From 8ccc12f0136e5acd629b3183de7f6cdddcb613a3 Mon Sep 17 00:00:00 2001 From: Sameer Puri Date: Tue, 10 Mar 2026 20:08:02 -0700 Subject: [PATCH 1/5] Revert "Use golden section search to calculate max deviation in arc flattening" This reverts commit 14be093ac56b72da7213a0b906d367f8fc5da3ab. --- 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, 1427 insertions(+), 2232 deletions(-) diff --git a/lib/src/arc.rs b/lib/src/arc.rs index 7bc9769..463c18a 100644 --- a/lib/src/arc.rs +++ b/lib/src/arc.rs @@ -8,41 +8,6 @@ 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, @@ -151,8 +116,14 @@ where ) .filter(|svg_arc| { let arc = svg_arc.to_arc(); - let (_, max_deviation) = - golden_section_max(|t| (arc.sample(t) - inner_bezier.sample(t)).length()); + 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()); + } max_deviation < tolerance }) { acc.push(ArcOrLineSegment::Arc(svg_arc)); @@ -191,8 +162,14 @@ where ) .filter(|approx_svg_arc| { let approx_arc = approx_svg_arc.to_arc(); - let (_, max_deviation) = - golden_section_max(|t| (approx_arc.sample(t) - self_arc.sample(t)).length()); + 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()); + } max_deviation < tolerance }) { vec![ArcOrLineSegment::Arc(svg_arc)] diff --git a/lib/tests/circular_interpolation.gcode b/lib/tests/circular_interpolation.gcode index 2bd7454..d45060d 100644 --- a/lib/tests/circular_interpolation.gcode +++ 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X27.557 Y17.67 R1.043 F300 +G3 X27.557 Y17.67 R1.013 F300 G3 X27.8 Y17.698 R1.053 F300 G3 X28.027 Y17.783 R0.955 F300 G3 X28.221 Y17.925 R0.805 F300 @@ -1251,10 +1275,10 @@ G1 X41.99 Y21.552 F300 G1 X41.939 Y21.272 F300 G1 X41.89 Y20.992 F300 G1 X41.843 Y20.711 F300 -G1 X41.799 Y20.43 F300 -G1 X41.756 Y20.148 F300 -G3 X41.677 Y19.582 R48.229 F300 -G3 X41.405 Y17.306 R94.282 F300 +G3 X41.677 Y19.582 R43.868 F300 +G3 X41.534 Y18.447 R68.388 F300 +G1 X41.468 Y17.877 F300 +G1 X41.405 Y17.306 F300 G3 X41.401 Y17.233 R0.665 F300 G3 X41.485 Y16.901 R0.719 F300 G3 X41.58 Y16.756 R0.885 F300 @@ -1374,7 +1398,8 @@ G2 X52.388 Y22.683 R35.126 F300 G3 X53.361 Y23.392 R2.183 F300 G1 X53.586 Y23.651 F300 G1 X53.81 Y23.914 F300 -G3 X54.25 Y24.45 R30.91 F300 +G1 X54.031 Y24.18 F300 +G1 X54.25 Y24.45 F300 G1 X54.482 Y24.736 F300 G1 X54.712 Y25.024 F300 G1 X54.94 Y25.313 F300 @@ -1385,7 +1410,8 @@ G1 X55.829 Y26.487 F300 G1 X56.047 Y26.784 F300 G3 X55.705 Y28.051 R0.934 F300;svg#Drawing > g#Layer_3 > path G0 X15.894 Y8.964 -G3 X16.108 Y9.223 R20.687 F300 +G1 X16.001 Y9.092 F300 +G1 X16.108 Y9.223 F300 G1 X16.214 Y9.356 F300 G1 X16.319 Y9.491 F300 G3 X16.7 Y10.059 R5.4 F300 @@ -1505,8 +1531,7 @@ G1 X14.317 Y4.636 F300 G0 X15.182 Y11.165 G1 X15.145 Y11.095 F300 G1 X15.113 Y11.028 F300 -G1 X15.051 Y10.925 F300 -G1 X14.986 Y10.821 F300 +G2 X14.986 Y10.821 R6.515 F300 G1 X14.846 Y10.623 F300 G1 X14.764 Y10.512 F300 G2 X14.622 Y10.335 R7.209 F300 From d81d1f736a4e109563d0a2f7b2d5a7d094cdec11 Mon Sep 17 00:00:00 2001 From: Sameer Puri Date: Tue, 10 Mar 2026 20:42:37 -0700 Subject: [PATCH 2/5] Add a Bezier tolerance test --- .github/workflows/lib.yml | 4 - Cargo.lock | 127 +---------------------- lib/Cargo.toml | 4 - lib/src/arc.rs | 206 +++++++++++++++----------------------- 4 files changed, 80 insertions(+), 261 deletions(-) diff --git a/.github/workflows/lib.yml b/.github/workflows/lib.yml index 8772ef9..8123aa7 100644 --- a/.github/workflows/lib.yml +++ b/.github/workflows/lib.yml @@ -24,8 +24,6 @@ jobs: with: components: clippy - uses: Swatinem/rust-cache@v2 - - name: Install dependencies - run: sudo apt-get update && sudo apt-get install -y libcairo2-dev - name: Fmt run: cargo +nightly-${{ steps.stable-date.outputs.date }} fmt --check -p svg2gcode - name: Clippy @@ -48,8 +46,6 @@ jobs: with: toolchain: nightly components: llvm-tools-preview - - name: Install dependencies - run: sudo apt-get update && sudo apt-get install -y libcairo2-dev - run: cargo install grcov - run: cargo build -p svg2gcode env: diff --git a/Cargo.lock b/Cargo.lock index 02a5951..28eae46 100644 --- a/Cargo.lock +++ b/Cargo.lock @@ -94,12 +94,6 @@ dependencies = [ "serde", ] -[[package]] -name = "bitflags" -version = "2.11.0" -source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "843867be96c8daad0d758b57df9392b6d8d271134fce549de6ce169ff98a92af" - [[package]] name = "boolinator" version = "2.4.0" @@ -124,37 +118,6 @@ version = "1.11.1" source = "registry+https://github.com/rust-lang/crates.io-index" checksum = "1e748733b7cbc798e1434b6ac524f0c1ff2ab456fe201501e6497c8417a4fc33" -[[package]] -name = "cairo-rs" -version = "0.22.0" -source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "5cc8d9aa793480744cd9a0524fef1a2e197d9eaa0f739cde19d16aba530dcb95" -dependencies = [ - "bitflags", - "cairo-sys-rs", - "libc", -] - -[[package]] -name = "cairo-sys-rs" -version = "0.22.0" -source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "f8b4985713047f5faee02b8db6a6ef32bbb50269ff53c1aee716d1d195b76d54" -dependencies = [ - "libc", - "system-deps", -] - -[[package]] -name = "cfg-expr" -version = "0.20.6" -source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "78cef5b5a1a6827c7322ae2a636368a573006b27cfa76c7ebd53e834daeaab6a" -dependencies = [ - "smallvec", - "target-lexicon", -] - [[package]] name = "cfg-if" version = "1.0.4" @@ -1083,12 +1046,6 @@ dependencies = [ "thiserror", ] -[[package]] -name = "pkg-config" -version = "0.3.32" -source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "7edddbd0b52d732b21ad9a5fab5c704c14cd949e5e9a1ec5929a24fded1b904c" - [[package]] name = "portable-atomic" version = "1.13.1" @@ -1330,15 +1287,6 @@ dependencies = [ "syn 2.0.117", ] -[[package]] -name = "serde_spanned" -version = "1.0.4" -source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "f8bbf91e5a4d6315eee45e704372590b30e260ee83af6639d64557f51b067776" -dependencies = [ - "serde_core", -] - [[package]] name = "serde_urlencoded" version = "0.7.1" @@ -1379,7 +1327,6 @@ checksum = "7da8b5736845d9f2fcb837ea5d9e2628564b3b043a70948a3f0b778838c5fb4f" name = "svg2gcode" version = "0.3.4" dependencies = [ - "cairo-rs", "euclid", "g-code", "log", @@ -1469,25 +1416,6 @@ dependencies = [ "unicode-ident", ] -[[package]] -name = "system-deps" -version = "7.0.7" -source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "48c8f33736f986f16d69b6cb8b03f55ddcad5c41acc4ccc39dd88e84aa805e7f" -dependencies = [ - "cfg-expr", - "heck", - "pkg-config", - "toml", - "version-compare", -] - -[[package]] -name = "target-lexicon" -version = "0.13.3" -source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "df7f62577c25e07834649fc3b39fafdc597c0a3527dc1c60129201ccfcbaa50c" - [[package]] name = "termcolor" version = "1.4.1" @@ -1537,36 +1465,12 @@ dependencies = [ "tokio", ] -[[package]] -name = "toml" -version = "0.9.12+spec-1.1.0" -source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "cf92845e79fc2e2def6a5d828f0801e29a2f8acc037becc5ab08595c7d5e9863" -dependencies = [ - "indexmap", - "serde_core", - "serde_spanned", - "toml_datetime 0.7.5+spec-1.1.0", - "toml_parser", - "toml_writer", - "winnow 0.7.14", -] - [[package]] name = "toml_datetime" version = "0.6.11" source = "registry+https://github.com/rust-lang/crates.io-index" checksum = "22cddaf88f4fbc13c51aebbf5f8eceb5c7c5a9da2ac40a13519eb5b0a0e8f11c" -[[package]] -name = "toml_datetime" -version = "0.7.5+spec-1.1.0" -source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "92e1cfed4a3038bc5a127e35a2d360f145e1f4b971b551a2ba5fd7aedf7e1347" -dependencies = [ - "serde_core", -] - [[package]] name = "toml_edit" version = "0.19.15" @@ -1574,25 +1478,10 @@ source = "registry+https://github.com/rust-lang/crates.io-index" checksum = "1b5bb770da30e5cbfde35a2d7b9b8a2c4b8ef89548a7a6aeab5c9a576e3e7421" dependencies = [ "indexmap", - "toml_datetime 0.6.11", - "winnow 0.5.40", + "toml_datetime", + "winnow", ] -[[package]] -name = "toml_parser" -version = "1.0.9+spec-1.1.0" -source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "702d4415e08923e7e1ef96cd5727c0dfed80b4d2fa25db9647fe5eb6f7c5a4c4" -dependencies = [ - "winnow 0.7.14", -] - -[[package]] -name = "toml_writer" -version = "1.0.6+spec-1.1.0" -source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "ab16f14aed21ee8bfd8ec22513f7287cd4a91aa92e44edfe2c17ddd004e92607" - [[package]] name = "tracing" version = "0.1.44" @@ -1658,12 +1547,6 @@ version = "0.2.2" source = "registry+https://github.com/rust-lang/crates.io-index" checksum = "06abde3611657adf66d383f00b093d7faecc7fa57071cce2578660c9f1010821" -[[package]] -name = "version-compare" -version = "0.2.1" -source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "03c2856837ef78f57382f06b2b8563a2f512f7185d732608fd9176cb3b8edf0e" - [[package]] name = "version_check" version = "0.9.5" @@ -1789,12 +1672,6 @@ dependencies = [ "memchr", ] -[[package]] -name = "winnow" -version = "0.7.14" -source = "registry+https://github.com/rust-lang/crates.io-index" -checksum = "5a5364e9d77fcdeeaa6062ced926ee3381faa2ee02d3eb83a5c27a8825540829" - [[package]] name = "yansi" version = "1.0.1" diff --git a/lib/Cargo.toml b/lib/Cargo.toml index 134c749..e182533 100644 --- a/lib/Cargo.toml +++ b/lib/Cargo.toml @@ -32,9 +32,5 @@ optional = true version = "0.1" [dev-dependencies] -cairo-rs = { version = "0.22", default-features = false, features = [ - "svg", - "v1_16", -] } serde_json.workspace = true pretty_assertions = "1.4.1" diff --git a/lib/src/arc.rs b/lib/src/arc.rs index 463c18a..9c5f128 100644 --- a/lib/src/arc.rs +++ b/lib/src/arc.rs @@ -276,138 +276,88 @@ impl Transformed for SvgArc { #[cfg(test)] mod tests { - use std::path::PathBuf; - - use cairo::{Context, SvgSurface}; - use lyon_geom::{CubicBezierSegment, Point, Vector, point, vector}; - use svgtypes::PathParser; + use lyon_geom::{CubicBezierSegment, point}; use crate::arc::{ArcOrLineSegment, FlattenWithArcs}; - #[test] - #[ignore = "Creates an image file, will revise later"] - fn flatten_returns_expected_arcs() { - const PATH: &str = "M 8.0549,11.9023 - c - 0.13447,1.69916 8.85753,-5.917903 7.35159,-6.170957 - z"; - let mut surf = - SvgSurface::new(128., 128., Some(PathBuf::from("approx_circle.svg"))).unwrap(); - surf.set_document_unit(cairo::SvgUnit::Mm); - let ctx = Context::new(&surf).unwrap(); - ctx.set_line_width(0.2); - - let mut current_position = Point::zero(); - - let mut acc = 0; - - for path in PathParser::from(PATH) { - use svgtypes::PathSegment::*; - match path.unwrap() { - MoveTo { x, y, abs } => { - if abs { - ctx.move_to(x, y); - current_position = point(x, y); - } else { - ctx.rel_move_to(x, y); - current_position += vector(x, y); - } - } - LineTo { x, y, abs } => { - if abs { - ctx.line_to(x, y); - current_position = point(x, y); - } else { - ctx.rel_line_to(x, y); - current_position += vector(x, y); - } - } - ClosePath { .. } => ctx.close_path(), - CurveTo { - x1, - y1, - x2, - y2, - x, - y, - abs, - } => { - ctx.set_dash(&[], 0.); - match acc { - 0 => ctx.set_source_rgb(1., 0., 0.), - 1 => ctx.set_source_rgb(0., 1., 0.), - 2 => ctx.set_source_rgb(0., 0., 1.), - 3 => ctx.set_source_rgb(0., 0., 0.), - _ => unreachable!(), - } - let curve = CubicBezierSegment { - from: current_position, - ctrl1: (vector(x1, y1) - + if !abs { - current_position.to_vector() - } else { - Vector::zero() - }) - .to_point(), - ctrl2: (vector(x2, y2) - + if !abs { - current_position.to_vector() - } else { - Vector::zero() - }) - .to_point(), - to: (vector(x, y) - + if !abs { - current_position.to_vector() - } else { - Vector::zero() - }) - .to_point(), - }; - for segment in FlattenWithArcs::flattened(&curve, 0.02) { - match segment { - ArcOrLineSegment::Arc(svg_arc) => { - let arc = svg_arc.to_arc(); - if svg_arc.flags.sweep { - ctx.arc( - arc.center.x, - arc.center.y, - arc.radii.x, - arc.start_angle.radians, - (arc.start_angle + arc.sweep_angle).radians, - ) - } else { - ctx.arc_negative( - arc.center.x, - arc.center.y, - arc.radii.x, - arc.start_angle.radians, - (arc.start_angle + arc.sweep_angle).radians, - ) - } - } - ArcOrLineSegment::Line(line) => ctx.line_to(line.to.x, line.to.y), + /// Magic constant for cubic Bézier approximation of a quarter circle: 4(√2-1)/3 + const KAPPA: f64 = 4.0 * (std::f64::consts::SQRT_2 - 1.0) / 3.0; + + /// Approximate one-sided Hausdorff distance: for each of `samples` on the Bézier, + /// find the closest point on any flattened segment and return the maximum deviation. + fn approx_max_bezier_deviation( + curve: &CubicBezierSegment, + segments: &[ArcOrLineSegment], + samples: usize, + ) -> f64 { + (0..=samples) + .map(|i| { + let t = i as f64 / samples as f64; + let p = curve.sample(t); + segments + .iter() + .map(|seg| match seg { + ArcOrLineSegment::Arc(svg_arc) => { + let arc = svg_arc.to_arc(); + let q_angle = (p - arc.center).angle_from_x_axis().radians; + let start = arc.start_angle.radians; + let sweep = arc.sweep_angle.radians; + let t_raw = (q_angle - start) / sweep; + let full_rev = std::f64::consts::TAU / sweep.abs(); + // Try t_raw and ±one full revolution to handle angle wrapping + [t_raw, t_raw + full_rev, t_raw - full_rev] + .iter() + .map(|&t| arc.sample(t.clamp(0.0, 1.0))) + .map(|pt| (p - pt).length()) + .fold(f64::INFINITY, f64::min) } - } - - ctx.stroke().unwrap(); - - current_position = curve.to; - ctx.set_dash(&[0.1], 0.); - ctx.move_to(curve.from.x, curve.from.y); - ctx.curve_to( - curve.ctrl1.x, - curve.ctrl1.y, - curve.ctrl2.x, - curve.ctrl2.y, - curve.to.x, - curve.to.y, - ); - ctx.stroke().unwrap(); - acc += 1; - } - other => unimplemented!("{:?}", other), - } + ArcOrLineSegment::Line(line) => (line.closest_point(p) - p).length(), + }) + .fold(f64::INFINITY, f64::min) + }) + .fold(0.0_f64, f64::max) + } + + #[test] + fn flattened_arcs_within_hausdorff_tolerance() { + let curves: &[CubicBezierSegment] = &[ + // Quarter circle approximation + CubicBezierSegment { + from: point(1.0, 0.0), + ctrl1: point(1.0, KAPPA), + ctrl2: point(KAPPA, 1.0), + to: point(0.0, 1.0), + }, + // S-curve with inflection + CubicBezierSegment { + from: point(0.0, 0.0), + ctrl1: point(1.0, 0.0), + ctrl2: point(0.0, 1.0), + to: point(1.0, 1.0), + }, + // Highly asymmetric curve + CubicBezierSegment { + from: point(0.0, 0.0), + ctrl1: point(0.1, 1.0), + ctrl2: point(0.9, 1.0), + to: point(1.0, 0.0), + }, + // Near-straight curve + CubicBezierSegment { + from: point(0.0, 0.0), + ctrl1: point(0.33, 0.01), + ctrl2: point(0.66, 0.01), + to: point(1.0, 0.0), + }, + ]; + let tolerance = 0.002; + for (i, curve) in curves.iter().enumerate() { + let segments = FlattenWithArcs::flattened(curve, tolerance); + let dist = approx_max_bezier_deviation(curve, &segments, 1_000); + assert!( + dist < tolerance, + "curve {i}: Hausdorff distance {dist} exceeds tolerance {tolerance}" + ); } } } From 92dec902f7b968d6214f00e20c327ce624992210 Mon Sep 17 00:00:00 2001 From: Sameer Puri Date: Tue, 10 Mar 2026 20:22:52 -0700 Subject: [PATCH 3/5] Swap to inflection points --- lib/src/arc.rs | 21 +- lib/tests/circular_interpolation.gcode | 132 +- ...smooth_curves_circular_interpolation.gcode | 3543 ++++++++++------- ...urves_circular_interpolation_release.gcode | 2097 +++++----- 4 files changed, 3355 insertions(+), 2438 deletions(-) diff --git a/lib/src/arc.rs b/lib/src/arc.rs index 9c5f128..04ee6b8 100644 --- a/lib/src/arc.rs +++ b/lib/src/arc.rs @@ -87,8 +87,6 @@ where { /// Implementation of [Modeling of Bézier Curves Using a Combination of Linear and Circular Arc Approximations](https://sci-hub.st/https://doi.org/10.1109/CGIV.2012.20) /// - /// There are some slight deviations like using monotonic ranges instead of bounding by inflection points. - /// /// Kaewsaiha, P., & Dejdumrong, N. (2012). Modeling of Bézier Curves Using a Combination of Linear and Circular Arc Approximations. 2012 Ninth International Conference on Computer Graphics, Imaging and Visualization. doi:10.1109/cgiv.2012.20 fn flattened(&self, tolerance: S) -> Vec> { if (self.to - self.from).square_length() < S::EPSILON { @@ -98,14 +96,23 @@ where } let mut acc = vec![]; - self.for_each_monotonic_range(&mut |range| { - let inner_bezier = self.split_range(range); + let mut splits = Vec::with_capacity(4); + splits.push(S::ZERO); + self.for_each_inflection_t(&mut |t| { + if t > S::ZERO { + splits.push(t); + } + }); + splits.push(S::ONE); + + for window in splits.windows(2) { + let inner_bezier = self.split_range(window[0]..window[1]); if (inner_bezier.to - inner_bezier.from).square_length() < S::EPSILON { - return; + continue; } else if inner_bezier.is_linear(tolerance) { acc.push(ArcOrLineSegment::Line(inner_bezier.baseline())); - return; + continue; } if let Some(svg_arc) = arc_from_endpoints_and_tangents( @@ -132,7 +139,7 @@ where acc.append(&mut FlattenWithArcs::flattened(&left, tolerance)); acc.append(&mut FlattenWithArcs::flattened(&right, tolerance)); } - }); + } acc } } diff --git a/lib/tests/circular_interpolation.gcode b/lib/tests/circular_interpolation.gcode index d45060d..261c235 100644 --- a/lib/tests/circular_interpolation.gcode +++ b/lib/tests/circular_interpolation.gcode @@ -1,83 +1,73 @@ G21 G90;svg#svg8 > g#layer1 > path G0 X1 Y9 -G1 X1.108 Y8.888 F300 -G1 X1.215 Y8.769 F300 -G1 X1.321 Y8.644 F300 -G1 X1.424 Y8.514 F300 -G1 X1.524 Y8.379 F300 -G1 X1.619 Y8.24 F300 -G2 X1.794 Y7.956 R4.602 F300 -G2 X1.872 Y7.812 R4.042 F300 -G2 X1.942 Y7.668 R3.605 F300 -G2 X2.003 Y7.524 R3.153 F300 -G1 X2.031 Y7.453 F300 -G1 X2.055 Y7.382 F300 -G1 X2.078 Y7.312 F300 -G1 X2.098 Y7.242 F300 -G1 X2.115 Y7.173 F300 -G1 X2.129 Y7.106 F300 -G1 X2.14 Y7.039 F300 -G1 X2.148 Y6.973 F300 -G2 X2.155 Y6.845 R1.276 F300 -G2 X2.151 Y6.755 R1.074 F300 -G2 X2.14 Y6.669 R0.935 F300 -G2 X2.093 Y6.507 R0.784 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R3.266 F300 -G3 X60.872 Y9.152 R4.276 F300 -G1 X60.99 Y9.258 F300 -G1 X61.105 Y9.367 F300 -G1 X61.218 Y9.479 F300 -G1 X61.328 Y9.593 F300 -G1 X61.544 Y9.822 F300 +G3 X60.334 Y8.756 R2.375 F300 +G3 X60.575 Y8.915 R3.133 F300 +G3 X60.806 Y9.095 R3.99 F300 +G1 X60.917 Y9.192 F300 +G1 X61.026 Y9.292 F300 +G1 X61.133 Y9.394 F300 +G1 X61.237 Y9.499 F300 +G1 X61.34 Y9.605 F300 +G1 X61.441 Y9.712 F300 +G1 X61.639 Y9.925 F300 G1 X61.754 Y10.049 F300 G3 X63.606 Y12.287 R28.89 F300 -G3 X63.714 Y12.496 R0.657 F300 -G3 X63.748 Y12.73 R0.787 F300 -G3 X63.714 Y12.98 R0.963 F300 -G3 X63.618 Y13.216 R1.05 F300 -G3 X63.55 Y13.323 R1.003 F300 -G3 X63.47 Y13.417 R0.918 F300 -G3 X63.38 Y13.498 R0.813 F300 -G3 X63.28 Y13.563 R0.71 F300 +G3 X63.696 Y12.446 R0.648 F300 +G3 X63.741 Y12.621 R0.731 F300 +G3 X63.745 Y12.806 R0.864 F300 +G3 X63.711 Y12.99 R0.992 F300 +G3 X63.644 Y13.167 R1.053 F300 +G3 X63.547 Y13.327 R1.013 F300 +G3 X63.489 Y13.398 R0.927 F300 +G3 X63.425 Y13.462 R0.851 F300 +G3 X63.28 Y13.563 R0.733 F300 G0 X59.251 Y10.298 G1 X59.195 Y10.284 F300 G2 X59.251 Y10.298 R0.143 F300 G0 X59.288 Y10.298 G1 X59.288 Y10.298 F300 G1 X59.333 Y10.273 F300 -G1 X59.333 Y10.273 F300 G1 X59.288 Y10.292 F300 G1 X59.288 Y10.298 F300 From 7e95186ee01bb8a5617d41db0f74cbff59125ba2 Mon Sep 17 00:00:00 2001 From: Sameer Puri Date: Tue, 10 Mar 2026 21:27:57 -0700 Subject: [PATCH 4/5] Simplify arc_from_endpoints_and_tangents calculation --- lib/src/arc.rs | 48 +- lib/tests/circular_interpolation.gcode | 10 +- ...smooth_curves_circular_interpolation.gcode | 421 +++++++++--------- ...urves_circular_interpolation_release.gcode | 421 +++++++++--------- 4 files changed, 439 insertions(+), 461 deletions(-) diff --git a/lib/src/arc.rs b/lib/src/arc.rs index 04ee6b8..4b5ab13 100644 --- a/lib/src/arc.rs +++ b/lib/src/arc.rs @@ -14,42 +14,22 @@ fn arc_from_endpoints_and_tangents( to: Point, to_tangent: Vector, ) -> Option> { - let from_to = (from - to).length(); - let incenter = { - let from_tangent = Line { - point: from, - vector: from_tangent, - }; - let to_tangent = Line { - point: to, - vector: to_tangent, - }; - - let intersection = from_tangent.intersection(&to_tangent)?; - let from_intersection = (from - intersection).length(); - let to_intersection = (to - intersection).length(); - - (((from * to_intersection).to_vector() - + (to * from_intersection).to_vector() - + (intersection * from_to).to_vector()) - / (from_intersection + to_intersection + from_to)) - .to_point() - }; - - let get_perpendicular_bisector = |a, b| { - let vector: Vector = a - b; - let perpendicular_vector = Vector::from([-vector.y, vector.x]).normalize(); - Line { - point: LineSegment { from: a, to: b }.sample(S::HALF), - vector: perpendicular_vector, - } - }; - - let from_incenter_bisector = get_perpendicular_bisector(from, incenter); - let to_incenter_bisector = get_perpendicular_bisector(to, incenter); - let center = from_incenter_bisector.intersection(&to_incenter_bisector)?; + // The arc center must be perpendicular to the tangent at each endpoint. + // Intersect the two normal lines to find it. + let perp = |v: Vector| Vector::from([-v.y, v.x]); + let center = Line { + point: from, + vector: perp(from_tangent), + } + .intersection(&Line { + point: to, + vector: perp(to_tangent), + })?; let radius = (from - center).length(); + if radius < S::EPSILON { + return None; + } // Use the 2D determinant + dot product to identify winding direction // See https://www.w3.org/TR/SVG/paths.html#PathDataEllipticalArcCommands for diff --git a/lib/tests/circular_interpolation.gcode b/lib/tests/circular_interpolation.gcode index 261c235..da5d76d 100644 --- a/lib/tests/circular_interpolation.gcode +++ b/lib/tests/circular_interpolation.gcode @@ -7,7 +7,7 @@ G1 X1.279 Y8.695 F300 G1 X1.369 Y8.584 F300 G1 X1.457 Y8.469 F300 G1 X1.543 Y8.352 F300 -G2 X1.703 Y8.109 R4.886 F300 +G2 X1.703 Y8.109 R4.885 F300 G2 X1.846 Y7.861 R4.319 F300 G1 X1.909 Y7.736 F300 G1 X1.967 Y7.611 F300 @@ -84,7 +84,7 @@ G3 X3.475 Y3.96 R16.084 F300 G3 X3.678 Y3.973 R15.572 F300 G3 X3.878 Y3.989 R14.972 F300 G3 X4.075 Y4.007 R14.292 F300 -G3 X4.268 Y4.028 R13.545 F300 +G3 X4.268 Y4.028 R13.544 F300 G3 X4.456 Y4.051 R12.739 F300 G3 X4.639 Y4.076 R11.886 F300 G3 X4.818 Y4.103 R10.992 F300 @@ -121,7 +121,7 @@ G3 X6.735 Y5.141 R0.34 F300 G3 X6.702 Y5.192 R0.426 F300 G3 X6.659 Y5.244 R0.553 F300 G3 X6.606 Y5.295 R0.728 F300 -G3 X6.544 Y5.345 R0.956 F300 +G3 X6.544 Y5.345 R0.957 F300 G3 X6.508 Y5.369 R1.169 F300 G3 X6.471 Y5.394 R1.329 F300 G3 X6.431 Y5.418 R1.506 F300 @@ -203,7 +203,7 @@ G3 X4.652 Y2.298 R0.92 F300 G3 X4.708 Y2.232 R1.009 F300 G3 X4.771 Y2.169 R1.106 F300 G3 X4.841 Y2.109 R1.211 F300 -G3 X4.917 Y2.053 R1.331 F300 +G3 X4.917 Y2.053 R1.332 F300 G3 X4.999 Y2 R1.454 F300 G3 X5.107 Y1.942 R1.581 F300 G3 X5.222 Y1.891 R1.732 F300 @@ -216,6 +216,6 @@ G3 X6.278 Y1.762 R2.219 F300 G3 X6.411 Y1.782 R2.13 F300 G3 X6.54 Y1.811 R2.037 F300 G3 X6.664 Y1.848 R1.923 F300 -G3 X6.783 Y1.891 R1.793 F300 +G3 X6.783 Y1.891 R1.792 F300 G3 X6.896 Y1.943 R1.646 F300 G3 X7.001 Y2 R1.496 F300 diff --git a/lib/tests/smooth_curves_circular_interpolation.gcode b/lib/tests/smooth_curves_circular_interpolation.gcode index 86ac474..78eaf57 100644 --- a/lib/tests/smooth_curves_circular_interpolation.gcode +++ b/lib/tests/smooth_curves_circular_interpolation.gcode @@ -71,7 +71,7 @@ G3 X43.934 Y32.548 R8.62 F300 G3 X44.884 Y32.421 R8.241 F300 G3 X45.36 Y32.399 R7.831 F300 G3 X45.836 Y32.408 R7.515 F300 -G3 X46.774 Y32.517 R7.019 F300 +G3 X46.774 Y32.517 R7.018 F300 G3 X47.683 Y32.755 R6.403 F300 G3 X47.938 Y32.852 R4.832 F300 G3 X48.182 Y32.96 R4.58 F300 @@ -131,11 +131,11 @@ G1 X50.759 Y53.492 F300 G1 X50.877 Y53.975 F300 G1 X50.877 Y53.975 F300 G3 X53.205 Y53.504 R8.903 F300 -G3 X53.837 Y53.487 R5.988 F300 +G3 X53.837 Y53.487 R5.987 F300 G3 X54.465 Y53.537 R5.712 F300 G3 X55.079 Y53.658 R5.329 F300 G3 X55.668 Y53.85 R4.903 F300 -G3 X56.737 Y54.461 R4.33 F300 +G3 X56.737 Y54.461 R4.328 F300 G3 X56.974 Y54.662 R4.006 F300 G3 X57.196 Y54.883 R3.945 F300 G3 X57.402 Y55.124 R3.929 F300 @@ -166,7 +166,7 @@ G3 X48.104 Y71.456 R5.384 F300 G1 X47.953 Y71.435 F300 G1 X47.798 Y71.407 F300 G1 X47.64 Y71.372 F300 -G3 X47.482 Y71.331 R4.042 F300 +G3 X47.482 Y71.331 R4.041 F300 G3 X47.168 Y71.227 R3.66 F300 G3 X46.868 Y71.094 R3.025 F300 G3 X46.726 Y71.015 R2.537 F300 @@ -202,7 +202,7 @@ G3 X40.89 Y67.412 R4.041 F300 G3 X40.736 Y67.128 R4.067 F300 G3 X40.606 Y66.835 R4.139 F300 G3 X40.499 Y66.535 R4.253 F300 -G3 X40.291 Y65.286 R4.679 F300 +G3 X40.291 Y65.286 R4.682 F300 G3 X40.308 Y64.648 R5.326 F300 G3 X40.4 Y64.013 R5.739 F300 G3 X40.56 Y63.391 R6.049 F300 @@ -250,24 +250,24 @@ G1 X40.253 Y53.836 F300 G1 X40.189 Y53.629 F300 G1 X40.129 Y53.421 F300 G1 X40.071 Y53.212 F300 -G3 X39.876 Y52.366 R13.836 F300 -G3 X39.635 Y50.647 R15.762 F300 +G3 X39.876 Y52.366 R13.837 F300 +G3 X39.635 Y50.647 R15.764 F300 G1 X39.635 Y50.647 F300 G1 X38.841 Y50.71 F300 G1 X38.048 Y50.77 F300 G3 X36.464 Y50.875 R139.951 F300 G3 X34.881 Y50.962 R139.138 F300 G3 X33.3 Y51.03 R138.382 F300 -G2 X32.787 Y51.054 R54.71 F300 -G3 X32.202 Y51.08 R48.899 F300 -G3 X31.615 Y51.092 R16.285 F300 +G2 X32.787 Y51.054 R54.711 F300 +G3 X32.202 Y51.08 R48.898 F300 +G3 X31.615 Y51.092 R16.284 F300 G3 X31.03 Y51.076 R9.684 F300 -G3 X30.448 Y51.017 R6.869 F300 +G3 X30.448 Y51.017 R6.868 F300 G1 X30.403 Y51.017 F300 G3 X30.388 Y51.464 R6.463 F300 G3 X30.342 Y51.905 R6.52 F300 G3 X30.165 Y52.765 R6.694 F300 -G3 X29.499 Y54.378 R7.272 F300 +G3 X29.499 Y54.378 R7.274 F300 G1 X29.39 Y54.568 F300 G1 X29.275 Y54.755 F300 G1 X29.155 Y54.938 F300 @@ -298,7 +298,7 @@ G1 X20.124 Y61.999 F300 G1 X19.974 Y62.135 F300 G1 X19.897 Y62.202 F300 G1 X19.819 Y62.267 F300 -G3 X19.497 Y62.512 R5.286 F300 +G3 X19.497 Y62.512 R5.285 F300 G3 X19.328 Y62.625 R4.69 F300 G3 X19.153 Y62.73 R4.401 F300 G3 X18.973 Y62.828 R4.185 F300 @@ -306,9 +306,9 @@ G3 X18.785 Y62.918 R4.032 F300 G3 X18.542 Y62.987 R0.82 F300 G3 X17.955 Y62.857 R0.627 F300 G3 X17.494 Y61.108 R1.68 F300 -G3 X17.665 Y60.686 R2.366 F300 -G3 X17.902 Y60.297 R3.36 F300 -G3 X18.183 Y59.931 R5.811 F300 +G3 X17.665 Y60.686 R2.367 F300 +G3 X17.902 Y60.297 R3.361 F300 +G3 X18.183 Y59.931 R5.812 F300 G1 X18.332 Y59.755 F300 G1 X18.482 Y59.582 F300 G1 X18.597 Y59.45 F300 @@ -330,13 +330,13 @@ G1 X20.516 Y56.626 F300 G1 X20.507 Y56.59 F300 G1 X20.444 Y56.33 F300 G1 X20.385 Y56.07 F300 -G3 X20.288 Y55.547 R7.547 F300 +G3 X20.288 Y55.547 R7.546 F300 G3 X20.206 Y54.535 R8.749 F300 G3 X20.242 Y53.522 R8.707 F300 G3 X20.395 Y52.524 R8.499 F300 G3 X20.667 Y51.555 R8.161 F300 -G3 X21.057 Y50.631 R7.752 F300 -G3 X21.297 Y50.19 R7.441 F300 +G3 X21.057 Y50.631 R7.751 F300 +G3 X21.297 Y50.19 R7.44 F300 G1 X21.362 Y50.083 F300 G1 X21.428 Y49.976 F300 G1 X21.497 Y49.871 F300 @@ -399,10 +399,10 @@ G1 X18.015 Y40.915 F300 G3 X17.917 Y40.523 R10.586 F300 G3 X17.767 Y39.73 R10.407 F300 G3 X17.68 Y38.929 R10.115 F300 -G3 X17.703 Y37.325 R9.597 F300 +G3 X17.703 Y37.325 R9.596 F300 G3 X17.841 Y36.461 R7.312 F300 G3 X18.082 Y35.62 R7.067 F300 -G3 X18.426 Y34.821 R6.563 F300 +G3 X18.426 Y34.821 R6.562 F300 G3 X18.637 Y34.443 R6.096 F300 G1 X18.693 Y34.352 F300 G1 X18.752 Y34.261 F300 @@ -413,7 +413,7 @@ G1 X19.001 Y33.912 F300 G3 X19.135 Y33.746 R5.377 F300 G3 X19.422 Y33.43 R5.162 F300 G3 X19.735 Y33.141 R4.912 F300 -G3 X20.074 Y32.879 R4.715 F300 +G3 X20.074 Y32.879 R4.714 F300 G3 X20.252 Y32.76 R4.605 F300 G3 X20.437 Y32.648 R4.555 F300 G3 X20.629 Y32.545 R4.524 F300 @@ -472,15 +472,15 @@ G2 X47.44 Y33.979 R3.831 F300 G2 X47.072 Y33.846 R4.238 F300 G2 X46.691 Y33.746 R4.607 F300 G2 X46.3 Y33.677 R5.037 F300 -G2 X45.901 Y33.638 R5.509 F300 +G2 X45.901 Y33.638 R5.51 F300 G2 X45.497 Y33.626 R6.005 F300 G2 X45.09 Y33.64 R6.498 F300 -G2 X44.278 Y33.743 R7.156 F300 +G2 X44.278 Y33.743 R7.157 F300 G2 X43.878 Y33.827 R7.671 F300 G2 X43.486 Y33.931 R7.857 F300 G2 X43.104 Y34.055 R7.896 F300 G2 X42.734 Y34.195 R7.772 F300 -G2 X42.379 Y34.351 R7.479 F300 +G2 X42.379 Y34.351 R7.478 F300 G1 X42.208 Y34.434 F300 G1 X42.042 Y34.52 F300 G2 X38.486 Y39.497 R6.996 F300 @@ -495,13 +495,13 @@ G2 X39.585 Y44.305 R2.857 F300 G2 X39.724 Y44.434 R2.574 F300 G2 X39.871 Y44.552 R2.318 F300 G2 X40.19 Y44.743 R2 F300 -G2 X40.541 Y44.867 R1.731 F300 +G2 X40.541 Y44.867 R1.73 F300 G2 X40.728 Y44.9 R1.652 F300 G1 X40.825 Y44.908 F300 G1 X40.923 Y44.91 F300 G3 X41.452 Y45.223 R0.561 F300 G1 X41.484 Y45.204 F300 -G3 X41.603 Y45.138 R2.063 F300 +G3 X41.603 Y45.138 R2.062 F300 G3 X43.114 Y44.786 R4.035 F300 G3 X43.217 Y44.659 R0.429 F300 G2 X47.485 Y36.547 R11.454 F300 @@ -515,7 +515,7 @@ G3 X47.915 Y35.989 R0.662 F300 G3 X48.146 Y35.952 R0.731 F300 G3 X48.262 Y35.961 R0.713 F300 G3 X48.372 Y35.989 R0.66 F300 -G3 X48.564 Y36.1 R0.56 F300 +G3 X48.564 Y36.1 R0.559 F300 G3 X48.638 Y36.184 R0.491 F300 G3 X48.668 Y36.233 R0.485 F300 G3 X48.692 Y36.286 R0.497 F300 @@ -538,7 +538,7 @@ G1 X57.206 Y57.51 F300 G2 X57.156 Y57.469 R0.168 F300 G2 X57.126 Y57.457 R0.143 F300 G2 X57.092 Y57.452 R0.157 F300 -G2 X57.054 Y57.454 R0.197 F300 +G2 X57.054 Y57.454 R0.198 F300 G2 X57.012 Y57.464 R0.274 F300 G1 X56.966 Y57.483 F300 G1 X56.915 Y57.51 F300 @@ -567,27 +567,27 @@ G3 X55.355 Y58.364 R1.498 F300 G3 X55.325 Y58.205 R1.474 F300 G3 X55.313 Y58.046 R1.481 F300 G3 X55.318 Y57.889 R1.514 F300 -G3 X55.374 Y57.58 R1.601 F300 +G3 X55.374 Y57.58 R1.602 F300 G3 X55.488 Y57.286 R1.758 F300 G3 X55.652 Y57.013 R1.918 F300 G3 X55.859 Y56.768 R2.033 F300 G3 X56.377 Y56.388 R2.04 F300 G3 X56.571 Y56.303 R1.381 F300 -G2 X56.483 Y56.039 R3.097 F300 +G2 X56.483 Y56.039 R3.099 F300 G3 X56.433 Y55.92 R0.394 F300 G2 X56.31 Y55.765 R2.487 F300 G2 X56.177 Y55.623 R2.524 F300 -G2 X55.883 Y55.372 R2.64 F300 +G2 X55.883 Y55.372 R2.641 F300 G2 X55.558 Y55.165 R2.887 F300 -G2 X55.208 Y55 R3.217 F300 -G2 X54.457 Y54.789 R3.779 F300 +G2 X55.208 Y55 R3.218 F300 +G2 X54.457 Y54.789 R3.78 F300 G2 X54.069 Y54.739 R4.31 F300 G2 X53.681 Y54.724 R4.526 F300 G2 X51.689 Y55.033 R7.705 F300 -G2 X51.249 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Y9.665 F300 @@ -2035,10 +2034,10 @@ G3 X48.163 Y2.839 R0.858 F300 G3 X48.184 Y2.749 R0.828 F300 G3 X48.213 Y2.665 R0.818 F300 G3 X48.296 Y2.51 R0.832 F300 -G3 X48.541 Y2.268 R0.926 F300 -G3 X48.857 Y2.123 R1.06 F300 +G3 X48.541 Y2.268 R0.927 F300 +G3 X48.857 Y2.123 R1.061 F300 G3 X49.201 Y2.086 R1.047 F300 -G3 X49.532 Y2.17 R0.896 F300 +G3 X49.532 Y2.17 R0.895 F300 G3 X49.679 Y2.261 R0.8 F300 G3 X49.745 Y2.319 R0.788 F300 G3 X49.806 Y2.387 R0.801 F300 @@ -2061,8 +2060,8 @@ G1 X53.013 Y5.896 F300 G1 X53.145 Y5.935 F300 G1 X53.276 Y5.977 F300 G1 X53.271 Y5.887 F300 -G3 X53.189 Y4.317 R75.356 F300 -G3 X53.173 Y2.744 R25.13 F300 +G3 X53.189 Y4.317 R75.353 F300 +G3 X53.173 Y2.744 R25.127 F300 G3 X53.181 Y2.635 R1.093 F300 G3 X53.199 Y2.533 R0.991 F300 G3 X53.226 Y2.438 R0.917 F300 @@ -2070,10 +2069,10 @@ G3 X53.262 Y2.35 R0.868 F300 G3 X53.306 Y2.269 R0.84 F300 G3 X53.357 Y2.195 R0.831 F300 G3 X53.479 Y2.069 R0.847 F300 -G3 X53.781 Y1.9 R0.939 F300 -G3 X54.124 Y1.843 R1.061 F300 +G3 X53.781 Y1.9 R0.94 F300 +G3 X54.124 Y1.843 R1.062 F300 G3 X54.464 Y1.899 R1.031 F300 -G3 X54.756 Y2.067 R0.871 F300 +G3 X54.756 Y2.067 R0.87 F300 G3 X54.871 Y2.194 R0.777 F300 G3 X54.919 Y2.268 R0.768 F300 G3 X54.958 Y2.349 R0.785 F300 @@ -2082,15 +2081,15 @@ G3 X55.011 Y2.532 R0.884 F300 G3 X55.024 Y2.634 R0.973 F300 G1 X55.026 Y2.688 F300 G1 X55.025 Y2.744 F300 -G2 X55.045 Y4.367 R26.259 F300 -G2 X55.131 Y5.989 R78.801 F300 -G3 X55.189 Y7.001 R126.832 F300 -G3 X55.231 Y8.102 R38.126 F300 -G3 X55.229 Y9.205 R21.901 F300 +G2 X55.045 Y4.367 R26.262 F300 +G2 X55.131 Y5.989 R78.803 F300 +G3 X55.189 Y7.001 R126.831 F300 +G3 X55.231 Y8.102 R38.125 F300 +G3 X55.229 Y9.205 R21.9 F300 G1 X55.223 Y9.463 F300 -G3 X55.21 Y9.723 R7.917 F300 -G3 X55.149 Y10.24 R4.771 F300 -G3 X55.018 Y10.739 R2.985 F300 +G3 X55.21 Y9.723 R7.916 F300 +G3 X55.149 Y10.24 R4.77 F300 +G3 X55.018 Y10.739 R2.984 F300 G3 X54.917 Y10.975 R2.317 F300 G3 X54.787 Y11.2 R2.073 F300 G0 X52.602 Y7.07 @@ -2114,7 +2113,7 @@ G1 X52.083 Y9.059 F300 G2 X52.557 Y9.962 R6.81 F300 G1 X52.614 Y10.041 F300 G1 X52.719 Y10.179 F300 -G2 X52.846 Y10.334 R5.083 F300 +G2 X52.846 Y10.334 R5.082 F300 G1 X52.909 Y10.406 F300 G1 X52.967 Y10.467 F300 G1 X53.076 Y10.362 F300 @@ -2138,7 +2137,7 @@ G1 X60.164 Y11.08 F300 G1 X59.959 Y10.868 F300 G1 X59.854 Y10.764 F300 G1 X59.748 Y10.66 F300 -G2 X59.633 Y10.55 R4.239 F300 +G2 X59.633 Y10.55 R4.24 F300 G1 X59.552 Y10.475 F300 G3 X59.507 Y10.425 R0.368 F300 G1 X59.457 Y10.398 F300 @@ -2169,18 +2168,18 @@ G3 X56.777 Y13.824 R0.935 F300 G3 X56.777 Y12.501 R0.935 F300 G1 X56.79 Y12.486 F300 G1 X56.79 Y12.486 F300 -G2 X56.838 Y12.308 R1.954 F300 +G2 X56.838 Y12.308 R1.953 F300 G1 X56.855 Y12.22 F300 G1 X56.862 Y12.181 F300 G1 X56.862 Y12.16 F300 -G3 X56.88 Y11.97 R1.303 F300 +G3 X56.88 Y11.97 R1.305 F300 G1 X56.893 Y11.874 F300 G3 X57.176 Y10.327 R11.377 F300 G3 X57.97 Y8.935 R3 F300 G3 X57.415 Y3.405 R27.781 F300 G3 X59.267 Y3.405 R0.931 F300 G2 X59.809 Y8.522 R24.585 F300 -G3 X60.334 Y8.756 R2.375 F300 +G3 X60.334 Y8.756 R2.376 F300 G3 X60.575 Y8.915 R3.133 F300 G3 X60.806 Y9.095 R3.99 F300 G1 X60.917 Y9.192 F300 @@ -2193,8 +2192,8 @@ G1 X61.639 Y9.925 F300 G1 X61.754 Y10.049 F300 G3 X63.606 Y12.287 R28.89 F300 G3 X63.696 Y12.446 R0.648 F300 -G3 X63.741 Y12.621 R0.731 F300 -G3 X63.745 Y12.806 R0.864 F300 +G3 X63.741 Y12.621 R0.732 F300 +G3 X63.745 Y12.806 R0.865 F300 G3 X63.711 Y12.99 R0.992 F300 G3 X63.644 Y13.167 R1.053 F300 G3 X63.547 Y13.327 R1.013 F300 diff --git a/lib/tests/smooth_curves_circular_interpolation_release.gcode b/lib/tests/smooth_curves_circular_interpolation_release.gcode index 86ac474..78eaf57 100644 --- a/lib/tests/smooth_curves_circular_interpolation_release.gcode +++ b/lib/tests/smooth_curves_circular_interpolation_release.gcode @@ -71,7 +71,7 @@ G3 X43.934 Y32.548 R8.62 F300 G3 X44.884 Y32.421 R8.241 F300 G3 X45.36 Y32.399 R7.831 F300 G3 X45.836 Y32.408 R7.515 F300 -G3 X46.774 Y32.517 R7.019 F300 +G3 X46.774 Y32.517 R7.018 F300 G3 X47.683 Y32.755 R6.403 F300 G3 X47.938 Y32.852 R4.832 F300 G3 X48.182 Y32.96 R4.58 F300 @@ -131,11 +131,11 @@ G1 X50.759 Y53.492 F300 G1 X50.877 Y53.975 F300 G1 X50.877 Y53.975 F300 G3 X53.205 Y53.504 R8.903 F300 -G3 X53.837 Y53.487 R5.988 F300 +G3 X53.837 Y53.487 R5.987 F300 G3 X54.465 Y53.537 R5.712 F300 G3 X55.079 Y53.658 R5.329 F300 G3 X55.668 Y53.85 R4.903 F300 -G3 X56.737 Y54.461 R4.33 F300 +G3 X56.737 Y54.461 R4.328 F300 G3 X56.974 Y54.662 R4.006 F300 G3 X57.196 Y54.883 R3.945 F300 G3 X57.402 Y55.124 R3.929 F300 @@ -166,7 +166,7 @@ G3 X48.104 Y71.456 R5.384 F300 G1 X47.953 Y71.435 F300 G1 X47.798 Y71.407 F300 G1 X47.64 Y71.372 F300 -G3 X47.482 Y71.331 R4.042 F300 +G3 X47.482 Y71.331 R4.041 F300 G3 X47.168 Y71.227 R3.66 F300 G3 X46.868 Y71.094 R3.025 F300 G3 X46.726 Y71.015 R2.537 F300 @@ -202,7 +202,7 @@ G3 X40.89 Y67.412 R4.041 F300 G3 X40.736 Y67.128 R4.067 F300 G3 X40.606 Y66.835 R4.139 F300 G3 X40.499 Y66.535 R4.253 F300 -G3 X40.291 Y65.286 R4.679 F300 +G3 X40.291 Y65.286 R4.682 F300 G3 X40.308 Y64.648 R5.326 F300 G3 X40.4 Y64.013 R5.739 F300 G3 X40.56 Y63.391 R6.049 F300 @@ -250,24 +250,24 @@ G1 X40.253 Y53.836 F300 G1 X40.189 Y53.629 F300 G1 X40.129 Y53.421 F300 G1 X40.071 Y53.212 F300 -G3 X39.876 Y52.366 R13.836 F300 -G3 X39.635 Y50.647 R15.762 F300 +G3 X39.876 Y52.366 R13.837 F300 +G3 X39.635 Y50.647 R15.764 F300 G1 X39.635 Y50.647 F300 G1 X38.841 Y50.71 F300 G1 X38.048 Y50.77 F300 G3 X36.464 Y50.875 R139.951 F300 G3 X34.881 Y50.962 R139.138 F300 G3 X33.3 Y51.03 R138.382 F300 -G2 X32.787 Y51.054 R54.71 F300 -G3 X32.202 Y51.08 R48.899 F300 -G3 X31.615 Y51.092 R16.285 F300 +G2 X32.787 Y51.054 R54.711 F300 +G3 X32.202 Y51.08 R48.898 F300 +G3 X31.615 Y51.092 R16.284 F300 G3 X31.03 Y51.076 R9.684 F300 -G3 X30.448 Y51.017 R6.869 F300 +G3 X30.448 Y51.017 R6.868 F300 G1 X30.403 Y51.017 F300 G3 X30.388 Y51.464 R6.463 F300 G3 X30.342 Y51.905 R6.52 F300 G3 X30.165 Y52.765 R6.694 F300 -G3 X29.499 Y54.378 R7.272 F300 +G3 X29.499 Y54.378 R7.274 F300 G1 X29.39 Y54.568 F300 G1 X29.275 Y54.755 F300 G1 X29.155 Y54.938 F300 @@ -298,7 +298,7 @@ G1 X20.124 Y61.999 F300 G1 X19.974 Y62.135 F300 G1 X19.897 Y62.202 F300 G1 X19.819 Y62.267 F300 -G3 X19.497 Y62.512 R5.286 F300 +G3 X19.497 Y62.512 R5.285 F300 G3 X19.328 Y62.625 R4.69 F300 G3 X19.153 Y62.73 R4.401 F300 G3 X18.973 Y62.828 R4.185 F300 @@ -306,9 +306,9 @@ G3 X18.785 Y62.918 R4.032 F300 G3 X18.542 Y62.987 R0.82 F300 G3 X17.955 Y62.857 R0.627 F300 G3 X17.494 Y61.108 R1.68 F300 -G3 X17.665 Y60.686 R2.366 F300 -G3 X17.902 Y60.297 R3.36 F300 -G3 X18.183 Y59.931 R5.811 F300 +G3 X17.665 Y60.686 R2.367 F300 +G3 X17.902 Y60.297 R3.361 F300 +G3 X18.183 Y59.931 R5.812 F300 G1 X18.332 Y59.755 F300 G1 X18.482 Y59.582 F300 G1 X18.597 Y59.45 F300 @@ -330,13 +330,13 @@ G1 X20.516 Y56.626 F300 G1 X20.507 Y56.59 F300 G1 X20.444 Y56.33 F300 G1 X20.385 Y56.07 F300 -G3 X20.288 Y55.547 R7.547 F300 +G3 X20.288 Y55.547 R7.546 F300 G3 X20.206 Y54.535 R8.749 F300 G3 X20.242 Y53.522 R8.707 F300 G3 X20.395 Y52.524 R8.499 F300 G3 X20.667 Y51.555 R8.161 F300 -G3 X21.057 Y50.631 R7.752 F300 -G3 X21.297 Y50.19 R7.441 F300 +G3 X21.057 Y50.631 R7.751 F300 +G3 X21.297 Y50.19 R7.44 F300 G1 X21.362 Y50.083 F300 G1 X21.428 Y49.976 F300 G1 X21.497 Y49.871 F300 @@ -399,10 +399,10 @@ G1 X18.015 Y40.915 F300 G3 X17.917 Y40.523 R10.586 F300 G3 X17.767 Y39.73 R10.407 F300 G3 X17.68 Y38.929 R10.115 F300 -G3 X17.703 Y37.325 R9.597 F300 +G3 X17.703 Y37.325 R9.596 F300 G3 X17.841 Y36.461 R7.312 F300 G3 X18.082 Y35.62 R7.067 F300 -G3 X18.426 Y34.821 R6.563 F300 +G3 X18.426 Y34.821 R6.562 F300 G3 X18.637 Y34.443 R6.096 F300 G1 X18.693 Y34.352 F300 G1 X18.752 Y34.261 F300 @@ -413,7 +413,7 @@ G1 X19.001 Y33.912 F300 G3 X19.135 Y33.746 R5.377 F300 G3 X19.422 Y33.43 R5.162 F300 G3 X19.735 Y33.141 R4.912 F300 -G3 X20.074 Y32.879 R4.715 F300 +G3 X20.074 Y32.879 R4.714 F300 G3 X20.252 Y32.76 R4.605 F300 G3 X20.437 Y32.648 R4.555 F300 G3 X20.629 Y32.545 R4.524 F300 @@ -472,15 +472,15 @@ G2 X47.44 Y33.979 R3.831 F300 G2 X47.072 Y33.846 R4.238 F300 G2 X46.691 Y33.746 R4.607 F300 G2 X46.3 Y33.677 R5.037 F300 -G2 X45.901 Y33.638 R5.509 F300 +G2 X45.901 Y33.638 R5.51 F300 G2 X45.497 Y33.626 R6.005 F300 G2 X45.09 Y33.64 R6.498 F300 -G2 X44.278 Y33.743 R7.156 F300 +G2 X44.278 Y33.743 R7.157 F300 G2 X43.878 Y33.827 R7.671 F300 G2 X43.486 Y33.931 R7.857 F300 G2 X43.104 Y34.055 R7.896 F300 G2 X42.734 Y34.195 R7.772 F300 -G2 X42.379 Y34.351 R7.479 F300 +G2 X42.379 Y34.351 R7.478 F300 G1 X42.208 Y34.434 F300 G1 X42.042 Y34.52 F300 G2 X38.486 Y39.497 R6.996 F300 @@ -495,13 +495,13 @@ G2 X39.585 Y44.305 R2.857 F300 G2 X39.724 Y44.434 R2.574 F300 G2 X39.871 Y44.552 R2.318 F300 G2 X40.19 Y44.743 R2 F300 -G2 X40.541 Y44.867 R1.731 F300 +G2 X40.541 Y44.867 R1.73 F300 G2 X40.728 Y44.9 R1.652 F300 G1 X40.825 Y44.908 F300 G1 X40.923 Y44.91 F300 G3 X41.452 Y45.223 R0.561 F300 G1 X41.484 Y45.204 F300 -G3 X41.603 Y45.138 R2.063 F300 +G3 X41.603 Y45.138 R2.062 F300 G3 X43.114 Y44.786 R4.035 F300 G3 X43.217 Y44.659 R0.429 F300 G2 X47.485 Y36.547 R11.454 F300 @@ -515,7 +515,7 @@ G3 X47.915 Y35.989 R0.662 F300 G3 X48.146 Y35.952 R0.731 F300 G3 X48.262 Y35.961 R0.713 F300 G3 X48.372 Y35.989 R0.66 F300 -G3 X48.564 Y36.1 R0.56 F300 +G3 X48.564 Y36.1 R0.559 F300 G3 X48.638 Y36.184 R0.491 F300 G3 X48.668 Y36.233 R0.485 F300 G3 X48.692 Y36.286 R0.497 F300 @@ -538,7 +538,7 @@ G1 X57.206 Y57.51 F300 G2 X57.156 Y57.469 R0.168 F300 G2 X57.126 Y57.457 R0.143 F300 G2 X57.092 Y57.452 R0.157 F300 -G2 X57.054 Y57.454 R0.197 F300 +G2 X57.054 Y57.454 R0.198 F300 G2 X57.012 Y57.464 R0.274 F300 G1 X56.966 Y57.483 F300 G1 X56.915 Y57.51 F300 @@ -567,27 +567,27 @@ G3 X55.355 Y58.364 R1.498 F300 G3 X55.325 Y58.205 R1.474 F300 G3 X55.313 Y58.046 R1.481 F300 G3 X55.318 Y57.889 R1.514 F300 -G3 X55.374 Y57.58 R1.601 F300 +G3 X55.374 Y57.58 R1.602 F300 G3 X55.488 Y57.286 R1.758 F300 G3 X55.652 Y57.013 R1.918 F300 G3 X55.859 Y56.768 R2.033 F300 G3 X56.377 Y56.388 R2.04 F300 G3 X56.571 Y56.303 R1.381 F300 -G2 X56.483 Y56.039 R3.097 F300 +G2 X56.483 Y56.039 R3.099 F300 G3 X56.433 Y55.92 R0.394 F300 G2 X56.31 Y55.765 R2.487 F300 G2 X56.177 Y55.623 R2.524 F300 -G2 X55.883 Y55.372 R2.64 F300 +G2 X55.883 Y55.372 R2.641 F300 G2 X55.558 Y55.165 R2.887 F300 -G2 X55.208 Y55 R3.217 F300 -G2 X54.457 Y54.789 R3.779 F300 +G2 X55.208 Y55 R3.218 F300 +G2 X54.457 Y54.789 R3.78 F300 G2 X54.069 Y54.739 R4.31 F300 G2 X53.681 Y54.724 R4.526 F300 G2 X51.689 Y55.033 R7.705 F300 -G2 X51.249 Y55.165 R9.175 F300 -G2 X50.828 Y55.328 R4.186 F300 -G2 X50.436 Y55.545 R2.688 F300 -G2 X50.255 Y55.682 R2.209 F300 +G2 X51.249 Y55.165 R9.174 F300 +G2 X50.828 Y55.328 R4.185 F300 +G2 X50.436 Y55.545 R2.687 F300 +G2 X50.255 Y55.682 R2.208 F300 G2 X50.086 Y55.84 R2.081 F300 G2 X49.117 Y57.391 R6.437 F300 G2 X48.437 Y59.214 R7.464 F300 @@ -598,11 +598,11 @@ G2 X55.316 Y61.746 R9.305 F300 G1 X55.425 Y61.643 F300 G1 X55.535 Y61.537 F300 G2 X55.754 Y61.317 R9.624 F300 -G2 X56.169 Y60.843 R6.267 F300 +G2 X56.169 Y60.843 R6.265 F300 G2 X56.354 Y60.589 R4.388 F300 G2 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F300 -G3 X53.189 Y4.317 R75.356 F300 -G3 X53.173 Y2.744 R25.13 F300 +G3 X53.189 Y4.317 R75.353 F300 +G3 X53.173 Y2.744 R25.127 F300 G3 X53.181 Y2.635 R1.093 F300 G3 X53.199 Y2.533 R0.991 F300 G3 X53.226 Y2.438 R0.917 F300 @@ -2070,10 +2069,10 @@ G3 X53.262 Y2.35 R0.868 F300 G3 X53.306 Y2.269 R0.84 F300 G3 X53.357 Y2.195 R0.831 F300 G3 X53.479 Y2.069 R0.847 F300 -G3 X53.781 Y1.9 R0.939 F300 -G3 X54.124 Y1.843 R1.061 F300 +G3 X53.781 Y1.9 R0.94 F300 +G3 X54.124 Y1.843 R1.062 F300 G3 X54.464 Y1.899 R1.031 F300 -G3 X54.756 Y2.067 R0.871 F300 +G3 X54.756 Y2.067 R0.87 F300 G3 X54.871 Y2.194 R0.777 F300 G3 X54.919 Y2.268 R0.768 F300 G3 X54.958 Y2.349 R0.785 F300 @@ -2082,15 +2081,15 @@ G3 X55.011 Y2.532 R0.884 F300 G3 X55.024 Y2.634 R0.973 F300 G1 X55.026 Y2.688 F300 G1 X55.025 Y2.744 F300 -G2 X55.045 Y4.367 R26.259 F300 -G2 X55.131 Y5.989 R78.801 F300 -G3 X55.189 Y7.001 R126.832 F300 -G3 X55.231 Y8.102 R38.126 F300 -G3 X55.229 Y9.205 R21.901 F300 +G2 X55.045 Y4.367 R26.262 F300 +G2 X55.131 Y5.989 R78.803 F300 +G3 X55.189 Y7.001 R126.831 F300 +G3 X55.231 Y8.102 R38.125 F300 +G3 X55.229 Y9.205 R21.9 F300 G1 X55.223 Y9.463 F300 -G3 X55.21 Y9.723 R7.917 F300 -G3 X55.149 Y10.24 R4.771 F300 -G3 X55.018 Y10.739 R2.985 F300 +G3 X55.21 Y9.723 R7.916 F300 +G3 X55.149 Y10.24 R4.77 F300 +G3 X55.018 Y10.739 R2.984 F300 G3 X54.917 Y10.975 R2.317 F300 G3 X54.787 Y11.2 R2.073 F300 G0 X52.602 Y7.07 @@ -2114,7 +2113,7 @@ G1 X52.083 Y9.059 F300 G2 X52.557 Y9.962 R6.81 F300 G1 X52.614 Y10.041 F300 G1 X52.719 Y10.179 F300 -G2 X52.846 Y10.334 R5.083 F300 +G2 X52.846 Y10.334 R5.082 F300 G1 X52.909 Y10.406 F300 G1 X52.967 Y10.467 F300 G1 X53.076 Y10.362 F300 @@ -2138,7 +2137,7 @@ G1 X60.164 Y11.08 F300 G1 X59.959 Y10.868 F300 G1 X59.854 Y10.764 F300 G1 X59.748 Y10.66 F300 -G2 X59.633 Y10.55 R4.239 F300 +G2 X59.633 Y10.55 R4.24 F300 G1 X59.552 Y10.475 F300 G3 X59.507 Y10.425 R0.368 F300 G1 X59.457 Y10.398 F300 @@ -2169,18 +2168,18 @@ G3 X56.777 Y13.824 R0.935 F300 G3 X56.777 Y12.501 R0.935 F300 G1 X56.79 Y12.486 F300 G1 X56.79 Y12.486 F300 -G2 X56.838 Y12.308 R1.954 F300 +G2 X56.838 Y12.308 R1.953 F300 G1 X56.855 Y12.22 F300 G1 X56.862 Y12.181 F300 G1 X56.862 Y12.16 F300 -G3 X56.88 Y11.97 R1.303 F300 +G3 X56.88 Y11.97 R1.305 F300 G1 X56.893 Y11.874 F300 G3 X57.176 Y10.327 R11.377 F300 G3 X57.97 Y8.935 R3 F300 G3 X57.415 Y3.405 R27.781 F300 G3 X59.267 Y3.405 R0.931 F300 G2 X59.809 Y8.522 R24.585 F300 -G3 X60.334 Y8.756 R2.375 F300 +G3 X60.334 Y8.756 R2.376 F300 G3 X60.575 Y8.915 R3.133 F300 G3 X60.806 Y9.095 R3.99 F300 G1 X60.917 Y9.192 F300 @@ -2193,8 +2192,8 @@ G1 X61.639 Y9.925 F300 G1 X61.754 Y10.049 F300 G3 X63.606 Y12.287 R28.89 F300 G3 X63.696 Y12.446 R0.648 F300 -G3 X63.741 Y12.621 R0.731 F300 -G3 X63.745 Y12.806 R0.864 F300 +G3 X63.741 Y12.621 R0.732 F300 +G3 X63.745 Y12.806 R0.865 F300 G3 X63.711 Y12.99 R0.992 F300 G3 X63.644 Y13.167 R1.053 F300 G3 X63.547 Y13.327 R1.013 F300 From e145937d7e8a5860856b3c0c431fdbaca7f2308f Mon Sep 17 00:00:00 2001 From: Sameer Puri Date: Tue, 10 Mar 2026 21:53:19 -0700 Subject: [PATCH 5/5] Use geometric distance to arc instead of equal t sampling --- lib/src/arc.rs | 22 +- lib/tests/circular_interpolation.gcode | 252 +-- ...smooth_curves_circular_interpolation.gcode | 1414 ++++++----------- ...urves_circular_interpolation_release.gcode | 1414 ++++++----------- 4 files changed, 995 insertions(+), 2107 deletions(-) diff --git a/lib/src/arc.rs b/lib/src/arc.rs index 4b5ab13..b12ff7b 100644 --- a/lib/src/arc.rs +++ b/lib/src/arc.rs @@ -1,6 +1,6 @@ use euclid::Angle; use lyon_geom::{ - ArcFlags, CubicBezierSegment, Line, LineSegment, Point, Scalar, SvgArc, Transform, Vector, + Arc, ArcFlags, CubicBezierSegment, Line, LineSegment, Point, Scalar, SvgArc, Transform, Vector, }; pub enum ArcOrLineSegment { @@ -8,6 +8,18 @@ pub enum ArcOrLineSegment { Line(LineSegment), } +/// Calcuates the distance from `p` to the nearest point on `arc`. +fn point_to_arc_dist(p: Point, arc: &Arc) -> S { + let t_raw = (p - arc.center).angle_from_x_axis().radians / arc.sweep_angle.radians + - arc.start_angle.radians / arc.sweep_angle.radians; + let full_rev = S::TWO * S::PI() / arc.sweep_angle.radians.abs(); + let calc_dist = |t: S| (arc.sample(t.clamp(S::ZERO, S::ONE)) - p).length(); + + calc_dist(t_raw) + .min(calc_dist(t_raw + full_rev)) + .min(calc_dist(t_raw - full_rev)) +} + fn arc_from_endpoints_and_tangents( from: Point, from_tangent: Vector, @@ -104,12 +116,10 @@ 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()); + max_deviation.max(point_to_arc_dist(inner_bezier.sample(t), &arc)); } max_deviation < tolerance }) { @@ -150,12 +160,10 @@ 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()); + max_deviation.max(point_to_arc_dist(self_arc.sample(t), &approx_arc)); } max_deviation < tolerance }) { diff --git a/lib/tests/circular_interpolation.gcode b/lib/tests/circular_interpolation.gcode index da5d76d..a5f1e6b 100644 --- a/lib/tests/circular_interpolation.gcode +++ b/lib/tests/circular_interpolation.gcode @@ -5,58 +5,25 @@ G1 X1.094 Y8.903 F300 G1 X1.187 Y8.802 F300 G1 X1.279 Y8.695 F300 G1 X1.369 Y8.584 F300 -G1 X1.457 Y8.469 F300 -G1 X1.543 Y8.352 F300 -G2 X1.703 Y8.109 R4.885 F300 -G2 X1.846 Y7.861 R4.319 F300 -G1 X1.909 Y7.736 F300 -G1 X1.967 Y7.611 F300 -G1 X2.018 Y7.487 F300 -G2 X2.061 Y7.365 R2.625 F300 -G2 X2.097 Y7.244 R2.262 F300 -G2 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F300 +G3 X7.479 Y2.809 R0.68 F300 +G3 X7.377 Y3.103 R0.747 F300 +G3 X7.149 Y3.364 R1.027 F300 +G3 X6.816 Y3.569 R1.468 F300 +G3 X6.408 Y3.701 R1.928 F300 +G3 X5.962 Y3.746 R2.207 F300 +G3 X5.518 Y3.7 R2.177 F300 +G3 X5.116 Y3.569 R1.853 F300 +G3 X4.792 Y3.364 R1.38 F300 +G3 X4.575 Y3.103 R0.961 F300 +G3 X4.486 Y2.809 R0.717 F300 +G3 X4.531 Y2.51 R0.692 F300 +G3 X4.708 Y2.232 R0.885 F300 +G3 X5 Y2 R1.268 F300 +G3 X5.469 Y1.811 R1.787 F300 +G3 X6.006 Y1.745 R2.184 F300 +G3 X6.54 Y1.811 R2.149 F300 +G3 X7 Y2 R1.703 F300 diff --git a/lib/tests/smooth_curves_circular_interpolation.gcode b/lib/tests/smooth_curves_circular_interpolation.gcode index 78eaf57..509b37b 100644 --- a/lib/tests/smooth_curves_circular_interpolation.gcode +++ b/lib/tests/smooth_curves_circular_interpolation.gcode @@ -49,9 +49,11 @@ G1 X32.249 Y40.411 F300 G1 X32.325 Y40.59 F300 G1 X32.398 Y40.771 F300 G1 X32.468 Y40.953 F300 -G3 X32.717 Y41.699 R11.044 F300 -G3 X32.822 Y42.082 R10.888 F300 -G3 X32.914 Y42.471 R10.842 F300 +G1 X32.535 Y41.137 F300 +G1 X32.599 Y41.323 F300 +G1 X32.659 Y41.51 F300 +G1 X32.717 Y41.699 F300 +G3 X32.914 Y42.471 R10.865 F300 G3 X32.914 Y42.786 R0.627 F300 G3 X37.56 Y43.185 R12.52 F300 G3 X37.155 Y40.719 R7.938 F300 @@ -64,34 +66,22 @@ G1 X40.96 Y33.727 F300 G1 X41.059 Y33.665 F300 G1 X41.16 Y33.604 F300 G1 X41.261 Y33.545 F300 -G3 X41.677 Y33.32 R8.407 F300 -G3 X42.107 Y33.117 R8.594 F300 -G3 X43.003 Y32.783 R8.719 F300 -G3 X43.934 Y32.548 R8.62 F300 -G3 X44.884 Y32.421 R8.241 F300 -G3 X45.36 Y32.399 R7.831 F300 -G3 X45.836 Y32.408 R7.515 F300 +G3 X42.107 Y33.117 R8.5 F300 +G3 X43.934 Y32.548 R8.669 F300 +G3 X45.836 Y32.408 R7.944 F300 G3 X46.774 Y32.517 R7.018 F300 G3 X47.683 Y32.755 R6.403 F300 -G3 X47.938 Y32.852 R4.832 F300 -G3 X48.182 Y32.96 R4.58 F300 -G3 X48.413 Y33.079 R4.39 F300 -G1 X48.524 Y33.143 F300 -G1 X48.633 Y33.21 F300 -G1 X48.739 Y33.279 F300 -G1 X48.842 Y33.352 F300 -G3 X49.04 Y33.504 R4.162 F300 -G3 X49.404 Y33.841 R4.234 F300 -G3 X49.729 Y34.218 R4.506 F300 -G1 X49.804 Y34.318 F300 -G1 X49.877 Y34.421 F300 -G1 X49.947 Y34.526 F300 -G1 X50.016 Y34.634 F300 -G1 X50.082 Y34.743 F300 -G1 X50.146 Y34.855 F300 -G3 X50.268 Y35.086 R5.953 F300 -G3 X50.382 Y35.325 R6.456 F300 -G3 X50.488 Y35.573 R7.036 F300 +G3 X48.633 Y33.21 R4.508 F300 +G3 X49.04 Y33.504 R4.172 F300 +G1 X49.135 Y33.584 F300 +G1 X49.227 Y33.667 F300 +G1 X49.317 Y33.753 F300 +G1 X49.404 Y33.841 F300 +G1 X49.489 Y33.931 F300 +G1 X49.571 Y34.024 F300 +G3 X49.729 Y34.218 R4.603 F300 +G3 X50.016 Y34.634 R4.998 F300 +G3 X50.488 Y35.573 R6.203 F300 G3 X51.051 Y39.664 R8.467 F300 G3 X46.895 Y46.114 R8.639 F300 G3 X47.636 Y46.757 R7.255 F300 @@ -131,27 +121,21 @@ G1 X50.759 Y53.492 F300 G1 X50.877 Y53.975 F300 G1 X50.877 Y53.975 F300 G3 X53.205 Y53.504 R8.903 F300 -G3 X53.837 Y53.487 R5.987 F300 -G3 X54.465 Y53.537 R5.712 F300 -G3 X55.079 Y53.658 R5.329 F300 -G3 X55.668 Y53.85 R4.903 F300 -G3 X56.737 Y54.461 R4.328 F300 -G3 X56.974 Y54.662 R4.006 F300 -G3 X57.196 Y54.883 R3.945 F300 -G3 X57.402 Y55.124 R3.929 F300 -G3 X57.499 Y55.252 R3.948 F300 -G3 X57.592 Y55.385 R3.978 F300 +G3 X54.465 Y53.537 R5.846 F300 +G3 X55.668 Y53.85 R5.106 F300 +G3 X56.224 Y54.117 R4.498 F300 +G3 X56.737 Y54.461 R4.173 F300 +G3 X57.592 Y55.385 R3.96 F300 G3 X57.695 Y55.697 R0.582 F300 G3 X57.801 Y56.036 R2.511 F300 G3 X57.864 Y56.444 R2.969 F300 G3 X58.439 Y57.219 R1.617 F300 G3 X58.071 Y59.439 R2.344 F300 -G3 X58.047 Y59.661 R3.117 F300 -G3 X58.009 Y59.879 R3.196 F300 -G3 X57.89 Y60.301 R3.411 F300 -G3 X57.721 Y60.705 R3.865 F300 -G3 X57.51 Y61.091 R4.528 F300 -G3 X57.263 Y61.459 R5.421 F300 +G3 X57.89 Y60.301 R3.279 F300 +G3 X57.51 Y61.091 R4.174 F300 +G3 X57.39 Y61.277 R5.177 F300 +G1 X57.327 Y61.369 F300 +G1 X57.263 Y61.459 F300 G1 X57.196 Y61.548 F300 G1 X57.128 Y61.636 F300 G3 X56.988 Y61.809 R6.932 F300 @@ -163,25 +147,15 @@ G1 X56.383 Y62.458 F300 G3 X53.835 Y64.286 R10.538 F300 G3 X52.959 Y69.339 R5.876 F300 G3 X48.104 Y71.456 R5.384 F300 -G1 X47.953 Y71.435 F300 -G1 X47.798 Y71.407 F300 -G1 X47.64 Y71.372 F300 -G3 X47.482 Y71.331 R4.041 F300 -G3 X47.168 Y71.227 R3.66 F300 -G3 X46.868 Y71.094 R3.025 F300 -G3 X46.726 Y71.015 R2.537 F300 -G3 X46.592 Y70.929 R2.226 F300 -G3 X46.468 Y70.834 R1.944 F300 -G3 X46.354 Y70.731 R1.699 F300 -G3 X46.252 Y70.62 R1.496 F300 -G3 X46.163 Y70.499 R1.338 F300 +G3 X47.482 Y71.331 R4.157 F300 +G3 X46.868 Y71.094 R3.311 F300 +G3 X46.592 Y70.929 R2.372 F300 +G3 X46.354 Y70.731 R1.814 F300 +G3 X46.163 Y70.499 R1.412 F300 G3 X46.032 Y70.231 R1.196 F300 G3 X44.974 Y70.067 R6.567 F300 -G3 X44.691 Y69.999 R8.768 F300 -G3 X44.409 Y69.921 R8.499 F300 -G3 X43.854 Y69.734 R8.043 F300 -G3 X43.315 Y69.507 R7.395 F300 -G3 X42.797 Y69.236 R6.745 F300 +G3 X43.854 Y69.734 R8.325 F300 +G3 X42.797 Y69.236 R7.054 F300 G1 X42.672 Y69.161 F300 G1 X42.548 Y69.083 F300 G1 X42.427 Y69.003 F300 @@ -196,19 +170,12 @@ G1 X41.537 Y68.254 F300 G1 X41.437 Y68.146 F300 G1 X41.34 Y68.036 F300 G1 X41.247 Y67.922 F300 -G1 X41.156 Y67.806 F300 -G1 X41.069 Y67.686 F300 -G3 X40.89 Y67.412 R4.041 F300 -G3 X40.736 Y67.128 R4.067 F300 -G3 X40.606 Y66.835 R4.139 F300 -G3 X40.499 Y66.535 R4.253 F300 +G3 X41.069 Y67.686 R4.906 F300 +G3 X40.499 Y66.535 R4.124 F300 G3 X40.291 Y65.286 R4.682 F300 -G3 X40.308 Y64.648 R5.326 F300 -G3 X40.4 Y64.013 R5.739 F300 -G3 X40.56 Y63.391 R6.049 F300 -G3 X40.783 Y62.791 R6.192 F300 -G3 X40.917 Y62.503 R5.955 F300 -G3 X41.065 Y62.223 R6.155 F300 +G3 X40.4 Y64.013 R5.527 F300 +G3 X40.783 Y62.791 R6.12 F300 +G3 X41.065 Y62.223 R6.053 F300 G1 X41.144 Y62.087 F300 G1 X41.226 Y61.953 F300 G1 X41.311 Y61.82 F300 @@ -216,7 +183,10 @@ G1 X41.4 Y61.69 F300 G1 X41.491 Y61.562 F300 G1 X41.586 Y61.436 F300 G3 X41.782 Y61.19 R7.519 F300 -G3 X42.205 Y60.722 R8.272 F300 +G1 X41.884 Y61.07 F300 +G1 X41.989 Y60.952 F300 +G1 X42.096 Y60.836 F300 +G1 X42.205 Y60.722 F300 G1 X42.316 Y60.609 F300 G1 X42.43 Y60.498 F300 G1 X42.545 Y60.39 F300 @@ -250,23 +220,19 @@ G1 X40.253 Y53.836 F300 G1 X40.189 Y53.629 F300 G1 X40.129 Y53.421 F300 G1 X40.071 Y53.212 F300 -G3 X39.876 Y52.366 R13.837 F300 +G1 X40.017 Y53.002 F300 +G1 X39.967 Y52.791 F300 +G3 X39.876 Y52.366 R14.151 F300 G3 X39.635 Y50.647 R15.764 F300 G1 X39.635 Y50.647 F300 -G1 X38.841 Y50.71 F300 -G1 X38.048 Y50.77 F300 -G3 X36.464 Y50.875 R139.951 F300 -G3 X34.881 Y50.962 R139.138 F300 -G3 X33.3 Y51.03 R138.382 F300 +G3 X33.3 Y51.03 R139.569 F300 G2 X32.787 Y51.054 R54.711 F300 G3 X32.202 Y51.08 R48.898 F300 G3 X31.615 Y51.092 R16.284 F300 G3 X31.03 Y51.076 R9.684 F300 G3 X30.448 Y51.017 R6.868 F300 G1 X30.403 Y51.017 F300 -G3 X30.388 Y51.464 R6.463 F300 -G3 X30.342 Y51.905 R6.52 F300 -G3 X30.165 Y52.765 R6.694 F300 +G3 X30.165 Y52.765 R6.592 F300 G3 X29.499 Y54.378 R7.274 F300 G1 X29.39 Y54.568 F300 G1 X29.275 Y54.755 F300 @@ -298,43 +264,31 @@ G1 X20.124 Y61.999 F300 G1 X19.974 Y62.135 F300 G1 X19.897 Y62.202 F300 G1 X19.819 Y62.267 F300 -G3 X19.497 Y62.512 R5.285 F300 -G3 X19.328 Y62.625 R4.69 F300 -G3 X19.153 Y62.73 R4.401 F300 -G3 X18.973 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G1 X20.444 Y56.33 F300 G1 X20.385 Y56.07 F300 G3 X20.288 Y55.547 R7.546 F300 -G3 X20.206 Y54.535 R8.749 F300 -G3 X20.242 Y53.522 R8.707 F300 -G3 X20.395 Y52.524 R8.499 F300 -G3 X20.667 Y51.555 R8.161 F300 +G3 X20.242 Y53.522 R8.728 F300 +G3 X20.667 Y51.555 R8.326 F300 G3 X21.057 Y50.631 R7.751 F300 G3 X21.297 Y50.19 R7.44 F300 G1 X21.362 Y50.083 F300 @@ -384,9 +338,7 @@ G1 X19.422 Y44.035 F300 G1 X19.312 Y43.865 F300 G1 X19.206 Y43.694 F300 G1 X19.103 Y43.52 F300 -G1 X19.003 Y43.345 F300 -G1 X18.906 Y43.167 F300 -G3 X18.723 Y42.807 R10.778 F300 +G3 X18.723 Y42.807 R10.751 F300 G3 X18.553 Y42.44 R10.809 F300 G1 X18.473 Y42.254 F300 G1 X18.397 Y42.066 F300 @@ -397,11 +349,9 @@ G1 X18.128 Y41.303 F300 G1 X18.07 Y41.11 F300 G1 X18.015 Y40.915 F300 G3 X17.917 Y40.523 R10.586 F300 -G3 X17.767 Y39.73 R10.407 F300 -G3 X17.68 Y38.929 R10.115 F300 +G3 X17.68 Y38.929 R10.259 F300 G3 X17.703 Y37.325 R9.596 F300 -G3 X17.841 Y36.461 R7.312 F300 -G3 X18.082 Y35.62 R7.067 F300 +G3 X18.082 Y35.62 R7.187 F300 G3 X18.426 Y34.821 R6.562 F300 G3 X18.637 Y34.443 R6.096 F300 G1 X18.693 Y34.352 F300 @@ -411,25 +361,27 @@ G1 X18.873 Y34.084 F300 G1 X18.936 Y33.998 F300 G1 X19.001 Y33.912 F300 G3 X19.135 Y33.746 R5.377 F300 -G3 X19.422 Y33.43 R5.162 F300 -G3 X19.735 Y33.141 R4.912 F300 +G1 X19.204 Y33.665 F300 +G1 X19.276 Y33.585 F300 +G1 X19.348 Y33.507 F300 +G1 X19.422 Y33.43 F300 +G1 X19.498 Y33.356 F300 +G1 X19.576 Y33.282 F300 +G1 X19.655 Y33.211 F300 +G1 X19.735 Y33.141 F300 G3 X20.074 Y32.879 R4.714 F300 -G3 X20.252 Y32.76 R4.605 F300 -G3 X20.437 Y32.648 R4.555 F300 -G3 X20.629 Y32.545 R4.524 F300 -G3 X20.826 Y32.451 R4.513 F300 -G3 X21.03 Y32.365 R4.523 F300 -G3 X21.241 Y32.289 R4.555 F300 -G3 X21.457 Y32.222 R4.612 F300 -G3 X21.68 Y32.165 R4.694 F300 +G3 X21.68 Y32.165 R4.573 F300 G0 X27.472 Y36.153 G3 X29.607 Y43.49 R23.625 F300 G3 X29.607 Y43.595 R0.352 F300 G3 X31.774 Y42.955 R11.449 F300 G3 X31.718 Y42.802 R0.616 F300 G2 X31.596 Y42.302 R10.028 F300 -G2 X31.45 Y41.814 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a/lib/tests/smooth_curves_circular_interpolation_release.gcode b/lib/tests/smooth_curves_circular_interpolation_release.gcode index 78eaf57..509b37b 100644 --- a/lib/tests/smooth_curves_circular_interpolation_release.gcode +++ b/lib/tests/smooth_curves_circular_interpolation_release.gcode @@ -49,9 +49,11 @@ G1 X32.249 Y40.411 F300 G1 X32.325 Y40.59 F300 G1 X32.398 Y40.771 F300 G1 X32.468 Y40.953 F300 -G3 X32.717 Y41.699 R11.044 F300 -G3 X32.822 Y42.082 R10.888 F300 -G3 X32.914 Y42.471 R10.842 F300 +G1 X32.535 Y41.137 F300 +G1 X32.599 Y41.323 F300 +G1 X32.659 Y41.51 F300 +G1 X32.717 Y41.699 F300 +G3 X32.914 Y42.471 R10.865 F300 G3 X32.914 Y42.786 R0.627 F300 G3 X37.56 Y43.185 R12.52 F300 G3 X37.155 Y40.719 R7.938 F300 @@ -64,34 +66,22 @@ G1 X40.96 Y33.727 F300 G1 X41.059 Y33.665 F300 G1 X41.16 Y33.604 F300 G1 X41.261 Y33.545 F300 -G3 X41.677 Y33.32 R8.407 F300 -G3 X42.107 Y33.117 R8.594 F300 -G3 X43.003 Y32.783 R8.719 F300 -G3 X43.934 Y32.548 R8.62 F300 -G3 X44.884 Y32.421 R8.241 F300 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X50.016 Y34.634 R4.998 F300 +G3 X50.488 Y35.573 R6.203 F300 G3 X51.051 Y39.664 R8.467 F300 G3 X46.895 Y46.114 R8.639 F300 G3 X47.636 Y46.757 R7.255 F300 @@ -131,27 +121,21 @@ G1 X50.759 Y53.492 F300 G1 X50.877 Y53.975 F300 G1 X50.877 Y53.975 F300 G3 X53.205 Y53.504 R8.903 F300 -G3 X53.837 Y53.487 R5.987 F300 -G3 X54.465 Y53.537 R5.712 F300 -G3 X55.079 Y53.658 R5.329 F300 -G3 X55.668 Y53.85 R4.903 F300 -G3 X56.737 Y54.461 R4.328 F300 -G3 X56.974 Y54.662 R4.006 F300 -G3 X57.196 Y54.883 R3.945 F300 -G3 X57.402 Y55.124 R3.929 F300 -G3 X57.499 Y55.252 R3.948 F300 -G3 X57.592 Y55.385 R3.978 F300 +G3 X54.465 Y53.537 R5.846 F300 +G3 X55.668 Y53.85 R5.106 F300 +G3 X56.224 Y54.117 R4.498 F300 +G3 X56.737 Y54.461 R4.173 F300 +G3 X57.592 Y55.385 R3.96 F300 G3 X57.695 Y55.697 R0.582 F300 G3 X57.801 Y56.036 R2.511 F300 G3 X57.864 Y56.444 R2.969 F300 G3 X58.439 Y57.219 R1.617 F300 G3 X58.071 Y59.439 R2.344 F300 -G3 X58.047 Y59.661 R3.117 F300 -G3 X58.009 Y59.879 R3.196 F300 -G3 X57.89 Y60.301 R3.411 F300 -G3 X57.721 Y60.705 R3.865 F300 -G3 X57.51 Y61.091 R4.528 F300 -G3 X57.263 Y61.459 R5.421 F300 +G3 X57.89 Y60.301 R3.279 F300 +G3 X57.51 Y61.091 R4.174 F300 +G3 X57.39 Y61.277 R5.177 F300 +G1 X57.327 Y61.369 F300 +G1 X57.263 Y61.459 F300 G1 X57.196 Y61.548 F300 G1 X57.128 Y61.636 F300 G3 X56.988 Y61.809 R6.932 F300 @@ -163,25 +147,15 @@ G1 X56.383 Y62.458 F300 G3 X53.835 Y64.286 R10.538 F300 G3 X52.959 Y69.339 R5.876 F300 G3 X48.104 Y71.456 R5.384 F300 -G1 X47.953 Y71.435 F300 -G1 X47.798 Y71.407 F300 -G1 X47.64 Y71.372 F300 -G3 X47.482 Y71.331 R4.041 F300 -G3 X47.168 Y71.227 R3.66 F300 -G3 X46.868 Y71.094 R3.025 F300 -G3 X46.726 Y71.015 R2.537 F300 -G3 X46.592 Y70.929 R2.226 F300 -G3 X46.468 Y70.834 R1.944 F300 -G3 X46.354 Y70.731 R1.699 F300 -G3 X46.252 Y70.62 R1.496 F300 -G3 X46.163 Y70.499 R1.338 F300 +G3 X47.482 Y71.331 R4.157 F300 +G3 X46.868 Y71.094 R3.311 F300 +G3 X46.592 Y70.929 R2.372 F300 +G3 X46.354 Y70.731 R1.814 F300 +G3 X46.163 Y70.499 R1.412 F300 G3 X46.032 Y70.231 R1.196 F300 G3 X44.974 Y70.067 R6.567 F300 -G3 X44.691 Y69.999 R8.768 F300 -G3 X44.409 Y69.921 R8.499 F300 -G3 X43.854 Y69.734 R8.043 F300 -G3 X43.315 Y69.507 R7.395 F300 -G3 X42.797 Y69.236 R6.745 F300 +G3 X43.854 Y69.734 R8.325 F300 +G3 X42.797 Y69.236 R7.054 F300 G1 X42.672 Y69.161 F300 G1 X42.548 Y69.083 F300 G1 X42.427 Y69.003 F300 @@ -196,19 +170,12 @@ G1 X41.537 Y68.254 F300 G1 X41.437 Y68.146 F300 G1 X41.34 Y68.036 F300 G1 X41.247 Y67.922 F300 -G1 X41.156 Y67.806 F300 -G1 X41.069 Y67.686 F300 -G3 X40.89 Y67.412 R4.041 F300 -G3 X40.736 Y67.128 R4.067 F300 -G3 X40.606 Y66.835 R4.139 F300 -G3 X40.499 Y66.535 R4.253 F300 +G3 X41.069 Y67.686 R4.906 F300 +G3 X40.499 Y66.535 R4.124 F300 G3 X40.291 Y65.286 R4.682 F300 -G3 X40.308 Y64.648 R5.326 F300 -G3 X40.4 Y64.013 R5.739 F300 -G3 X40.56 Y63.391 R6.049 F300 -G3 X40.783 Y62.791 R6.192 F300 -G3 X40.917 Y62.503 R5.955 F300 -G3 X41.065 Y62.223 R6.155 F300 +G3 X40.4 Y64.013 R5.527 F300 +G3 X40.783 Y62.791 R6.12 F300 +G3 X41.065 Y62.223 R6.053 F300 G1 X41.144 Y62.087 F300 G1 X41.226 Y61.953 F300 G1 X41.311 Y61.82 F300 @@ -216,7 +183,10 @@ G1 X41.4 Y61.69 F300 G1 X41.491 Y61.562 F300 G1 X41.586 Y61.436 F300 G3 X41.782 Y61.19 R7.519 F300 -G3 X42.205 Y60.722 R8.272 F300 +G1 X41.884 Y61.07 F300 +G1 X41.989 Y60.952 F300 +G1 X42.096 Y60.836 F300 +G1 X42.205 Y60.722 F300 G1 X42.316 Y60.609 F300 G1 X42.43 Y60.498 F300 G1 X42.545 Y60.39 F300 @@ -250,23 +220,19 @@ G1 X40.253 Y53.836 F300 G1 X40.189 Y53.629 F300 G1 X40.129 Y53.421 F300 G1 X40.071 Y53.212 F300 -G3 X39.876 Y52.366 R13.837 F300 +G1 X40.017 Y53.002 F300 +G1 X39.967 Y52.791 F300 +G3 X39.876 Y52.366 R14.151 F300 G3 X39.635 Y50.647 R15.764 F300 G1 X39.635 Y50.647 F300 -G1 X38.841 Y50.71 F300 -G1 X38.048 Y50.77 F300 -G3 X36.464 Y50.875 R139.951 F300 -G3 X34.881 Y50.962 R139.138 F300 -G3 X33.3 Y51.03 R138.382 F300 +G3 X33.3 Y51.03 R139.569 F300 G2 X32.787 Y51.054 R54.711 F300 G3 X32.202 Y51.08 R48.898 F300 G3 X31.615 Y51.092 R16.284 F300 G3 X31.03 Y51.076 R9.684 F300 G3 X30.448 Y51.017 R6.868 F300 G1 X30.403 Y51.017 F300 -G3 X30.388 Y51.464 R6.463 F300 -G3 X30.342 Y51.905 R6.52 F300 -G3 X30.165 Y52.765 R6.694 F300 +G3 X30.165 Y52.765 R6.592 F300 G3 X29.499 Y54.378 R7.274 F300 G1 X29.39 Y54.568 F300 G1 X29.275 Y54.755 F300 @@ -298,43 +264,31 @@ G1 X20.124 Y61.999 F300 G1 X19.974 Y62.135 F300 G1 X19.897 Y62.202 F300 G1 X19.819 Y62.267 F300 -G3 X19.497 Y62.512 R5.285 F300 -G3 X19.328 Y62.625 R4.69 F300 -G3 X19.153 Y62.73 R4.401 F300 -G3 X18.973 Y62.828 R4.185 F300 -G3 X18.785 Y62.918 R4.032 F300 +G3 X19.66 Y62.392 R5.531 F300 +G3 X19.497 Y62.512 R5.061 F300 +G3 X18.785 Y62.918 R4.31 F300 G3 X18.542 Y62.987 R0.82 F300 G3 X17.955 Y62.857 R0.627 F300 G3 X17.494 Y61.108 R1.68 F300 G3 X17.665 Y60.686 R2.367 F300 G3 X17.902 Y60.297 R3.361 F300 -G3 X18.183 Y59.931 R5.812 F300 +G3 X18.039 Y60.112 R4.95 F300 +G3 X18.183 Y59.931 R7.031 F300 G1 X18.332 Y59.755 F300 G1 X18.482 Y59.582 F300 G1 X18.597 Y59.45 F300 G1 X18.709 Y59.32 F300 G1 X20.251 Y57.491 F300 -G1 X20.343 Y57.383 F300 -G1 X20.382 Y57.332 F300 -G1 X20.418 Y57.284 F300 -G1 X20.45 Y57.236 F300 -G1 X20.477 Y57.189 F300 -G2 X20.519 Y57.095 R0.658 F300 -G2 X20.545 Y56.997 R0.569 F300 -G1 X20.551 Y56.944 F300 -G1 X20.553 Y56.889 F300 -G1 X20.551 Y56.836 F300 -G1 X20.543 Y56.767 F300 -G1 X20.532 Y56.699 F300 -G1 X20.516 Y56.626 F300 +G2 X20.418 Y57.284 R2.684 F300 +G2 X20.519 Y57.095 R0.791 F300 +G2 X20.553 Y56.889 R0.605 F300 +G2 X20.516 Y56.626 R1.152 F300 G1 X20.507 Y56.59 F300 G1 X20.444 Y56.33 F300 G1 X20.385 Y56.07 F300 G3 X20.288 Y55.547 R7.546 F300 -G3 X20.206 Y54.535 R8.749 F300 -G3 X20.242 Y53.522 R8.707 F300 -G3 X20.395 Y52.524 R8.499 F300 -G3 X20.667 Y51.555 R8.161 F300 +G3 X20.242 Y53.522 R8.728 F300 +G3 X20.667 Y51.555 R8.326 F300 G3 X21.057 Y50.631 R7.751 F300 G3 X21.297 Y50.19 R7.44 F300 G1 X21.362 Y50.083 F300 @@ -384,9 +338,7 @@ G1 X19.422 Y44.035 F300 G1 X19.312 Y43.865 F300 G1 X19.206 Y43.694 F300 G1 X19.103 Y43.52 F300 -G1 X19.003 Y43.345 F300 -G1 X18.906 Y43.167 F300 -G3 X18.723 Y42.807 R10.778 F300 +G3 X18.723 Y42.807 R10.751 F300 G3 X18.553 Y42.44 R10.809 F300 G1 X18.473 Y42.254 F300 G1 X18.397 Y42.066 F300 @@ -397,11 +349,9 @@ G1 X18.128 Y41.303 F300 G1 X18.07 Y41.11 F300 G1 X18.015 Y40.915 F300 G3 X17.917 Y40.523 R10.586 F300 -G3 X17.767 Y39.73 R10.407 F300 -G3 X17.68 Y38.929 R10.115 F300 +G3 X17.68 Y38.929 R10.259 F300 G3 X17.703 Y37.325 R9.596 F300 -G3 X17.841 Y36.461 R7.312 F300 -G3 X18.082 Y35.62 R7.067 F300 +G3 X18.082 Y35.62 R7.187 F300 G3 X18.426 Y34.821 R6.562 F300 G3 X18.637 Y34.443 R6.096 F300 G1 X18.693 Y34.352 F300 @@ -411,25 +361,27 @@ G1 X18.873 Y34.084 F300 G1 X18.936 Y33.998 F300 G1 X19.001 Y33.912 F300 G3 X19.135 Y33.746 R5.377 F300 -G3 X19.422 Y33.43 R5.162 F300 -G3 X19.735 Y33.141 R4.912 F300 +G1 X19.204 Y33.665 F300 +G1 X19.276 Y33.585 F300 +G1 X19.348 Y33.507 F300 +G1 X19.422 Y33.43 F300 +G1 X19.498 Y33.356 F300 +G1 X19.576 Y33.282 F300 +G1 X19.655 Y33.211 F300 +G1 X19.735 Y33.141 F300 G3 X20.074 Y32.879 R4.714 F300 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