Comments (4)
FWIW, I just implemented this using an iterative approximation:
public getPointAtDistance(offset: number, ϵ: number = 1) {
let l = this.length();
if (offset < 0) return this.get(0);
if (offset > l) return this.get(1);
let i = 0, maxIterations = 10;
let error = l;
let guess = offset / l;
//interpolate
while (error > ϵ && i < maxIterations) {
let segmentLength = this.split(guess).left.length();
error = segmentLength - offset;
guess = guess - (error / l);
i += 1;
}
return this.get(guess);
}
It converges pretty fast, generally, within 3 or 4 iterations it achieves subpixel accuracy.
I should also note that my version works on the interval [0, length]
from bezierjs.
let's consider this a naming issue: getPointAtLength(...)
should absolutely take a value in [0,curve.length], whereas getPointAtDistance(...)
feels more like a 0%-100% call, but I can see how someone else might still consider [0,length] more appropriate.
So let's say this:
- getPointAtDistance: based on actual curve length
- getPointAtPercentage: based on 0%-100% (rather than [0,1])
from bezierjs.
it would be useful to make maxIterations
an overridable value as well.
A few notes:
- You don't need to spend time on calculating
.length()
for <0 and >1 cases, putting it after will make <0 and >1 perform in O(1) - While
guess = offset/length
works, I suspectguess = offset
works a little better on average. Generally the initial guess is going to be way too low, as it starts off dividing a number in [0,1] by a value orders of magnitude higher, so in this implementation we start at "barely above zero" in the vast majority of cases. - you can cache the
this.split(guess).left
during iteration in a variable declared outside thewhile
loop, which removes the need to recomputethis.get(guess)
at return, as that yields the point corresponding to the last iterations'sleft.get(1)
.
from bezierjs.
This version works with offset on the range [0, length], rather than [0,1], which seemed more natural to me. Hence the first guess (for t) is offset / length
The rest of the notes are very useful, thanks
from bezierjs.
Related Issues (20)
- Release v6.1.2 broken HOT 3
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- Example usage of `dist/bezier.js` HOT 4
- How to make a "strict" version of bezier.project(point)? HOT 2
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- intersects bug Bezier to Bezier HOT 3
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- The intersection of the two bezier is empty HOT 10
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- Intersect line method does not always return existing intersections HOT 6
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- Artifact when offsetting an SVG path
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- Missing LICENSE file HOT 1
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from bezierjs.