| New file |
|---|
| 0,0 → 1,139 |
|---|
| if(!dojo._hasResource["dojox.gfx.decompose"]){ //_hasResource checks added by build. Do not use _hasResource directly in your code. |
| dojo._hasResource["dojox.gfx.decompose"] = true; |
| dojo.provide("dojox.gfx.decompose"); |
| |
| dojo.require("dojox.gfx.matrix"); |
| |
| (function(){ |
| var m = dojox.gfx.matrix; |
| |
| var eq = function(/* Number */ a, /* Number */ b){ |
| // summary: compare two FP numbers for equality |
| return Math.abs(a - b) <= 1e-6 * (Math.abs(a) + Math.abs(b)); // Boolean |
| }; |
| |
| var calcFromValues = function(/* Number */ r1, /* Number */ m1, /* Number */ r2, /* Number */ m2){ |
| // summary: uses two close FP ration and their original magnitudes to approximate the result |
| if(!isFinite(r1)){ |
| return r2; // Number |
| }else if(!isFinite(r2)){ |
| return r1; // Number |
| } |
| m1 = Math.abs(m1), m2 = Math.abs(m2); |
| return (m1 * r1 + m2 * r2) / (m1 + m2); // Number |
| }; |
| |
| var transpose = function(/* dojox.gfx.matrix.Matrix2D */ matrix){ |
| // matrix: dojox.gfx.matrix.Matrix2D: a 2D matrix-like object |
| var M = new m.Matrix2D(matrix); |
| return dojo.mixin(M, {dx: 0, dy: 0, xy: M.yx, yx: M.xy}); // dojox.gfx.matrix.Matrix2D |
| }; |
| |
| var scaleSign = function(/* dojox.gfx.matrix.Matrix2D */ matrix){ |
| return (matrix.xx * matrix.yy < 0 || matrix.xy * matrix.yx > 0) ? -1 : 1; // Number |
| }; |
| |
| var eigenvalueDecomposition = function(/* dojox.gfx.matrix.Matrix2D */ matrix){ |
| // matrix: dojox.gfx.matrix.Matrix2D: a 2D matrix-like object |
| var M = m.normalize(matrix), |
| b = -M.xx - M.yy, |
| c = M.xx * M.yy - M.xy * M.yx, |
| d = Math.sqrt(b * b - 4 * c), |
| l1 = -(b + (b < 0 ? -d : d)) / 2, |
| l2 = c / l1, |
| vx1 = M.xy / (l1 - M.xx), vy1 = 1, |
| vx2 = M.xy / (l2 - M.xx), vy2 = 1; |
| if(eq(l1, l2)){ |
| vx1 = 1, vy1 = 0, vx2 = 0, vy2 = 1; |
| } |
| if(!isFinite(vx1)){ |
| vx1 = 1, vy1 = (l1 - M.xx) / M.xy; |
| if(!isFinite(vy1)){ |
| vx1 = (l1 - M.yy) / M.yx, vy1 = 1; |
| if(!isFinite(vx1)){ |
| vx1 = 1, vy1 = M.yx / (l1 - M.yy); |
| } |
| } |
| } |
| if(!isFinite(vx2)){ |
| vx2 = 1, vy2 = (l2 - M.xx) / M.xy; |
| if(!isFinite(vy2)){ |
| vx2 = (l2 - M.yy) / M.yx, vy2 = 1; |
| if(!isFinite(vx2)){ |
| vx2 = 1, vy2 = M.yx / (l2 - M.yy); |
| } |
| } |
| } |
| var d1 = Math.sqrt(vx1 * vx1 + vy1 * vy1), |
| d2 = Math.sqrt(vx2 * vx2 + vy2 * vy2); |
| if(!isFinite(vx1 /= d1)){ vx1 = 0; } |
| if(!isFinite(vy1 /= d1)){ vy1 = 0; } |
| if(!isFinite(vx2 /= d2)){ vx2 = 0; } |
| if(!isFinite(vy2 /= d2)){ vy2 = 0; } |
| return { // Object |
| value1: l1, |
| value2: l2, |
| vector1: {x: vx1, y: vy1}, |
| vector2: {x: vx2, y: vy2} |
| }; |
| }; |
| |
| var decomposeSR = function(/* dojox.gfx.matrix.Matrix2D */ M, /* Object */ result){ |
| // summary: decomposes a matrix into [scale, rotate]; no checks are done. |
| var sign = scaleSign(M), |
| a = result.angle1 = (Math.atan2(M.yx, M.yy) + Math.atan2(-sign * M.xy, sign * M.xx)) / 2, |
| cos = Math.cos(a), sin = Math.sin(a); |
| result.sx = calcFromValues(M.xx / cos, cos, -M.xy / sin, sin); |
| result.sy = calcFromValues(M.yy / cos, cos, M.yx / sin, sin); |
| return result; // Object |
| }; |
| |
| var decomposeRS = function(/* dojox.gfx.matrix.Matrix2D */ M, /* Object */ result){ |
| // summary: decomposes a matrix into [rotate, scale]; no checks are done |
| var sign = scaleSign(M), |
| a = result.angle2 = (Math.atan2(sign * M.yx, sign * M.xx) + Math.atan2(-M.xy, M.yy)) / 2, |
| cos = Math.cos(a), sin = Math.sin(a); |
| result.sx = calcFromValues(M.xx / cos, cos, M.yx / sin, sin); |
| result.sy = calcFromValues(M.yy / cos, cos, -M.xy / sin, sin); |
| return result; // Object |
| }; |
| |
| dojox.gfx.decompose = function(matrix){ |
| // summary: decompose a 2D matrix into translation, scaling, and rotation components |
| // description: this function decompose a matrix into four logical components: |
| // translation, rotation, scaling, and one more rotation using SVD. |
| // The components should be applied in following order: |
| // | [translate, rotate(angle2), scale, rotate(angle1)] |
| // matrix: dojox.gfx.matrix.Matrix2D: a 2D matrix-like object |
| var M = m.normalize(matrix), |
| result = {dx: M.dx, dy: M.dy, sx: 1, sy: 1, angle1: 0, angle2: 0}; |
| // detect case: [scale] |
| if(eq(M.xy, 0) && eq(M.yx, 0)){ |
| return dojo.mixin(result, {sx: M.xx, sy: M.yy}); // Object |
| } |
| // detect case: [scale, rotate] |
| if(eq(M.xx * M.yx, -M.xy * M.yy)){ |
| return decomposeSR(M, result); // Object |
| } |
| // detect case: [rotate, scale] |
| if(eq(M.xx * M.xy, -M.yx * M.yy)){ |
| return decomposeRS(M, result); // Object |
| } |
| // do SVD |
| var MT = transpose(M), |
| u = eigenvalueDecomposition([M, MT]), |
| v = eigenvalueDecomposition([MT, M]), |
| U = new m.Matrix2D({xx: u.vector1.x, xy: u.vector2.x, yx: u.vector1.y, yy: u.vector2.y}), |
| VT = new m.Matrix2D({xx: v.vector1.x, xy: v.vector1.y, yx: v.vector2.x, yy: v.vector2.y}), |
| S = new m.Matrix2D([m.invert(U), M, m.invert(VT)]); |
| decomposeSR(VT, result); |
| S.xx *= result.sx; |
| S.yy *= result.sy; |
| decomposeRS(U, result); |
| S.xx *= result.sx; |
| S.yy *= result.sy; |
| return dojo.mixin(result, {sx: S.xx, sy: S.yy}); // Object |
| }; |
| })(); |
| |
| } |