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Use golden section search to calculate max deviation in arc flattening #96

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Merged
sameer merged 1 commit into from
Mar 8, 2026
Merged

Use golden section search to calculate max deviation in arc flattening #96

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55 changes: 39 additions & 16 deletions lib/src/arc.rs
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Original file line number Diff line number Diff line change
Expand Up @@ -8,6 +8,41 @@ pub enum ArcOrLineSegment<S> {
Line(LineSegment<S>),
}

/// 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: Scalar, F: Fn(S) -> 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<S: Scalar>(
from: Point<S>,
from_tangent: Vector<S>,
Expand Down Expand Up @@ -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));
Expand Down Expand Up @@ -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)]
Expand Down
4 changes: 3 additions & 1 deletion lib/tests/circular_interpolation.gcode
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Original file line number Diff line number Diff line change
Expand Up @@ -153,7 +153,9 @@ G3 X5.341 Y5.798 R7.42 F300
G3 X5.262 Y5.815 R7.846 F300
G3 X5.098 Y5.848 R8.529 F300
G3 X4.928 Y5.879 R9.472 F300
G3 X4.752 Y5.908 R10.413 F300
G3 X4.883 Y5.886 R10.073 F300
G3 X4.84 Y5.894 R10.307 F300
G3 X4.752 Y5.908 R10.652 F300
G3 X4.572 Y5.934 R11.33 F300
G3 X4.386 Y5.958 R12.21 F300
G3 X4.196 Y5.98 R13.047 F300
Expand Down
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