From e598651bd9d6c3268bd7b5e9ab8ac5d7c7050ea9 Mon Sep 17 00:00:00 2001 From: Sameer Puri Date: Sat, 7 Mar 2026 15:54:05 -0800 Subject: [PATCH] Use golden section search to calculate max deviation in arc flattening --- lib/src/arc.rs | 55 +- lib/tests/circular_interpolation.gcode | 4 +- ...smooth_curves_circular_interpolation.gcode | 3473 ++++++++++------- ...urves_circular_interpolation_release.gcode | 127 +- 4 files changed, 2232 insertions(+), 1427 deletions(-) diff --git a/lib/src/arc.rs b/lib/src/arc.rs index 463c18a..7bc9769 100644 --- a/lib/src/arc.rs +++ b/lib/src/arc.rs @@ -8,6 +8,41 @@ pub enum ArcOrLineSegment { Line(LineSegment), } +/// Golden-section search for the maximum of a unimodal function f on [0, 1]. +/// Returns (t_max, f(t_max)). +/// +/// https://en.wikipedia.org/wiki/Golden-section_search +fn golden_section_max S>(f: F) -> (S, S) { + let tolerance = S::from(1E-5_f64).unwrap(); + + let inv_phi = (S::from(5.0_f64).unwrap().sqrt() - S::ONE) / S::TWO; + let mut x_1 = S::ZERO; + let mut x_4 = S::ONE; + let mut x_2 = x_4 - inv_phi * (x_4 - x_1); + let mut x_3 = x_1 + inv_phi * (x_4 - x_1); + let mut f_x_2 = f(x_2); + let mut f_x_3 = f(x_3); + + while x_4 - x_1 > tolerance { + if f_x_2 < f_x_3 { + x_1 = x_2; + x_2 = x_3; + f_x_2 = f_x_3; + x_3 = x_1 + inv_phi * (x_4 - x_1); + f_x_3 = f(x_3); + } else { + x_4 = x_3; + x_3 = x_2; + f_x_3 = f_x_2; + x_2 = x_4 - inv_phi * (x_4 - x_1); + f_x_2 = f(x_2); + } + } + + let t_max = (x_1 + x_4) / S::TWO; + (t_max, f(t_max)) +} + fn arc_from_endpoints_and_tangents( from: Point, from_tangent: Vector, @@ -116,14 +151,8 @@ where ) .filter(|svg_arc| { let arc = svg_arc.to_arc(); - let mut max_deviation = S::ZERO; - // TODO: find a better way to check tolerance - // Ideally: derivative of |f(x) - g(x)| and look at 0 crossings - for i in 1..20 { - let t = S::from(i).unwrap() / S::from(20).unwrap(); - max_deviation = - max_deviation.max((arc.sample(t) - inner_bezier.sample(t)).length()); - } + let (_, max_deviation) = + golden_section_max(|t| (arc.sample(t) - inner_bezier.sample(t)).length()); max_deviation < tolerance }) { acc.push(ArcOrLineSegment::Arc(svg_arc)); @@ -162,14 +191,8 @@ where ) .filter(|approx_svg_arc| { let approx_arc = approx_svg_arc.to_arc(); - let mut max_deviation = S::ZERO; - // TODO: find a better way to check tolerance - // Ideally: derivative of |f(x) - g(x)| and look at 0 crossings - for i in 1..20 { - let t = S::from(i).unwrap() / S::from(20).unwrap(); - max_deviation = - max_deviation.max((approx_arc.sample(t) - self_arc.sample(t)).length()); - } + let (_, max_deviation) = + golden_section_max(|t| (approx_arc.sample(t) - self_arc.sample(t)).length()); max_deviation < tolerance }) { vec![ArcOrLineSegment::Arc(svg_arc)] diff --git a/lib/tests/circular_interpolation.gcode b/lib/tests/circular_interpolation.gcode index d45060d..2bd7454 100644 --- a/lib/tests/circular_interpolation.gcode +++ b/lib/tests/circular_interpolation.gcode @@ -153,7 +153,9 @@ G3 X5.341 Y5.798 R7.42 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