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444 lines
17 KiB
JavaScript
444 lines
17 KiB
JavaScript
15 years ago
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dojo.provide("dojox.gfx.matrix");
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(function(){
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var m = dojox.gfx.matrix;
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// candidates for dojox.math:
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var _degToRadCache = {};
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m._degToRad = function(degree){
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return _degToRadCache[degree] || (_degToRadCache[degree] = (Math.PI * degree / 180));
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};
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m._radToDeg = function(radian){ return radian / Math.PI * 180; };
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m.Matrix2D = function(arg){
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// summary: a 2D matrix object
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// description: Normalizes a 2D matrix-like object. If arrays is passed,
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// all objects of the array are normalized and multiplied sequentially.
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// arg: Object
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// a 2D matrix-like object, a number, or an array of such objects
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if(arg){
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if(typeof arg == "number"){
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this.xx = this.yy = arg;
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}else if(arg instanceof Array){
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if(arg.length > 0){
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var matrix = m.normalize(arg[0]);
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// combine matrices
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for(var i = 1; i < arg.length; ++i){
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var l = matrix, r = dojox.gfx.matrix.normalize(arg[i]);
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matrix = new m.Matrix2D();
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matrix.xx = l.xx * r.xx + l.xy * r.yx;
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matrix.xy = l.xx * r.xy + l.xy * r.yy;
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matrix.yx = l.yx * r.xx + l.yy * r.yx;
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matrix.yy = l.yx * r.xy + l.yy * r.yy;
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matrix.dx = l.xx * r.dx + l.xy * r.dy + l.dx;
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matrix.dy = l.yx * r.dx + l.yy * r.dy + l.dy;
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}
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dojo.mixin(this, matrix);
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}
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}else{
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dojo.mixin(this, arg);
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}
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}
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};
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// the default (identity) matrix, which is used to fill in missing values
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dojo.extend(m.Matrix2D, {xx: 1, xy: 0, yx: 0, yy: 1, dx: 0, dy: 0});
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dojo.mixin(m, {
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// summary: class constants, and methods of dojox.gfx.matrix
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// matrix constants
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// identity: dojox.gfx.matrix.Matrix2D
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// an identity matrix constant: identity * (x, y) == (x, y)
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identity: new m.Matrix2D(),
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// flipX: dojox.gfx.matrix.Matrix2D
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// a matrix, which reflects points at x = 0 line: flipX * (x, y) == (-x, y)
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flipX: new m.Matrix2D({xx: -1}),
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// flipY: dojox.gfx.matrix.Matrix2D
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// a matrix, which reflects points at y = 0 line: flipY * (x, y) == (x, -y)
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flipY: new m.Matrix2D({yy: -1}),
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// flipXY: dojox.gfx.matrix.Matrix2D
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// a matrix, which reflects points at the origin of coordinates: flipXY * (x, y) == (-x, -y)
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flipXY: new m.Matrix2D({xx: -1, yy: -1}),
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// matrix creators
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translate: function(a, b){
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// summary: forms a translation matrix
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// description: The resulting matrix is used to translate (move) points by specified offsets.
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// a: Number: an x coordinate value
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// b: Number: a y coordinate value
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if(arguments.length > 1){
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return new m.Matrix2D({dx: a, dy: b}); // dojox.gfx.matrix.Matrix2D
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}
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// branch
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// a: dojox.gfx.Point: a point-like object, which specifies offsets for both dimensions
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// b: null
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return new m.Matrix2D({dx: a.x, dy: a.y}); // dojox.gfx.matrix.Matrix2D
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},
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scale: function(a, b){
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// summary: forms a scaling matrix
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// description: The resulting matrix is used to scale (magnify) points by specified offsets.
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// a: Number: a scaling factor used for the x coordinate
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// b: Number: a scaling factor used for the y coordinate
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if(arguments.length > 1){
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return new m.Matrix2D({xx: a, yy: b}); // dojox.gfx.matrix.Matrix2D
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}
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if(typeof a == "number"){
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// branch
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// a: Number: a uniform scaling factor used for the both coordinates
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// b: null
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return new m.Matrix2D({xx: a, yy: a}); // dojox.gfx.matrix.Matrix2D
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}
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// branch
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// a: dojox.gfx.Point: a point-like object, which specifies scale factors for both dimensions
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// b: null
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return new m.Matrix2D({xx: a.x, yy: a.y}); // dojox.gfx.matrix.Matrix2D
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},
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rotate: function(angle){
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// summary: forms a rotating matrix
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// description: The resulting matrix is used to rotate points
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// around the origin of coordinates (0, 0) by specified angle.
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// angle: Number: an angle of rotation in radians (>0 for CW)
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var c = Math.cos(angle);
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var s = Math.sin(angle);
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return new m.Matrix2D({xx: c, xy: -s, yx: s, yy: c}); // dojox.gfx.matrix.Matrix2D
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},
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rotateg: function(degree){
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// summary: forms a rotating matrix
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// description: The resulting matrix is used to rotate points
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// around the origin of coordinates (0, 0) by specified degree.
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// See dojox.gfx.matrix.rotate() for comparison.
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// degree: Number: an angle of rotation in degrees (>0 for CW)
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return m.rotate(m._degToRad(degree)); // dojox.gfx.matrix.Matrix2D
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},
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skewX: function(angle) {
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// summary: forms an x skewing matrix
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// description: The resulting matrix is used to skew points in the x dimension
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// around the origin of coordinates (0, 0) by specified angle.
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// angle: Number: an skewing angle in radians
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return new m.Matrix2D({xy: Math.tan(angle)}); // dojox.gfx.matrix.Matrix2D
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},
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skewXg: function(degree){
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// summary: forms an x skewing matrix
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// description: The resulting matrix is used to skew points in the x dimension
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// around the origin of coordinates (0, 0) by specified degree.
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// See dojox.gfx.matrix.skewX() for comparison.
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// degree: Number: an skewing angle in degrees
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return m.skewX(m._degToRad(degree)); // dojox.gfx.matrix.Matrix2D
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},
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skewY: function(angle){
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// summary: forms a y skewing matrix
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// description: The resulting matrix is used to skew points in the y dimension
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// around the origin of coordinates (0, 0) by specified angle.
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// angle: Number: an skewing angle in radians
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return new m.Matrix2D({yx: Math.tan(angle)}); // dojox.gfx.matrix.Matrix2D
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},
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skewYg: function(degree){
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// summary: forms a y skewing matrix
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// description: The resulting matrix is used to skew points in the y dimension
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// around the origin of coordinates (0, 0) by specified degree.
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// See dojox.gfx.matrix.skewY() for comparison.
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// degree: Number: an skewing angle in degrees
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return m.skewY(m._degToRad(degree)); // dojox.gfx.matrix.Matrix2D
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},
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reflect: function(a, b){
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// summary: forms a reflection matrix
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// description: The resulting matrix is used to reflect points around a vector,
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// which goes through the origin.
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// a: dojox.gfx.Point: a point-like object, which specifies a vector of reflection
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// b: null
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if(arguments.length == 1){
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b = a.y;
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a = a.x;
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}
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// branch
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// a: Number: an x coordinate value
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// b: Number: a y coordinate value
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// make a unit vector
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var a2 = a * a, b2 = b * b, n2 = a2 + b2, xy = 2 * a * b / n2;
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return new m.Matrix2D({xx: 2 * a2 / n2 - 1, xy: xy, yx: xy, yy: 2 * b2 / n2 - 1}); // dojox.gfx.matrix.Matrix2D
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},
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project: function(a, b){
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// summary: forms an orthogonal projection matrix
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// description: The resulting matrix is used to project points orthogonally on a vector,
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// which goes through the origin.
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// a: dojox.gfx.Point: a point-like object, which specifies a vector of projection
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// b: null
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if(arguments.length == 1){
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b = a.y;
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a = a.x;
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}
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// branch
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// a: Number: an x coordinate value
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// b: Number: a y coordinate value
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// make a unit vector
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var a2 = a * a, b2 = b * b, n2 = a2 + b2, xy = a * b / n2;
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return new m.Matrix2D({xx: a2 / n2, xy: xy, yx: xy, yy: b2 / n2}); // dojox.gfx.matrix.Matrix2D
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},
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// ensure matrix 2D conformance
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normalize: function(matrix){
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// summary: converts an object to a matrix, if necessary
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// description: Converts any 2D matrix-like object or an array of
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// such objects to a valid dojox.gfx.matrix.Matrix2D object.
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// matrix: Object: an object, which is converted to a matrix, if necessary
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return (matrix instanceof m.Matrix2D) ? matrix : new m.Matrix2D(matrix); // dojox.gfx.matrix.Matrix2D
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},
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// common operations
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clone: function(matrix){
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// summary: creates a copy of a 2D matrix
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// matrix: dojox.gfx.matrix.Matrix2D: a 2D matrix-like object to be cloned
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var obj = new m.Matrix2D();
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for(var i in matrix){
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if(typeof(matrix[i]) == "number" && typeof(obj[i]) == "number" && obj[i] != matrix[i]) obj[i] = matrix[i];
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}
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return obj; // dojox.gfx.matrix.Matrix2D
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},
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invert: function(matrix){
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// summary: inverts a 2D matrix
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// matrix: dojox.gfx.matrix.Matrix2D: a 2D matrix-like object to be inverted
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var M = m.normalize(matrix),
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D = M.xx * M.yy - M.xy * M.yx,
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M = new m.Matrix2D({
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xx: M.yy/D, xy: -M.xy/D,
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yx: -M.yx/D, yy: M.xx/D,
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dx: (M.xy * M.dy - M.yy * M.dx) / D,
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dy: (M.yx * M.dx - M.xx * M.dy) / D
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});
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return M; // dojox.gfx.matrix.Matrix2D
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},
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_multiplyPoint: function(matrix, x, y){
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// summary: applies a matrix to a point
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// matrix: dojox.gfx.matrix.Matrix2D: a 2D matrix object to be applied
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// x: Number: an x coordinate of a point
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// y: Number: a y coordinate of a point
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return {x: matrix.xx * x + matrix.xy * y + matrix.dx, y: matrix.yx * x + matrix.yy * y + matrix.dy}; // dojox.gfx.Point
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},
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multiplyPoint: function(matrix, /* Number||Point */ a, /* Number, optional */ b){
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// summary: applies a matrix to a point
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// matrix: dojox.gfx.matrix.Matrix2D: a 2D matrix object to be applied
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// a: Number: an x coordinate of a point
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// b: Number: a y coordinate of a point
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var M = m.normalize(matrix);
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if(typeof a == "number" && typeof b == "number"){
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return m._multiplyPoint(M, a, b); // dojox.gfx.Point
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}
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// branch
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// matrix: dojox.gfx.matrix.Matrix2D: a 2D matrix object to be applied
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// a: dojox.gfx.Point: a point
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// b: null
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return m._multiplyPoint(M, a.x, a.y); // dojox.gfx.Point
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},
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multiply: function(matrix){
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// summary: combines matrices by multiplying them sequentially in the given order
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// matrix: dojox.gfx.matrix.Matrix2D...: a 2D matrix-like object,
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// all subsequent arguments are matrix-like objects too
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var M = m.normalize(matrix);
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// combine matrices
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for(var i = 1; i < arguments.length; ++i){
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var l = M, r = m.normalize(arguments[i]);
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M = new m.Matrix2D();
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M.xx = l.xx * r.xx + l.xy * r.yx;
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M.xy = l.xx * r.xy + l.xy * r.yy;
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M.yx = l.yx * r.xx + l.yy * r.yx;
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M.yy = l.yx * r.xy + l.yy * r.yy;
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M.dx = l.xx * r.dx + l.xy * r.dy + l.dx;
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M.dy = l.yx * r.dx + l.yy * r.dy + l.dy;
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}
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return M; // dojox.gfx.matrix.Matrix2D
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},
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// high level operations
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_sandwich: function(matrix, x, y){
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// summary: applies a matrix at a centrtal point
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// matrix: dojox.gfx.matrix.Matrix2D: a 2D matrix-like object, which is applied at a central point
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// x: Number: an x component of the central point
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// y: Number: a y component of the central point
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return m.multiply(m.translate(x, y), matrix, m.translate(-x, -y)); // dojox.gfx.matrix.Matrix2D
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},
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scaleAt: function(a, b, c, d){
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// summary: scales a picture using a specified point as a center of scaling
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// description: Compare with dojox.gfx.matrix.scale().
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// a: Number: a scaling factor used for the x coordinate
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// b: Number: a scaling factor used for the y coordinate
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// c: Number: an x component of a central point
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// d: Number: a y component of a central point
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// accepts several signatures:
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// 1) uniform scale factor, Point
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// 2) uniform scale factor, x, y
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// 3) x scale, y scale, Point
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// 4) x scale, y scale, x, y
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switch(arguments.length){
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case 4:
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// a and b are scale factor components, c and d are components of a point
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return m._sandwich(m.scale(a, b), c, d); // dojox.gfx.matrix.Matrix2D
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case 3:
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if(typeof c == "number"){
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// branch
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// a: Number: a uniform scaling factor used for both coordinates
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// b: Number: an x component of a central point
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// c: Number: a y component of a central point
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// d: null
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return m._sandwich(m.scale(a), b, c); // dojox.gfx.matrix.Matrix2D
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}
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// branch
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// a: Number: a scaling factor used for the x coordinate
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// b: Number: a scaling factor used for the y coordinate
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// c: dojox.gfx.Point: a central point
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// d: null
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return m._sandwich(m.scale(a, b), c.x, c.y); // dojox.gfx.matrix.Matrix2D
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}
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// branch
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// a: Number: a uniform scaling factor used for both coordinates
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// b: dojox.gfx.Point: a central point
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// c: null
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// d: null
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return m._sandwich(m.scale(a), b.x, b.y); // dojox.gfx.matrix.Matrix2D
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},
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rotateAt: function(angle, a, b){
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// summary: rotates a picture using a specified point as a center of rotation
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// description: Compare with dojox.gfx.matrix.rotate().
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// angle: Number: an angle of rotation in radians (>0 for CW)
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// a: Number: an x component of a central point
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// b: Number: a y component of a central point
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|
|
|
||
|
|
// accepts several signatures:
|
||
|
|
// 1) rotation angle in radians, Point
|
||
|
|
// 2) rotation angle in radians, x, y
|
||
|
|
|
||
|
|
if(arguments.length > 2){
|
||
|
|
return m._sandwich(m.rotate(angle), a, b); // dojox.gfx.matrix.Matrix2D
|
||
|
|
}
|
||
|
|
|
||
|
|
// branch
|
||
|
|
// angle: Number: an angle of rotation in radians (>0 for CCW)
|
||
|
|
// a: dojox.gfx.Point: a central point
|
||
|
|
// b: null
|
||
|
|
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: an x component of a central point
|
||
|
|
// b: Number: a y component of a central point
|
||
|
|
|
||
|
|
// accepts several signatures:
|
||
|
|
// 1) rotation angle in degrees, Point
|
||
|
|
// 2) rotation angle in degrees, x, y
|
||
|
|
|
||
|
|
if(arguments.length > 2){
|
||
|
|
return m._sandwich(m.rotateg(degree), a, b); // dojox.gfx.matrix.Matrix2D
|
||
|
|
}
|
||
|
|
|
||
|
|
// branch
|
||
|
|
// degree: Number: an angle of rotation in degrees (>0 for CCW)
|
||
|
|
// a: dojox.gfx.Point: a central point
|
||
|
|
// b: null
|
||
|
|
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: an skewing angle in radians
|
||
|
|
// a: Number: an x component of a central point
|
||
|
|
// b: Number: a y component of a central point
|
||
|
|
|
||
|
|
// accepts several signatures:
|
||
|
|
// 1) skew angle in radians, Point
|
||
|
|
// 2) skew angle in radians, x, y
|
||
|
|
|
||
|
|
if(arguments.length > 2){
|
||
|
|
return m._sandwich(m.skewX(angle), a, b); // dojox.gfx.matrix.Matrix2D
|
||
|
|
}
|
||
|
|
|
||
|
|
// branch
|
||
|
|
// angle: Number: an skewing angle in radians
|
||
|
|
// a: dojox.gfx.Point: a central point
|
||
|
|
// b: null
|
||
|
|
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: an skewing angle in degrees
|
||
|
|
// a: Number: an x component of a central point
|
||
|
|
// b: Number: a y component of a central point
|
||
|
|
|
||
|
|
// accepts several signatures:
|
||
|
|
// 1) skew angle in degrees, Point
|
||
|
|
// 2) skew angle in degrees, x, y
|
||
|
|
|
||
|
|
if(arguments.length > 2){
|
||
|
|
return m._sandwich(m.skewXg(degree), a, b); // dojox.gfx.matrix.Matrix2D
|
||
|
|
}
|
||
|
|
|
||
|
|
// branch
|
||
|
|
// degree: Number: an skewing angle in degrees
|
||
|
|
// a: dojox.gfx.Point: a central point
|
||
|
|
// b: null
|
||
|
|
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: an skewing angle in radians
|
||
|
|
// a: Number: an x component of a central point
|
||
|
|
// b: Number: a y component of a central point
|
||
|
|
|
||
|
|
// accepts several signatures:
|
||
|
|
// 1) skew angle in radians, Point
|
||
|
|
// 2) skew angle in radians, x, y
|
||
|
|
|
||
|
|
if(arguments.length > 2){
|
||
|
|
return m._sandwich(m.skewY(angle), a, b); // dojox.gfx.matrix.Matrix2D
|
||
|
|
}
|
||
|
|
|
||
|
|
// branch
|
||
|
|
// angle: Number: an skewing angle in radians
|
||
|
|
// a: dojox.gfx.Point: a central point
|
||
|
|
// b: null
|
||
|
|
return m._sandwich(m.skewY(angle), a.x, a.y); // dojox.gfx.matrix.Matrix2D
|
||
|
|
},
|
||
|
|
skewYgAt: function(/* Number */ degree, /* Number||Point */ a, /* Number, optional */ 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: an skewing angle in degrees
|
||
|
|
// a: Number: an x component of a central point
|
||
|
|
// b: Number: a y component of a central point
|
||
|
|
|
||
|
|
// accepts several signatures:
|
||
|
|
// 1) skew angle in degrees, Point
|
||
|
|
// 2) skew angle in degrees, x, y
|
||
|
|
|
||
|
|
if(arguments.length > 2){
|
||
|
|
return m._sandwich(m.skewYg(degree), a, b); // dojox.gfx.matrix.Matrix2D
|
||
|
|
}
|
||
|
|
|
||
|
|
// branch
|
||
|
|
// degree: Number: an skewing angle in degrees
|
||
|
|
// a: dojox.gfx.Point: a central point
|
||
|
|
// b: null
|
||
|
|
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
|
||
|
|
dojox.gfx.Matrix2D = dojox.gfx.matrix.Matrix2D;
|