrix to a rectangle.
                        // description:
                        //              The method applies the transformation on all corners of the
                        //              rectangle and returns the smallest rectangle enclosing the 4 transformed
                        //              points.
                        // matrix: dojox/gfx/matrix.Matrix2D
                        //              a 2D matrix object to be applied.
                        // rect: Rectangle
                        //              the rectangle to transform.
                        // returns: dojox/gfx.Rectangle
                        var M = m.normalize(matrix);
                        rect = rect || {x:0, y:0, width:0, height:0}; 
                        if(m.isIdentity(M))
                                return {x: rect.x, y: rect.y, width: rect.width, height: rect.height}; // dojo/gfx.Rectangle
                        var p0 = m.multiplyPoint(M, rect.x, rect.y),
                                p1 = m.multiplyPoint(M, rect.x, rect.y + rect.height),
                                p2 = m.multiplyPoint(M, rect.x + rect.width, rect.y),
                                p3 = m.multiplyPoint(M, rect.x + rect.width, rect.y + rect.height),
                                minx = Math.min(p0.x, p1.x, p2.x, p3.x),
                                miny = Math.min(p0.y, p1.y, p2.y, p3.y),
                                maxx = Math.max(p0.x, p1.x, p2.x, p3.x),
                                maxy = Math.max(p0.y, p1.y, p2.y, p3.y);
                        return{ // dojo/gfx.Rectangle
                                x: minx,
                                y: miny,
                                width: maxx - minx,
                                height: maxy - miny
                        };
                },
                multiply: function(matrix){
                        // summary:
                        //              combines matrices by multiplying them sequentially in the given order
                        // matrix: dojox/gfx/matrix.Matrix2D
                        //              a 2D matrix-like object,
                        //              all subsequent arguments are matrix-like objects too
                        var M = m.normalize(matrix);
                        // combine matrices
                        for(var i = 1; i < arguments.length; ++i){
                                var l = M, r = m.normalize(arguments[i]);
                                M = new m.Matrix2D();
                                M.xx = l.xx * r.xx + l.xy * r.yx;
                                M.xy = l.xx * r.xy + l.xy * r.yy;
                                M.yx = l.yx * r.xx + l.yy * r.yx;
                                M.yy = l.yx * r.xy + l.yy * r.yy;
                                M.dx = l.xx * r.dx + l.xy * r.dy + l.dx;
                                M.dy = l.yx * r.dx + l.yy * r.dy + l.dy;
                        }
                        return M; // dojox/gfx/matrix.Matrix2D
                },

                // high level operations

                _sandwich: function(matrix, x, y){
                        // summary:
                        //              applies a matrix at a central point
                        // matrix: dojox/gfx/matrix.Matrix2D
                        //              a 2D matrix-like object, which is applied at a central point
                        // x: Number
                        //              an x component of the central point
                        // y: Number
                        //              a y component of the central point
                        return m.multiply(m.translate(x, y), matrix, m.translate(-x, -y)); // dojox/gfx/matrix.Matrix2D
                },
                scaleAt: function(a, b, c, d){
                        // summary:
                        //              scales a picture using a specified point as a center of scaling
                        // description:
                        //              Compare with dojox/gfx/matrix.scale().
                        // a: Number
                        //              a scaling factor used for the x coordinate, or a uniform scaling factor used for both coordinates
                        // b: Number?
                        //              a scaling factor used for the y coordinate
                        // c: Number|Point
                        //              an x component of a central point, or a central point
                        // d: Number
                        //              a y component of a central point
                        // returns: dojox/gfx/matrix.Matrix2D
                        switch(arguments.length){
                                case 4:
                                        // a and b are scale factor components, c and d are components of a point
                                        return m._sandwich(m.scale(a, b), c, d); // dojox/gfx/matrix.Matrix2D
                                case 3:
                                        if(typeof c == "number"){
                                                return m._sandwich(m.scale(a), b, c); // dojox/gfx/matrix.Matrix2D
                                        }
                                        return m._sandwich(m.scale(a, b), c.x, c.y); // dojox/gfx/matrix.Matrix2D
                        }
                        return m._sandwich(m.scale(a), b.x, b.y); // dojox/gfx/matrix.Matrix2D
                },
                rotateAt: function(angle, a, b){
                        // summary:
                        //              rotates a picture using a specified point as a center of rotation
                        // description:
                        //              Compare with dojox/gfx/matrix.rotate().
                        // angle: Number
                        //              an angle of rotation in radians (>0 for CW)
                        // a: Number|dojox/gfx.Point
                        //              an x component of a central point, or a central point
                        // b: Number?
                        //              a y component of a central point
                        // returns: dojox/gfx/matrix.Matrix2D
                        if(arguments.length > 2){
                                return m._sandwich(m.rotate(angle), a, b); // dojox/gfx/matrix.Matrix2D
                        }
                        return m._sandwich(m.rotate(angle), a.x, a.y); // dojox/gfx/matrix.Matrix2D
                },
                rotategAt: function(degree, a, b){
                        // summary:
                        //              rotates a picture using a specified point as a center of rotation
                        // description:
                        //              Compare with dojox/gfx/matrix.rotateg().
                        // degree: Number
                        //              an angle of rotation in degrees (>0 for CW)
                        // a: Number|dojox/gfx.Point
                        //              an x component of a central point, or a central point
                        // b: Number?
                        //              a y component of a central point
                        // returns: dojox/gfx/matrix.Matrix2D
                        if(arguments.length > 2){
                                return m._sandwich(m.rotateg(degree), a, b); // dojox/gfx/matrix.Matrix2D
                        }
                        return m._sandwich(m.rotateg(degree), a.x, a.y); // dojox/gfx/matrix.Matrix2D
                },
                skewXAt: function(angle, a, b){
                        // summary:
                        //              skews a picture along the x axis using a specified point as a center of skewing
                        // description:
                        //              Compare with dojox/gfx/matrix.skewX().
                        // angle: Number
                        //              a skewing angle in radians
                        // a: Number|dojox/gfx.Point
                        //              an x component of a central point, or a central point
                        // b: Number?
                        //              a y component of a central point
                        // returns: dojox/gfx/matrix.Matrix2D
                        if(arguments.length > 2){
                                return m._sandwich(m.skewX(angle), a, b); // dojox/gfx/matrix.Matrix2D
                        }
                        return m._sandwich(m.skewX(angle), a.x, a.y); // dojox/gfx/matrix.Matrix2D
                },
                skewXgAt: function(degree, a, b){
                        // summary:
                        //              skews a picture along the x axis using a specified point as a center of skewing
                        // description:
                        //              Compare with dojox/gfx/matrix.skewXg().
                        // degree: Number
                        //              a skewing angle in degrees
                        // a: Number|dojox/gfx.Point
                        //              an x component of a central point, or a central point
                        // b: Number?
                        //              a y component of a central point
                        // returns: dojox/gfx/matrix.Matrix2D
                        if(arguments.length > 2){
                                return m._sandwich(m.skewXg(degree), a, b); // dojox/gfx/matrix.Matrix2D
                        }
                        return m._sandwich(m.skewXg(degree), a.x, a.y); // dojox/gfx/matrix.Matrix2D
                },
                skewYAt: function(angle, a, b){
                        // summary:
                        //              skews a picture along the y axis using a specified point as a center of skewing
                        // description:
                        //              Compare with dojox/gfx/matrix.skewY().
                        // angle: Number
                        //              a skewing angle in radians
                        // a: Number|dojox/gfx.Point
                        //              an x component of a central point, or a central point
                        // b: Number?
                        //              a y component of a central point
                        // returns: dojox/gfx/matrix.Matrix2D
                        if(arguments.length > 2){
                                return m._sandwich(m.skewY(angle), a, b); // dojox/gfx/matrix.Matrix2D
                        }
                        return m._sandwich(m.skewY(angle), a.x, a.y); // dojox/gfx/matrix.Matrix2D
                },
                skewYgAt: function(/* Number */ degree, /* Number||Point */ a, /* Number? */ b){
                        // summary:
                        //              skews a picture along the y axis using a specified point as a center of skewing
                        // description:
                        //              Compare with dojox/gfx/matrix.skewYg().
                        // degree: Number
                        //              a skewing angle in degrees
                        // a: Number|dojox/gfx.Point
                        //              an x component of a central point, or a central point
                        // b: Number?
                        //              a y component of a central point
                        // returns: dojox/gfx/matrix.Matrix2D
                        if(arguments.length > 2){
                                return m._sandwich(m.skewYg(degree), a, b); // dojox/gfx/matrix.Matrix2D
                        }
                        return m._sandwich(m.skewYg(degree), a.x, a.y); // dojox/gfx/matrix.Matrix2D
                }

                //TODO: rect-to-rect mapping, scale-to-fit (isotropic and anisotropic versions)

        });
        // propagate Matrix2D up
        g.Matrix2D = m.Matrix2D;

        return m;
});