2D Matrix Decomposition
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d3.transform = function(string) { | |
d3_transformG.setAttribute("transform", string); | |
var m = d3_transformG.transform.baseVal.consolidate().matrix; | |
if (m.a * m.d - m.b * m.c) return new d3_transform(m); // if invertible | |
}; | |
// Compute x-scale and normalize the first row. | |
// Compute shear and make second row orthogonal to first. | |
// Compute y-scale and normalize the second row. | |
// Finally, compute the rotation. | |
function d3_transform(m) { | |
var r0 = [m.a, m.b], | |
r1 = [m.c, m.d], | |
kx = d3_transformNormalize(r0), | |
kz = d3_transformDot(r0, r1), | |
ky = d3_transformNormalize(d3_transformCombine(r1, r0, -kz)); | |
this.translate = [m.e, m.f]; | |
this.rotate = Math.atan2(m.b, m.a) * d3_transformDegrees; | |
this.scale = [kx, ky]; | |
this.skew = kz / ky * d3_transformDegrees; | |
}; | |
d3_transform.prototype.toString = function() { | |
return "translate(" + this.translate | |
+ ")rotate(" + this.rotate | |
+ ")skewX(" + this.skew | |
+ ")scale(" + this.scale | |
+ ")"; | |
}; | |
function d3_transformDot(a, b) { | |
return a[0] * b[0] + a[1] * b[1]; | |
} | |
function d3_transformNormalize(a) { | |
var k = Math.sqrt(d3_transformDot(a, a)); | |
a[0] /= k; | |
a[1] /= k; | |
return k; | |
} | |
function d3_transformCombine(a, b, k) { | |
a[0] += k * b[0]; | |
a[1] += k * b[1]; | |
return a; | |
} | |
var d3_transformG = document.createElementNS(d3.ns.prefix.svg, "g"), | |
d3_transformDegrees = 180 / Math.PI; |
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