+++ /dev/null
-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
- };
-})();
-
-}
projects / eow / blobdiff