Trait kurbo::ParamCurveArclen[−][src]

pub trait ParamCurveArclen: ParamCurve {
    fn arclen(&self, accuracy: f64) -> f64;

    fn inv_arclen(&self, arclen: f64, accuracy: f64) -> f64 { ... }
}

A parametrized curve that can have its arc length measured.

Required methods

fn arclen(&self, accuracy: f64) -> f64[src]

The arc length of the curve.

The result is accurate to the given accuracy (subject to roundoff errors for ridiculously low values). Compute time may vary with accuracy, if the curve needs to be subdivided.

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Provided methods

fn inv_arclen(&self, arclen: f64, accuracy: f64) -> f64[src]

Solve for the parameter that has the given arc length from the start.

This implementation uses the IPT method, as provided by common::solve_itp. This is as robust as bisection but typically converges faster. In addition, the method takes care to compute arc lengths of increasingly smaller segments of the curve, as that is likely faster than repeatedly computing the arc length of the segment starting at t=0.

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Implementors

impl ParamCurveArclen for PathSeg[src]

impl ParamCurveArclen for ConstPoint[src]

impl ParamCurveArclen for CubicBez[src]

fn arclen(&self, accuracy: f64) -> f64[src]

Arclength of a cubic Bézier segment.

This is an adaptive subdivision approach using Legendre-Gauss quadrature in the base case, and an error estimate to decide when to subdivide.

impl ParamCurveArclen for Line[src]

impl ParamCurveArclen for QuadBez[src]

fn arclen(&self, _accuracy: f64) -> f64[src]

Arclength of a quadratic Bézier segment.

This computation is based on an analytical formula. Since that formula suffers from numerical instability when the curve is very close to a straight line, we detect that case and fall back to Legendre-Gauss quadrature.

Accuracy should be better than 1e-13 over the entire range.

Adapted from http://www.malczak.linuxpl.com/blog/quadratic-bezier-curve-length/ with permission.

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