Fix #374: Shape Builder cuts regions with open paths and lines

The Shape Builder only used the filled areas of the selected paths, so a
stroke-only line or open path across a shape did nothing. Like the
reference app's Shape Builder, open paths now act as cutting edges:

- pathops::shape_builder: with an open path in the selection, the
  regions are the Live Paint planar map's faces (every path an edge), so a
  line across a shape splits it and lines can enclose a region of their
  own; it also returns each open path cut where other paths meet it. Closed
  shapes alone, more than SHAPE_BUILDER_MAX_SEGMENTS segments, or a map
  that can't be built fall back to the filled-area arrangement.
- Filled open paths count as closed (an invisible closing edge) where that
  encloses an area; unfilled open paths and straight lines stay edges.
- shapeBuilder.merge: merging or deleting regions on both sides of a line
  piece removes that piece (the line is split, its other pieces kept); an
  area only lines enclose takes the current fill and the front-most
  object's look. Alt (erase) within `tolerance` of a line piece deletes it.
  Returns `lines` (pieces deleted).
- shapeBuilder.regions also lists the line pieces.
- The tool shares BuilderMap/Touched with the command, highlights the line
  piece under the pointer while Alt is held and passes its tolerance.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

crates/tools/src/builder.rs

@@ -1,7 +1,8 @@
 //! Shape Builder (Shift+M), Live Paint Bucket (K) and Live Paint Selection (Shift+L).
 //!
 //! The tools only emit commands (`shapeBuilder.merge`, `livePaint.fill`, `livePaint.strokeEdge`,
-//! `select.*`); the planar arrangement comes from `vectorcraft_pathops::regions`.
+//! `select.*`); the planar arrangement comes from `vectorcraft_pathops::shape_builder` (Shape
+//! Builder) and `vectorcraft_pathops::live_paint` (Live Paint).
 //!
 //! **Live Paint groups** are ordinary groups (no special node kind): the group's name starts with
 //! [`LIVE_PAINT_PREFIX`]; its first child is a hidden group named [`SOURCES_NAME`] holding the
@@ -151,6 +152,141 @@ pub fn shapes_for<'a>(doc: &'a Document, roots: &[NodeId]) -> (Vec<po::Shape>, V
     (shapes, used)
 }
 
+/// Shape Builder inputs: [`shapes_for`], with the open subpaths of filled paths closed where that
+/// encloses an area (the fill bounds a region, as if an invisible edge closed it). Unfilled open
+/// paths and straight lines stay open and cut the regions they cross.
+fn shape_builder_shapes<'a>(doc: &'a Document, roots: &[NodeId]) -> (Vec<po::Shape>, Vec<&'a Node>) {
+    let (mut shapes, leaves) = shapes_for(doc, roots);
+    for (s, l) in shapes.iter_mut().zip(&leaves) {
+        if l.appearance.fill_paint().is_none() {
+            continue;
+        }
+        for sp in s.path.subpaths.iter_mut().filter(|sp| !sp.closed) {
+            let mut closed = sp.clone();
+            closed.closed = true;
+            let mut bp = BezPath::new();
+            closed.to_bezpath_into(&mut bp);
+            let size = bp.bounding_box().size();
+            sp.closed = bp.area().abs() > 1e-9 * (size.width * size.width + size.height * size.height);
+        }
+    }
+    (shapes, leaves)
+}
+
+/// A planar-map face with its outline and bounds, ready for hit tests.
+pub type Face = (po::Region, BezPath, Rect);
+
+fn faces_of(regions: Vec<po::Region>) -> Vec<Face> {
+    regions
+        .into_iter()
+        .filter_map(|r| {
+            let bp = r.path.to_bezpath();
+            let b = r.path.bounds()?;
+            Some((r, bp, b))
+        })
+        .collect()
+}
+
+/// The Shape Builder's planar map of a selection.
+#[derive(Default)]
+pub struct BuilderMap {
+    /// The inputs, back → front (see [`po::shape_builder`]).
+    pub shapes: Vec<po::Shape>,
+    pub regions: Vec<Face>,
+    /// Pieces of the unfilled open paths, keyed by input index, with their bounds.
+    pub lines: Vec<(po::Shape, Rect)>,
+}
+
+/// What a Shape Builder gesture touches at a point.
+#[derive(Clone, Copy, Debug, PartialEq, Eq)]
+pub enum Hit {
+    Region(usize),
+    Line(usize),
+}
+
+impl BuilderMap {
+    /// The map of `roots` (sorted back → front), with the leaves the inputs came from.
+    pub fn new<'a>(doc: &'a Document, roots: &[NodeId]) -> (Self, Vec<&'a Node>) {
+        let (shapes, leaves) = shape_builder_shapes(doc, roots);
+        if shapes.is_empty() {
+            return (Self::default(), leaves);
+        }
+        let (regions, lines) = po::shape_builder(&shapes);
+        let lines = lines.into_iter().filter_map(|l| Some((l.path.bounds()?, l))).map(|(b, l)| (l, b)).collect();
+        (Self { shapes, regions: faces_of(regions), lines }, leaves)
+    }
+
+    /// The region containing `p`.
+    pub fn region_at(&self, p: Point) -> Option<usize> {
+        self.regions.iter().position(|(_, bp, b)| b.contains(p) && bp.winding(p) != 0)
+    }
+
+    /// The line piece nearest `p`, within `tol`.
+    pub fn line_near(&self, p: Point, tol: f64) -> Option<usize> {
+        let mut best: Option<(f64, usize)> = None;
+        for (i, (l, b)) in self.lines.iter().enumerate() {
+            if b.inflate(tol, tol).contains(p)
+                && let Some((.., d)) = l.path.nearest(p)
+                && d <= tol
+                && best.is_none_or(|b| d < b.0)
+            {
+                best = Some((d, i));
+            }
+        }
+        best.map(|b| b.1)
+    }
+
+    /// What a gesture at `p` touches: with `line_tol` (erasing), a line piece that close, else the
+    /// region under it.
+    pub fn hit(&self, p: Point, line_tol: Option<f64>) -> Option<Hit> {
+        line_tol.and_then(|t| self.line_near(p, t)).map(Hit::Line).or_else(|| self.region_at(p).map(Hit::Region))
+    }
+
+    /// Does line piece `i` run between two of `regions` (an edge that merging or deleting them
+    /// removes)?
+    pub fn line_between(&self, i: usize, regions: &[usize]) -> bool {
+        let Some(sp) = self.lines.get(i).and_then(|(l, _)| l.path.subpaths.first()) else { return false };
+        let n = sp.segment_count();
+        if n == 0 {
+            return false;
+        }
+        let c = sp.segment(n / 2);
+        use kurbo::{ParamCurve as _, ParamCurveDeriv as _};
+        let (m, d) = (c.eval(0.5), c.deriv().eval(0.5).to_vec2());
+        let len = d.hypot();
+        if !(len.is_finite() && len > 0.0) {
+            return false;
+        }
+        // A little to each side: inside the faces next to it, which share it exactly.
+        let off = d.turn_90() * (0.05f64.min(0.05 * c.p0.distance(c.p3)).max(1e-6) / len);
+        [m + off, m - off].into_iter().all(|q| self.region_at(q).is_some_and(|r| regions.contains(&r)))
+    }
+}
+
+/// The regions and line pieces a Shape Builder gesture has touched, in the order touched.
+#[derive(Clone, Debug, Default, PartialEq)]
+pub struct Touched {
+    pub regions: Vec<usize>,
+    pub lines: Vec<usize>,
+}
+
+impl Touched {
+    pub fn add(&mut self, hit: Option<Hit>) {
+        let (list, i) = match hit {
+            Some(Hit::Region(i)) => (&mut self.regions, i),
+            Some(Hit::Line(i)) => (&mut self.lines, i),
+            None => return,
+        };
+        if !list.contains(&i) {
+            list.push(i);
+        }
+    }
+
+    pub fn is_empty(&self) -> bool {
+        self.regions.is_empty() && self.lines.is_empty()
+    }
+}
+
 /// Selected roots sorted back → front in document order.
 pub fn sorted_roots(doc: &Document, ids: &[NodeId]) -> Vec<NodeId> {
     let mut v: Vec<(Vec<usize>, NodeId)> = ids.iter().filter_map(|id| doc.index_path(*id).map(|p| (p, *id))).collect();
@@ -238,13 +374,12 @@ pub fn hatch(path: &BezPath, gap: f64) -> BezPath {
     out
 }
 
-/// Regions of the current selection, cached by document identity and selection.
+/// The planar map of the current selection, cached by document identity and selection.
 #[derive(Default)]
 struct RegionCache {
     key: Option<(usize, Vec<NodeId>)>,
-    regions: Vec<(po::Region, BezPath, Rect)>,
-    /// Live Paint faces (every path an edge, open ones included) rather than Shape Builder
-    /// regions (the filled areas of the shapes).
+    map: BuilderMap,
+    /// Live Paint faces (every path an edge, filled or not) rather than Shape Builder regions.
     live: bool,
 }
 
@@ -252,58 +387,57 @@ impl RegionCache {
     fn live_paint() -> Self {
         Self { live: true, ..Default::default() }
     }
-    fn get(&mut self, cx: &ToolContext) -> &[(po::Region, BezPath, Rect)] {
+    fn get(&mut self, cx: &ToolContext) -> &BuilderMap {
         let key = (cx.doc as *const Document as usize, cx.selection.objects.clone());
         if self.key.as_ref() != Some(&key) {
             let roots = sorted_roots(cx.doc, &cx.selection.objects);
-            let (shapes, _) = shapes_for(cx.doc, &roots);
-            self.regions = if shapes.is_empty() {
-                vec![]
+            self.map = if self.live {
+                let (shapes, _) = shapes_for(cx.doc, &roots);
+                let regions = if shapes.is_empty() { vec![] } else { faces_of(po::live_paint(&shapes).0) };
+                BuilderMap { regions, ..Default::default() }
             } else {
-                let regions = if self.live { po::live_paint(&shapes).0 } else { po::regions(&shapes) };
-                regions
-                    .into_iter()
-                    .filter_map(|r| {
-                        let bp = r.path.to_bezpath();
-                        let b = r.path.bounds()?;
-                        Some((r, bp, b))
-                    })
-                    .collect()
+                BuilderMap::new(cx.doc, &roots).0
             };
             self.key = Some(key);
         }
-        &self.regions
+        &self.map
     }
     fn at(&mut self, cx: &ToolContext, p: Point) -> Option<usize> {
-        self.get(cx).iter().position(|(_, bp, b)| b.contains(p) && bp.winding(p) != 0)
+        self.get(cx).region_at(p)
     }
 }
 
 // ---------- Shape Builder ----------
 
-/// Shape Builder tool: drag across regions to merge them, Alt-drag to delete them.
+/// Shape Builder tool: drag across regions to merge them, Alt-drag to delete them (and the pieces
+/// of open paths it passes over).
 #[derive(Default)]
 pub struct ShapeBuilderTool {
     cache: RegionCache,
-    hover: Option<usize>,
+    hover: Option<Hit>,
     points: Vec<Point>,
-    touched: Vec<usize>,
+    touched: Touched,
     dragging: bool,
     alt: bool,
 }
 
+/// How close (screen px) the pointer must come to a line piece to delete it.
+const LINE_TOL_PX: f64 = 4.0;
+
 impl ShapeBuilderTool {
+    fn line_tol(cx: &ToolContext, alt: bool) -> Option<f64> {
+        alt.then(|| cx.tol(LINE_TOL_PX))
+    }
+
     fn touch(&mut self, cx: &ToolContext, from: Option<Point>, to: Point) {
         let pts = match from {
             Some(a) => sample_polyline(&[a, to], cx.tol(2.0)),
             None => vec![to],
         };
+        let tol = Self::line_tol(cx, self.alt);
         for p in pts {
-            if let Some(i) = self.cache.at(cx, p)
-                && !self.touched.contains(&i)
-            {
-                self.touched.push(i);
-            }
+            let hit = self.cache.get(cx).hit(p, tol);
+            self.touched.add(hit);
         }
     }
 }
@@ -317,7 +451,7 @@ impl Tool for ShapeBuilderTool {
         let p = ev.pos;
         match ev.kind {
             PointerKind::Move => {
-                self.hover = self.cache.at(cx, p);
+                self.hover = self.cache.get(cx).hit(p, Self::line_tol(cx, ev.mods.alt));
                 vec![]
             }
             PointerKind::Down => {
@@ -327,7 +461,7 @@ impl Tool for ShapeBuilderTool {
                 self.dragging = true;
                 self.alt = ev.mods.alt;
                 self.points = vec![p];
-                self.touched.clear();
+                self.touched = Touched::default();
                 self.touch(cx, None, p);
                 vec![]
             }
@@ -353,7 +487,12 @@ impl Tool for ShapeBuilderTool {
                 self.cache.key = None;
                 let roots = sorted_roots(cx.doc, &cx.selection.objects);
                 let pts: Vec<Value> = points.iter().map(|q| json!([q.x, q.y])).collect();
-                vec![Action::Exec("shapeBuilder.merge".into(), json!({ "ids": json_ids(&roots), "points": pts, "erase": self.alt || ev.mods.alt }))]
+                let erase = self.alt || ev.mods.alt;
+                let mut params = json!({ "ids": json_ids(&roots), "points": pts, "erase": erase });
+                if let Some(t) = Self::line_tol(cx, erase) {
+                    params["tolerance"] = json!(t);
+                }
+                vec![Action::Exec("shapeBuilder.merge".into(), params)]
             }
             _ => vec![],
         }
@@ -361,13 +500,26 @@ impl Tool for ShapeBuilderTool {
 
     fn overlays(&self, cx: &ToolContext) -> Vec<Overlay> {
         let mut out = vec![];
-        let regions = &self.cache.regions;
+        let map = &self.cache.map;
         let color = if self.dragging && self.alt { HIGHLIGHT_RED } else { HATCH };
-        let show: Vec<usize> = if self.dragging { self.touched.clone() } else { self.hover.into_iter().collect() };
-        for i in show {
-            if let Some((_, bp, _)) = regions.get(i) {
-                out.push(Overlay::Path { path: hatch(bp, cx.tol(4.0)), color, width: 1.0, dashed: false });
-                out.push(Overlay::Path { path: bp.clone(), color, width: 1.0, dashed: false });
+        let show: Vec<Hit> = if self.dragging {
+            self.touched.regions.iter().map(|&i| Hit::Region(i)).chain(self.touched.lines.iter().map(|&i| Hit::Line(i))).collect()
+        } else {
+            self.hover.into_iter().collect()
+        };
+        for hit in show {
+            match hit {
+                Hit::Region(i) => {
+                    if let Some((_, bp, _)) = map.regions.get(i) {
+                        out.push(Overlay::Path { path: hatch(bp, cx.tol(4.0)), color, width: 1.0, dashed: false });
+                        out.push(Overlay::Path { path: bp.clone(), color, width: 1.0, dashed: false });
+                    }
+                }
+                Hit::Line(i) => {
+                    if let Some((l, _)) = map.lines.get(i) {
+                        out.push(Overlay::Path { path: l.path.to_bezpath(), color: HIGHLIGHT_RED, width: 3.0, dashed: false });
+                    }
+                }
             }
         }
         if self.dragging && self.points.len() > 1 {
@@ -434,6 +586,7 @@ fn lp_overlays(h: &LpHover, cache: &RegionCache) -> Vec<Overlay> {
         LpHover::None => vec![],
         LpHover::Part(bp) => vec![Overlay::Path { path: bp.clone(), color: HIGHLIGHT_RED, width: 4.0, dashed: false }],
         LpHover::Region(i) => cache
+            .map
             .regions
             .get(*i)
             .map(|(_, bp, _)| vec![Overlay::Path { path: bp.clone(), color: HIGHLIGHT_RED, width: 4.0, dashed: false }])
@@ -623,7 +776,7 @@ mod tests {
         let mut t = ShapeBuilderTool::default();
         t.pointer(&cx, &ev(PointerKind::Down, 25.0, 50.0));
         t.pointer(&cx, &ev(PointerKind::Drag, 75.0, 50.0));
-        assert_eq!(t.touched.len(), 2);
+        assert_eq!(t.touched.regions.len(), 2);
         assert!(t.busy());
         let acts = t.pointer(&cx, &ev(PointerKind::Up, 75.0, 50.0));
         let Action::Exec(id, v) = &acts[0] else { panic!("{acts:?}") };