Empirical measurement of cubic bez arclength bound

arclen_bound.rs

use kurbo::{CubicBez, ParamCurveArclen, Point};

fn randpt() -> Point {
    Point::new(rand::random(), rand::random())
}

fn randbez() -> CubicBez {
    CubicBez::new(randpt(), randpt(), randpt(), randpt())
}

fn main() {
    let thresh = 0.1;
    let mut max_ratio = 0.0;
    let mut worst_bez = randbez();
    for _ in 0..10_000_000 {
        let b = randbez();
        let true_arclen = b.arclen(1e-12);
        let excess = (b.p1 - b.p0).hypot2() + (b.p2 - b.p3).hypot2();
        let error = true_arclen - (b.p3 - b.p0).hypot();
        let ratio = error * error / excess;
        if ratio > max_ratio {
            max_ratio = ratio;
            worst_bez = b;
        }
        max_ratio = ratio.max(max_ratio);
        if excess < 1.0 * thresh * thresh && error > thresh {
            println!("{:?}, {}", b, ratio);
        }
    }
    println!("max ratio: {} {:?}", max_ratio, worst_bez);

    // output as SVG
    let path_seg: kurbo::PathSeg = (kurbo::Affine::scale(200.0) * worst_bez).into();
    let path = kurbo::BezPath::from_path_segments(std::iter::once(path_seg));
    println!("{}", path.to_svg());
}