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 }; })();