d3.transform = function(string) {

  d3_transformG.setAttribute("transform", string);

  return new d3_transform(d3_transformG.transform.baseVal.consolidate().matrix);

};

// 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 || 0];

  this.skew = ky ? kz / ky * d3_transformDegrees : 0;

};

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;