//! FigCraft path operations. //! //! - [`boolean`]: Union, Subtract, Intersect and Exclude over any number of closed paths (robust //! sweep-line topology from `linesweeper`); results use the even-odd rule. //! - [`stroke_outline`]: a stroke as a fill, with Figma's Inside / Center / Outside alignment, //! dashes, caps, joins, arrowheads, variable width profiles ([`width`]) and brushes ([`brush`]). #![deny(clippy::unwrap_used, clippy::expect_used, clippy::panic, clippy::unimplemented, clippy::todo, clippy::unreachable)] pub mod brush; #[cfg(test)] mod brush_tests; #[cfg(test)] mod ops_tests; mod points; #[cfg(test)] mod sides_tests; pub mod width; #[cfg(test)] mod width_tests; use figcraft_doc::{BoolOp, StrokeAlign, StrokeCap, StrokeJoin, StrokeProps, VectorNetwork}; use figcraft_geom::kurbo::{self, BezPath, Cap, Join, PathEl, PathSeg, Point, Shape, Vec2}; #[derive(Debug, PartialEq)] pub enum PathOpsError { /// The inputs contain NaN or infinite coordinates. BadInput, } impl std::fmt::Display for PathOpsError { fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result { write!(f, "path contains invalid coordinates") } } /// Close every open subpath (a filled open path paints as if closed). pub fn closed(path: &BezPath) -> BezPath { let mut out = BezPath::new(); let mut open = false; for el in path.elements() { match el { PathEl::MoveTo(_) => { if open { out.close_path(); } open = true; } PathEl::ClosePath => open = false, _ => {} } out.push(*el); } if open { out.close_path(); } out } /// Every coordinate is finite and of a sane magnitude (the sweep needs bounded input). pub use figcraft_geom::measure::finite_path as finite; /// Run the sweep library on `f`. Version 0.4 can panic on rare near-degenerate input (an internal /// `unwrap` while ordering curves, hit by some font outlines): that is bad input, not a crash. // shortcut: no catch where panics abort (wasm32); drop this once a linesweeper release no longer panics there. fn sweep(f: impl FnOnce() -> Result) -> Result { std::panic::catch_unwind(std::panic::AssertUnwindSafe(f)).unwrap_or(Err(PathOpsError::BadInput)) } fn binary(a: &BezPath, b: &BezPath, op: linesweeper::BinaryOp) -> Result { if a.elements().is_empty() && b.elements().is_empty() { return Ok(BezPath::new()); } if !finite(a) || !finite(b) { return Err(PathOpsError::BadInput); } let contours = sweep(|| linesweeper::binary_op(&closed(a), &closed(b), linesweeper::FillRule::NonZero, op).map_err(|_| PathOpsError::BadInput))?; let mut out = BezPath::new(); for c in contours.contours() { out.extend(c.path.elements().iter().copied()); } Ok(out) } /// Normalise a single path's winding (non-zero) into simple even-odd contours. pub fn simplify(path: &BezPath) -> Result { binary(path, &BezPath::new(), linesweeper::BinaryOp::Union) } /// Combine `acc` (the operands so far) with the next operand `p` by `op`. pub fn boolean_step(acc: &BezPath, p: &BezPath, op: BoolOp) -> Result { let op = match op { BoolOp::Union => linesweeper::BinaryOp::Union, BoolOp::Intersect => linesweeper::BinaryOp::Intersection, BoolOp::Exclude => linesweeper::BinaryOp::Xor, BoolOp::Subtract => linesweeper::BinaryOp::Difference, }; binary(acc, p, op) } /// Apply a boolean operation to `paths` in order (bottom to top, like a boolean group's children): /// Subtract removes every later shape from the first one. pub fn boolean(paths: &[BezPath], op: BoolOp) -> Result { boolean_ops(paths.iter().map(|p| (p, op))) } /// Fold `operands` bottom to top, each combined with the result of those below it by its own /// operation (the bottom operand's operation is unused): what a boolean group whose operands carry /// their own operations paints. A lone operand comes out simplified. pub fn boolean_ops<'a>(operands: impl IntoIterator) -> Result { let mut it = operands.into_iter(); let Some((first, _)) = it.next() else { return Ok(BezPath::new()) }; let mut acc: Option = None; for (p, op) in it { acc = Some(boolean_step(acc.as_ref().unwrap_or(first), p, op)?); } match acc { Some(a) => Ok(a), None => simplify(first), } } /// Per-input winding numbers for [`faces`] (index = input path; trailing zeros trimmed so equal /// coverage compares equal). #[derive(Clone, Debug, Default, PartialEq, Eq)] struct Windings(Vec); impl Windings { fn trimmed(mut self) -> Self { while self.0.last() == Some(&0) { self.0.pop(); } self } } impl std::ops::Add for Windings { type Output = Self; fn add(mut self, rhs: Self) -> Self { self += rhs; self } } impl std::ops::AddAssign for Windings { fn add_assign(&mut self, rhs: Self) { if self.0.len() < rhs.0.len() { self.0.resize(rhs.0.len(), 0); } for (a, b) in self.0.iter_mut().zip(rhs.0) { *a += b; } *self = std::mem::take(self).trimmed(); } } impl linesweeper::topology::WindingNumber for Windings { type Tag = usize; fn single(tag: usize, positive: bool) -> Self { let mut v = vec![0; tag + 1]; if let Some(w) = v.last_mut() { *w = if positive { 1 } else { -1 }; } Self(v) } fn of_tag(&self, tag: usize) -> Self { let mut v = vec![0; tag + 1]; if let (Some(w), Some(src)) = (v.last_mut(), self.0.get(tag)) { *w = *src; } Self(v).trimmed() } } /// One face of the arrangement of several closed paths: a connected area that the same set of /// inputs covers. #[derive(Clone, Debug)] pub struct ArrangementFace { /// The face's outer contour and its holes (fill with either rule). pub path: BezPath, /// The inputs covering the face, by index, ascending. pub cover: Vec, } /// The most inputs [`faces`] accepts, and the most faces it returns. pub const MAX_ARRANGEMENT_INPUTS: usize = 256; const MAX_FACES: usize = 4096; /// Split the plane by the outlines of `paths` (each filled with its own rule: `true` = even-odd) /// into faces: the connected areas covered by the same inputs. Areas no input covers are left /// out. Open subpaths are closed first. pub fn faces(paths: &[(BezPath, bool)]) -> Result, PathOpsError> { if paths.len() > MAX_ARRANGEMENT_INPUTS || paths.iter().any(|(p, _)| !finite(p)) { return Err(PathOpsError::BadInput); } let closed_paths: Vec = paths.iter().map(|(p, _)| closed(p)).collect(); if closed_paths.iter().all(|p| p.elements().is_empty()) { return Ok(Vec::new()); } let bbox = closed_paths.iter().filter(|p| !p.elements().is_empty()).map(Shape::bounding_box).reduce(|a, b| a.union(b)); let m = bbox.map(|b| b.x0.abs().max(b.x1.abs()).max(b.y0.abs()).max(b.y1.abs())).unwrap_or(0.0); let eps = (m * f64::EPSILON * 64.0).max(1e-6); let even_odd: Vec = paths.iter().map(|(_, e)| *e).collect(); sweep(|| arrange(&closed_paths, &even_odd, eps)) } /// [`faces`] of the closed `paths`, swept with tolerance `eps`. fn arrange(closed_paths: &[BezPath], even_odd: &[bool], eps: f64) -> Result, PathOpsError> { let topo = linesweeper::topology::Topology::::from_paths(closed_paths.iter().enumerate().map(|(i, p)| (p, i)), eps) .map_err(|_| PathOpsError::BadInput)?; let cover_of = |w: &Windings| -> Vec { w.0.iter() .enumerate() .filter(|(i, n)| if even_odd.get(*i).copied().unwrap_or(false) { *n % 2 != 0 } else { **n != 0 }) .map(|(i, _)| i) .collect() }; // Every coverage that occurs on either side of an output segment. let mut covers: std::collections::BTreeSet> = std::collections::BTreeSet::new(); for seg in topo.segment_indices() { let half = seg.first_half(); for w in [topo.winding_clockwise(half), topo.winding_counter_clockwise(half)] { let c = cover_of(w); if !c.is_empty() { covers.insert(c); } } } let mut out = Vec::new(); for cover in covers { let contours = topo.contours(|w| cover_of(w) == cover); let all: Vec<&linesweeper::topology::Contour> = contours.contours().collect(); // Each outer contour with its direct holes is one connected face (islands inside the // holes are faces of their own). for (i, c) in all.iter().enumerate().filter(|(_, c)| c.outer) { let mut path = c.path.clone(); for hole in all.iter().filter(|h| !h.outer && h.parent.map(|p| p.0) == Some(i)) { path.extend(hole.path.elements().iter().copied()); } out.push(ArrangementFace { path, cover: cover.clone() }); if out.len() >= MAX_FACES { return Ok(out); } } } Ok(out) } /// The union of disjoint faces (shared edges dissolve) as one clean path. pub fn union_faces<'a>(faces: impl IntoIterator) -> Result { let mut all = BezPath::new(); for f in faces { all.extend(f.elements().iter().copied()); } simplify(&all) } pub(crate) fn kcap(c: StrokeCap) -> Cap { match c { StrokeCap::Round | StrokeCap::CircleFilled => Cap::Round, StrokeCap::Square | StrokeCap::DiamondFilled => Cap::Square, _ => Cap::Butt, } } pub(crate) fn kjoin(j: StrokeJoin) -> Join { match j { StrokeJoin::Miter => Join::Miter, StrokeJoin::Bevel => Join::Bevel, StrokeJoin::Round => Join::Round, } } /// The widest stroke outlined: past this the rasteriser's fixed-point maths overflows and panics, /// and nothing visible changes (a stroke this wide covers any canvas already). pub const MAX_STROKE_WIDTH: f64 = 1e6; /// Plain centred stroke of `path` at `width` (capped at [`MAX_STROKE_WIDTH`]). pub fn stroke_center(path: &BezPath, width: f64, props: &StrokeProps) -> BezPath { if !(width.is_finite() && width > 0.0 && finite(path)) { return BezPath::new(); } let width = width.min(MAX_STROKE_WIDTH); let mut style = kurbo::Stroke::new(width) .with_join(kjoin(props.join)) .with_miter_limit(props.miter_limit.clamp(1.0, 100.0)) .with_start_cap(kcap(props.cap_start)) .with_end_cap(kcap(props.cap_end)); if let Some(pat) = width::dash_pattern(props) { style = style.with_dashes(0.0, pat); } kurbo::stroke(path.iter(), &style, &kurbo::StrokeOpts::default(), 0.05) } /// The painted stroke area of a shape as a fill path (local coordinates). `closed` says whether the /// shape is closed (Inside/Outside only apply to closed shapes). A width profile makes the width /// vary along the path (fill the result non-zero when centred). pub fn stroke_outline(path: &BezPath, props: &StrokeProps, closed_shape: bool) -> BezPath { stroke_outline_of(path, props, closed_shape, None) } /// [`stroke_outline`] of a shape whose stroke follows vector network `net` (`path` is its stroke /// path): points with a cap or join of their own draw them there. pub fn stroke_outline_of(path: &BezPath, props: &StrokeProps, closed_shape: bool, net: Option<&VectorNetwork>) -> BezPath { if !(props.weight.is_finite() && props.weight > 0.0) { return BezPath::new(); } let capped; let props = if props.weight > MAX_STROKE_WIDTH { capped = StrokeProps { weight: MAX_STROKE_WIDTH, ..props.clone() }; &capped } else { props }; let w = props.weight; let styled = net.and_then(|n| points::Styled::new(n, props)); // Centred at `width` (twice the weight for Inside/Outside, which clip half of it away). let centred = |width: f64| match (&styled, &props.brush, props.profile()) { (Some(st), ..) => st.outline(width, props), (None, Some(b), _) => brush::outline(path, width, props, b).unwrap_or_else(|| stroke_center(path, width, props)), (None, None, Some(p)) => width::variable_outline(path, width, props, p).unwrap_or_else(|| stroke_center(path, width, props)), (None, None, None) => stroke_center(path, width, props), }; let align = if closed_shape { props.align } else { StrokeAlign::Center }; let mut out = match align { StrokeAlign::Center => centred(w), StrokeAlign::Inside => { let s = centred(w * 2.0); binary(&s, path, linesweeper::BinaryOp::Intersection).unwrap_or(s) } StrokeAlign::Outside => { let s = centred(w * 2.0); binary(&s, path, linesweeper::BinaryOp::Difference).unwrap_or(s) } }; if let Some(st) = styled.as_ref().filter(|_| !closed_shape) { out.extend(st.arrowheads(w, props).elements().iter().copied()); } else if !closed_shape { for (at_end, cap) in [(false, props.cap_start), (true, props.cap_end)] { if cap.is_arrow() && let Some(head) = arrowhead(path, cap, w, at_end) { out.extend(head.elements().iter().copied()); } } } out } /// End point and outward direction of an open path at its start or end. fn path_end(path: &BezPath, at_end: bool) -> Option<(Point, Vec2)> { let segs: Vec = path.segments().collect(); let seg = if at_end { segs.last()? } else { segs.first()? }; use kurbo::ParamCurve; use kurbo::ParamCurveDeriv; let (p, d) = if at_end { let d = match seg { PathSeg::Line(l) => l.p1 - l.p0, PathSeg::Quad(q) => q.deriv().eval(1.0).to_vec2(), PathSeg::Cubic(c) => { let d = c.deriv().eval(1.0).to_vec2(); if d.hypot() < 1e-9 { c.p3 - c.p2 } else { d } } }; (seg.end(), d) } else { let d = match seg { PathSeg::Line(l) => l.p0 - l.p1, PathSeg::Quad(q) => -q.deriv().eval(0.0).to_vec2(), PathSeg::Cubic(c) => { let d = -c.deriv().eval(0.0).to_vec2(); if d.hypot() < 1e-9 { c.p0 - c.p1 } else { d } } }; (seg.start(), d) }; let len = d.hypot(); if len < 1e-12 { return None; } Some((p, d / len)) } /// The filled arrowhead shape for `cap` at one end of an open path. pub fn arrowhead(path: &BezPath, cap: StrokeCap, weight: f64, at_end: bool) -> Option { let (tip, dir) = path_end(path, at_end)?; let n = Vec2::new(-dir.y, dir.x); let s = (weight * 3.0).max(6.0); let mut p = BezPath::new(); match cap { StrokeCap::TriangleArrow => { p.move_to(tip + dir * (weight * 0.5)); p.line_to(tip - dir * s + n * (s * 0.6)); p.line_to(tip - dir * s - n * (s * 0.6)); p.close_path(); } StrokeCap::ReversedTriangle => { p.move_to(tip - dir * s); p.line_to(tip + n * (s * 0.6)); p.line_to(tip - n * (s * 0.6)); p.close_path(); } StrokeCap::LineArrow => { let mut l = BezPath::new(); l.move_to(tip - dir * s + n * (s * 0.7)); l.line_to(tip); l.line_to(tip - dir * s - n * (s * 0.7)); let props = StrokeProps { weight, cap_start: StrokeCap::Round, cap_end: StrokeCap::Round, join: StrokeJoin::Round, ..StrokeProps::default() }; return Some(stroke_center(&l, weight, &props)); } StrokeCap::CircleFilled => { p = kurbo::Circle::new(tip, s * 0.4).to_path(0.05); } StrokeCap::DiamondFilled => { let r = s * 0.5; p.move_to(tip + dir * r); p.line_to(tip + n * r); p.line_to(tip - dir * r); p.line_to(tip - n * r); p.close_path(); } _ => return None, } Some(p) } /// Per-side stroke of a rectangle `[top, right, bottom, left]`, painted inside/center/outside. pub fn rect_side_strokes(w: f64, h: f64, sides: [f64; 4], align: StrokeAlign) -> BezPath { let [t, r, b, l] = sides.map(|v| if v.is_finite() { v.max(0.0) } else { 0.0 }); let f = match align { StrokeAlign::Inside => 0.0, StrokeAlign::Center => 0.5, StrokeAlign::Outside => 1.0, }; let rect = |x0: f64, y0: f64, x1: f64, y1: f64| figcraft_geom::Rect::new(x0, y0, x1, y1).to_path(0.1); let mut p = BezPath::new(); // Outer box edges. let (ox0, oy0, ox1, oy1) = (-l * f, -t * f, w + r * f, h + b * f); if t > 0.0 { p.extend(rect(ox0, oy0, ox1, oy0 + t).elements().iter().copied()); } if b > 0.0 { p.extend(rect(ox0, oy1 - b, ox1, oy1).elements().iter().copied()); } if l > 0.0 { p.extend(rect(ox0, oy0 + t, ox0 + l, oy1 - b).elements().iter().copied()); } if r > 0.0 { p.extend(rect(ox1 - r, oy0 + t, ox1, oy1 - b).elements().iter().copied()); } p } #[cfg(test)] mod tests { use super::*; use figcraft_geom::Rect; fn sq(x: f64, y: f64, s: f64) -> BezPath { Rect::new(x, y, x + s, y + s).to_path(0.1) } fn area_eo(p: &BezPath) -> f64 { // Sum of absolute contour areas with even-odd nesting approximated by signed area sum. p.area().abs() } #[test] fn a_panic_in_the_sweep_is_bad_input() { let r: Result<(), PathOpsError> = sweep(|| panic!("sweep bug")); assert!(matches!(r, Err(PathOpsError::BadInput))); assert!(matches!(sweep(|| Ok(1)), Ok(1))); } #[test] fn union_intersect_subtract_exclude() { let a = sq(0.0, 0.0, 10.0); let b = sq(5.0, 5.0, 10.0); let u = boolean(&[a.clone(), b.clone()], BoolOp::Union).unwrap(); assert!((area_eo(&u) - 175.0).abs() < 0.5, "{}", area_eo(&u)); let i = boolean(&[a.clone(), b.clone()], BoolOp::Intersect).unwrap(); assert!((area_eo(&i) - 25.0).abs() < 0.5); let s = boolean(&[a.clone(), b.clone()], BoolOp::Subtract).unwrap(); assert!((area_eo(&s) - 75.0).abs() < 0.5); let x = boolean(&[a, b], BoolOp::Exclude).unwrap(); let bb = x.bounding_box(); assert_eq!((bb.x0, bb.y0, bb.x1, bb.y1), (0.0, 0.0, 15.0, 15.0)); } #[test] fn arrangement_faces() { // Two overlapping squares: A only, B only, both. let f = faces(&[(sq(0.0, 0.0, 10.0), false), (sq(5.0, 5.0, 10.0), false)]).unwrap(); let mut got: Vec<(Vec, i64)> = f.iter().map(|x| (x.cover.clone(), x.path.area().abs().round() as i64)).collect(); got.sort(); assert_eq!(got, vec![(vec![0], 75), (vec![0, 1], 25), (vec![1], 75)]); // Uniting faces dissolves their shared edges. let u = union_faces(f.iter().map(|x| &x.path)).unwrap(); assert!((u.area().abs() - 175.0).abs() < 1e-6); assert_eq!(u.elements().iter().filter(|e| matches!(e, PathEl::MoveTo(_))).count(), 1); // A square inside a ring (even-odd): the ring, the square, and the gap between them is // not covered; the square's area under the ring's hole is a face of its own. let mut ring = sq(0.0, 0.0, 30.0); ring.extend(sq(10.0, 10.0, 10.0).elements().iter().copied()); let f = faces(&[(ring, true), (sq(12.0, 12.0, 4.0), false)]).unwrap(); let mut got: Vec<(Vec, i64)> = f.iter().map(|x| (x.cover.clone(), x.path.area().abs().round() as i64)).collect(); got.sort(); assert_eq!(got, vec![(vec![0], 800), (vec![1], 16)]); // Two overlapping circles: three faces with curved edges. let c = |x: f64| kurbo::Circle::new((x, 0.0), 10.0).to_path(0.01); let f = faces(&[(c(0.0), false), (c(10.0), false)]).unwrap(); assert_eq!(f.len(), 3); assert!(f.iter().all(|x| x.path.elements().iter().any(|e| matches!(e, PathEl::CurveTo(..))))); // Hostile and empty input. let mut bad = BezPath::new(); bad.move_to((f64::NAN, 0.0)); bad.line_to((1.0, 1.0)); assert!(faces(&[(bad, false)]).is_err()); assert!(faces(&[]).unwrap().is_empty()); assert!(faces(&vec![(sq(0.0, 0.0, 1.0), false); MAX_ARRANGEMENT_INPUTS + 1]).is_err()); } #[test] fn hostile_inputs() { let mut bad = BezPath::new(); bad.move_to((f64::NAN, 0.0)); bad.line_to((1.0, 1.0)); assert!(boolean(&[bad, sq(0.0, 0.0, 1.0)], BoolOp::Union).is_err()); assert!(boolean(&[], BoolOp::Union).unwrap().elements().is_empty()); let _ = stroke_outline(&sq(0.0, 0.0, 10.0), &StrokeProps { weight: f64::INFINITY, ..Default::default() }, true); } #[test] fn stroke_alignment_bounds() { let r = sq(0.0, 0.0, 100.0); let props = StrokeProps { weight: 10.0, align: StrokeAlign::Inside, ..Default::default() }; let inside = stroke_outline(&r, &props, true); let b = inside.bounding_box(); assert!(b.x0 >= -0.01 && b.x1 <= 100.01, "{b:?}"); let outside = stroke_outline(&r, &StrokeProps { align: StrokeAlign::Outside, ..props.clone() }, true); let b = outside.bounding_box(); assert!((b.x0 + 10.0).abs() < 0.01 && (b.x1 - 110.0).abs() < 0.01, "{b:?}"); let center = stroke_outline(&r, &StrokeProps { align: StrokeAlign::Center, ..props }, true); let b = center.bounding_box(); assert!((b.x0 + 5.0).abs() < 0.01); } #[test] fn arrows_on_open_paths() { let mut line = BezPath::new(); line.move_to((0.0, 0.0)); line.line_to((100.0, 0.0)); let props = StrokeProps { weight: 2.0, cap_end: StrokeCap::TriangleArrow, ..Default::default() }; let s = stroke_outline(&line, &props, false); assert!(s.bounding_box().height() > 4.0); assert!(arrowhead(&BezPath::new(), StrokeCap::LineArrow, 1.0, true).is_none()); } #[test] fn equal_point_joins_keep_the_layer_stroke_and_differing_ones_apply() { let mut path = BezPath::new(); path.move_to((0.0, 0.0)); path.line_to((10.0, 10.0)); path.line_to((20.0, 0.0)); let net = VectorNetwork { vertices: vec![ figcraft_doc::Vertex { cap: Some(StrokeCap::Square), ..figcraft_doc::Vertex::new(0.0, 0.0) }, figcraft_doc::Vertex { x: 10.0, y: 10.0, radius: 2.0, join: Some(StrokeJoin::Miter), ..figcraft_doc::Vertex::new(10.0, 10.0) }, figcraft_doc::Vertex { cap: Some(StrokeCap::Square), ..figcraft_doc::Vertex::new(20.0, 0.0) }, ], segments: vec![figcraft_doc::Segment::line(0, 1), figcraft_doc::Segment::line(1, 2)], ..Default::default() }; let props = StrokeProps { weight: 4.0, ..Default::default() }; let inherited = stroke_outline_of(&path, &props, false, Some(&net)); let mut without_join = net.clone(); without_join.vertices[1].join = None; let baseline = stroke_outline_of(&path, &props, false, Some(&without_join)); assert_eq!(inherited, baseline); let different_layer = StrokeProps { join: StrokeJoin::Bevel, ..props }; let explicit = stroke_outline_of(&path, &different_layer, false, Some(&net)); let layer_only = stroke_outline_of(&path, &different_layer, false, Some(&without_join)); assert_ne!(explicit, layer_only); } #[test] fn equal_joins_do_not_break_closed_stroke_runs() { let path = sq(0.0, 0.0, 20.0); let mut net = VectorNetwork::from_points(&[Point::new(0.0, 0.0), Point::new(20.0, 0.0), Point::new(20.0, 20.0), Point::new(0.0, 20.0)], true); for vertex in &mut net.vertices { vertex.join = Some(StrokeJoin::Round); } let props = StrokeProps { join: StrokeJoin::Round, weight: 4.0, ..Default::default() }; let styled = stroke_outline_of(&path, &props, true, Some(&net)); for vertex in &mut net.vertices { vertex.join = None; } let inherited = stroke_outline_of(&path, &props, true, Some(&net)); assert_eq!(styled, inherited); } #[test] fn dashes() { let mut line = BezPath::new(); line.move_to((0.0, 0.0)); line.line_to((100.0, 0.0)); let props = StrokeProps { weight: 2.0, dashes: vec![10.0, 10.0], align: StrokeAlign::Center, ..Default::default() }; let s = stroke_center(&line, 2.0, &props); assert!((s.area().abs() - 100.0).abs() < 2.0, "{}", s.area()); } }