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Add support for sub ranges and negatives lengths in Curve#getParameter(), a prerequirement for adding dash support.

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This commit is contained in:
Jürg Lehni 2011-03-07 11:37:42 +00:00
parent 2ac9a13e2a
commit 0ddfc9ef33
1 changed files with 39 additions and 19 deletions
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58
src/path/Curve.js
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@ -171,9 +171,10 @@ var Curve = this.Curve = Base.extend({
&& this._segment2._handleIn.isZero();
},
getParameter: function(length) {
getParameter: function(length, t) {
var args = this.getCurveValues();
args.push(length)
args.push(length);
args.push(t == undefined ? length < 0 ? 1 : 0 : t);
return Curve.getParameter.apply(Curve, args);
},
@ -317,7 +318,7 @@ var Curve = this.Curve = Base.extend({
// Straight line
var dx = p2x - p1x,
dy = p2y - p1y;
return Math.sqrt(dx * dx + dy * dy) * (b - a);
return (b - a) * Math.sqrt(dx * dx + dy * dy);
}
var ds = getLengthIntegrand(
p1x, p1y, c1x, c1y, c2x, c2y, p2x, p2y);
@ -325,32 +326,51 @@ var Curve = this.Curve = Base.extend({
},
getParameter: function(p1x, p1y, c1x, c1y, c2x, c2y, p2x, p2y,
length) {
if (length <= 0)
return 0;
length, t) {
if (length == 0) {
return t;
}
if (p1x == c1x && p1y == c1y && p2x == c2x && p2y == c2y) {
// Straight line, calculate directly
// t = length / lineLength:
var dx = p2x - p1x,
dy = p2y - p1y;
return Math.min(length / Math.sqrt(dx * dx + dy * dy), 1);
return Math.max(Math.min(
t + length / Math.sqrt(dx * dx + dy * dy), 0, 1));
}
var ds = getLengthIntegrand(
p1x, p1y, c1x, c1y, c2x, c2y, p2x, p2y);
// Use integrand both to calculate total length and part lengths
// in f(t) below.
var bezierLength = Numerical.integrate(ds, 0, 1, 8);
if (length >= bezierLength)
return 1;
// Let's use the Van Wijngaarden–Dekker–Brent Method to find
// solutions more reliably than with False Position Method.
function f(t) {
// The precision of 5 iterations seems enough for this
return length - Numerical.integrate(ds, 0, t, 5);
// The precision of 5 iterations seems enough for this
// See if we're going backwards and handle case differently
var a, b, f,
forward = length > 0,
// Use integrand to calculate both range length and part
// lengths in f(t) below.
ds = getLengthIntegrand(
p1x, p1y, c1x, c1y, c2x, c2y, p2x, p2y);
if (forward) { // Normal way
a = t;
b = 1;
f = function(t) {
return length - Numerical.integrate(ds, a, t, 5);
}
} else { // Going backwards
a = 0;
b = t;
length = -length;
f = function(t) {
return length - Numerical.integrate(ds, t, b, 5);
}
}
// Use length / bezierLength for an initial guess for b, to
var rangeLength = Numerical.integrate(ds, a, b, 8);
if (length >= rangeLength)
return forward ? b : a;
// Use length / rangeLength for an initial guess for t, to
// bring us closer:
return Numerical.findRoot(f, 0, length / bezierLength,
var guess = length / rangeLength;
return Numerical.findRoot(f,
forward ? a : b - guess, // a
forward ? a + guess : b, // b
Numerical.TOLERANCE);
},