add a proto.getPointAtDistance([0,1]) about bezierjs HOT 4 OPEN

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.

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 suspect guess = 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 the while loop, which removes the need to recompute this.get(guess) at return, as that yields the point corresponding to the last iterations's left.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.

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.