| /* |
| Copyright (c) 2004-2006, The Dojo Foundation |
| All Rights Reserved. |
| |
| Licensed under the Academic Free License version 2.1 or above OR the |
| modified BSD license. For more information on Dojo licensing, see: |
| |
| http://dojotoolkit.org/community/licensing.shtml |
| */ |
| |
| dojo.provide("dojo.gfx.matrix"); |
| |
| dojo.require("dojo.lang.common"); |
| dojo.require("dojo.math.*"); |
| |
| dojo.gfx.matrix.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, or an array of such objects |
| if(arg){ |
| if(arg instanceof Array){ |
| if(arg.length > 0){ |
| var m = dojo.gfx.matrix.normalize(arg[0]); |
| // combine matrices |
| for(var i = 1; i < arg.length; ++i){ |
| var l = m; |
| var r = dojo.gfx.matrix.normalize(arg[i]); |
| m = new dojo.gfx.matrix.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; |
| } |
| dojo.mixin(this, m); |
| } |
| }else{ |
| dojo.mixin(this, arg); |
| } |
| } |
| }; |
| |
| // the default (identity) matrix, which is used to fill in missing values |
| dojo.extend(dojo.gfx.matrix.Matrix2D, {xx: 1, xy: 0, yx: 0, yy: 1, dx: 0, dy: 0}); |
| |
| dojo.mixin(dojo.gfx.matrix, { |
| // summary: class constants, and methods of dojo.gfx.matrix |
| |
| // matrix constants |
| |
| // identity: dojo.gfx.matrix.Matrix2D |
| // an identity matrix constant: identity * (x, y) == (x, y) |
| identity: new dojo.gfx.matrix.Matrix2D(), |
| |
| // flipX: dojo.gfx.matrix.Matrix2D |
| // a matrix, which reflects points at x = 0 line: flipX * (x, y) == (-x, y) |
| flipX: new dojo.gfx.matrix.Matrix2D({xx: -1}), |
| |
| // flipY: dojo.gfx.matrix.Matrix2D |
| // a matrix, which reflects points at y = 0 line: flipY * (x, y) == (x, -y) |
| flipY: new dojo.gfx.matrix.Matrix2D({yy: -1}), |
| |
| // flipXY: dojo.gfx.matrix.Matrix2D |
| // a matrix, which reflects points at the origin of coordinates: flipXY * (x, y) == (-x, -y) |
| flipXY: new dojo.gfx.matrix.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: an x coordinate value |
| // b: Number: a y coordinate value |
| if(arguments.length > 1){ |
| return new dojo.gfx.matrix.Matrix2D({dx: a, dy: b}); // dojo.gfx.matrix.Matrix2D |
| } |
| // branch |
| // a: dojo.gfx.Point: a point-like object, which specifies offsets for both dimensions |
| // b: null |
| return new dojo.gfx.matrix.Matrix2D({dx: a.x, dy: a.y}); // dojo.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: a scaling factor used for the x coordinate |
| // b: Number: a scaling factor used for the y coordinate |
| if(arguments.length > 1){ |
| return new dojo.gfx.matrix.Matrix2D({xx: a, yy: b}); // dojo.gfx.matrix.Matrix2D |
| } |
| if(typeof a == "number"){ |
| // branch |
| // a: Number: a uniform scaling factor used for the both coordinates |
| // b: null |
| return new dojo.gfx.matrix.Matrix2D({xx: a, yy: a}); // dojo.gfx.matrix.Matrix2D |
| } |
| // branch |
| // a: dojo.gfx.Point: a point-like object, which specifies scale factors for both dimensions |
| // b: null |
| return new dojo.gfx.matrix.Matrix2D({xx: a.x, yy: a.y}); // dojo.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 CCW) |
| var c = Math.cos(angle); |
| var s = Math.sin(angle); |
| return new dojo.gfx.matrix.Matrix2D({xx: c, xy: s, yx: -s, yy: c}); // dojo.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 dojo.gfx.matrix.rotate() for comparison. |
| // degree: Number: an angle of rotation in degrees (>0 for CCW) |
| return dojo.gfx.matrix.rotate(dojo.math.degToRad(degree)); // dojo.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: an skewing angle in radians |
| return new dojo.gfx.matrix.Matrix2D({xy: Math.tan(angle)}); // dojo.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 dojo.gfx.matrix.skewX() for comparison. |
| // degree: Number: an skewing angle in degrees |
| return dojo.gfx.matrix.skewX(dojo.math.degToRad(degree)); // dojo.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: an skewing angle in radians |
| return new dojo.gfx.matrix.Matrix2D({yx: -Math.tan(angle)}); // dojo.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 dojo.gfx.matrix.skewY() for comparison. |
| // degree: Number: an skewing angle in degrees |
| return dojo.gfx.matrix.skewY(dojo.math.degToRad(degree)); // dojo.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 dojo.gfx.matrix.Matrix2D object. |
| // matrix: Object: an object, which is converted to a matrix, if necessary |
| return (matrix instanceof dojo.gfx.matrix.Matrix2D) ? matrix : new dojo.gfx.matrix.Matrix2D(matrix); // dojo.gfx.matrix.Matrix2D |
| }, |
| |
| // common operations |
| |
| clone: function(matrix){ |
| // summary: creates a copy of a 2D matrix |
| // matrix: dojo.gfx.matrix.Matrix2D: a 2D matrix-like object to be cloned |
| var obj = new dojo.gfx.matrix.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; // dojo.gfx.matrix.Matrix2D |
| }, |
| invert: function(matrix){ |
| // summary: inverts a 2D matrix |
| // matrix: dojo.gfx.matrix.Matrix2D: a 2D matrix-like object to be inverted |
| var m = dojo.gfx.matrix.normalize(matrix); |
| var D = m.xx * m.yy - m.xy * m.yx; |
| var M = new dojo.gfx.matrix.Matrix2D({ |
| xx: m.yy/D, xy: -m.xy/D, |
| yx: -m.yx/D, yy: m.xx/D, |
| dx: (m.yx * m.dy - m.yy * m.dx) / D, |
| dy: (m.xy * m.dx - m.xx * m.dy) / D |
| }); |
| return M; // dojo.gfx.matrix.Matrix2D |
| }, |
| _multiplyPoint: function(m, x, y){ |
| // summary: applies a matrix to a point |
| // matrix: dojo.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 |
| return {x: m.xx * x + m.xy * y + m.dx, y: m.yx * x + m.yy * y + m.dy}; // dojo.gfx.Point |
| }, |
| multiplyPoint: function(matrix, /* Number||Point */ a, /* Number, optional */ b){ |
| // summary: applies a matrix to a point |
| // matrix: dojo.gfx.matrix.Matrix2D: a 2D matrix object to be applied |
| // a: Number: an x coordinate of a point |
| // b: Number: a y coordinate of a point |
| var m = dojo.gfx.matrix.normalize(matrix); |
| if(typeof a == "number" && typeof b == "number"){ |
| return dojo.gfx.matrix._multiplyPoint(m, a, b); // dojo.gfx.Point |
| } |
| // branch |
| // matrix: dojo.gfx.matrix.Matrix2D: a 2D matrix object to be applied |
| // a: dojo.gfx.Point: a point |
| // b: null |
| return dojo.gfx.matrix._multiplyPoint(m, a.x, a.y); // dojo.gfx.Point |
| }, |
| multiply: function(matrix){ |
| // summary: combines matrices by multiplying them sequentially in the given order |
| // matrix: dojo.gfx.matrix.Matrix2D...: a 2D matrix-like object, |
| // all subsequent arguments are matrix-like objects too |
| var m = dojo.gfx.matrix.normalize(matrix); |
| // combine matrices |
| for(var i = 1; i < arguments.length; ++i){ |
| var l = m; |
| var r = dojo.gfx.matrix.normalize(arguments[i]); |
| m = new dojo.gfx.matrix.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; // dojo.gfx.matrix.Matrix2D |
| }, |
| |
| // high level operations |
| |
| _sandwich: function(m, x, y){ |
| // summary: applies a matrix at a centrtal point |
| // m: dojo.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 dojo.gfx.matrix.multiply(dojo.gfx.matrix.translate(x, y), m, dojo.gfx.matrix.translate(-x, -y)); // dojo.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 dojo.gfx.matrix.scale(). |
| // a: Number: a scaling factor used for the x coordinate |
| // b: Number: a scaling factor used for the y coordinate |
| // c: Number: an x component of a central point |
| // d: Number: a y component of a central point |
| |
| // accepts several signatures: |
| // 1) uniform scale factor, Point |
| // 2) uniform scale factor, x, y |
| // 3) x scale, y scale, Point |
| // 4) x scale, y scale, x, y |
| |
| switch(arguments.length){ |
| case 4: |
| // a and b are scale factor components, c and d are components of a point |
| return dojo.gfx.matrix._sandwich(dojo.gfx.matrix.scale(a, b), c, d); // dojo.gfx.matrix.Matrix2D |
| case 3: |
| if(typeof c == "number"){ |
| // branch |
| // a: Number: a uniform scaling factor used for both coordinates |
| // b: Number: an x component of a central point |
| // c: Number: a y component of a central point |
| // d: null |
| return dojo.gfx.matrix._sandwich(dojo.gfx.matrix.scale(a), b, c); // dojo.gfx.matrix.Matrix2D |
| } |
| // branch |
| // a: Number: a scaling factor used for the x coordinate |
| // b: Number: a scaling factor used for the y coordinate |
| // c: dojo.gfx.Point: a central point |
| // d: null |
| return dojo.gfx.matrix._sandwich(dojo.gfx.matrix.scale(a, b), c.x, c.y); // dojo.gfx.matrix.Matrix2D |
| } |
| // branch |
| // a: Number: a uniform scaling factor used for both coordinates |
| // b: dojo.gfx.Point: a central point |
| // c: null |
| // d: null |
| return dojo.gfx.matrix._sandwich(dojo.gfx.matrix.scale(a), b.x, b.y); // dojo.gfx.matrix.Matrix2D |
| }, |
| rotateAt: function(angle, a, b){ |
| // summary: rotates a picture using a specified point as a center of rotation |
| // description: Compare with dojo.gfx.matrix.rotate(). |
| // angle: Number: an angle of rotation in radians (>0 for CCW) |
| // 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 radians, Point |
| // 2) rotation angle in radians, x, y |
| |
| if(arguments.length > 2){ |
| return dojo.gfx.matrix._sandwich(dojo.gfx.matrix.rotate(angle), a, b); // dojo.gfx.matrix.Matrix2D |
| } |
| |
| // branch |
| // angle: Number: an angle of rotation in radians (>0 for CCW) |
| // a: dojo.gfx.Point: a central point |
| // b: null |
| return dojo.gfx.matrix._sandwich(dojo.gfx.matrix.rotate(angle), a.x, a.y); // dojo.gfx.matrix.Matrix2D |
| }, |
| rotategAt: function(degree, a, b){ |
| // summary: rotates a picture using a specified point as a center of rotation |
| // description: Compare with dojo.gfx.matrix.rotateg(). |
| // degree: Number: an angle of rotation in degrees (>0 for CCW) |
| // 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 dojo.gfx.matrix._sandwich(dojo.gfx.matrix.rotateg(degree), a, b); // dojo.gfx.matrix.Matrix2D |
| } |
| |
| // branch |
| // degree: Number: an angle of rotation in degrees (>0 for CCW) |
| // a: dojo.gfx.Point: a central point |
| // b: null |
| return dojo.gfx.matrix._sandwich(dojo.gfx.matrix.rotateg(degree), a.x, a.y); // dojo.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 dojo.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 dojo.gfx.matrix._sandwich(dojo.gfx.matrix.skewX(angle), a, b); // dojo.gfx.matrix.Matrix2D |
| } |
| |
| // branch |
| // angle: Number: an skewing angle in radians |
| // a: dojo.gfx.Point: a central point |
| // b: null |
| return dojo.gfx.matrix._sandwich(dojo.gfx.matrix.skewX(angle), a.x, a.y); // dojo.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 dojo.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 dojo.gfx.matrix._sandwich(dojo.gfx.matrix.skewXg(degree), a, b); // dojo.gfx.matrix.Matrix2D |
| } |
| |
| // branch |
| // degree: Number: an skewing angle in degrees |
| // a: dojo.gfx.Point: a central point |
| // b: null |
| return dojo.gfx.matrix._sandwich(dojo.gfx.matrix.skewXg(degree), a.x, a.y); // dojo.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 dojo.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 dojo.gfx.matrix._sandwich(dojo.gfx.matrix.skewY(angle), a, b); // dojo.gfx.matrix.Matrix2D |
| } |
| |
| // branch |
| // angle: Number: an skewing angle in radians |
| // a: dojo.gfx.Point: a central point |
| // b: null |
| return dojo.gfx.matrix._sandwich(dojo.gfx.matrix.skewY(angle), a.x, a.y); // dojo.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 dojo.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 dojo.gfx.matrix._sandwich(dojo.gfx.matrix.skewYg(degree), a, b); // dojo.gfx.matrix.Matrix2D |
| } |
| |
| // branch |
| // degree: Number: an skewing angle in degrees |
| // a: dojo.gfx.Point: a central point |
| // b: null |
| return dojo.gfx.matrix._sandwich(dojo.gfx.matrix.skewYg(degree), a.x, a.y); // dojo.gfx.matrix.Matrix2D |
| } |
| |
| // TODO: rect-to-rect mapping, scale-to-fit (isotropic and anisotropic versions) |
| |
| }); |
