Sheet metal: a cut names the pieces it parts from the base (#1338)

A sheet-metal cut that parts pieces from the base names them, and the guide explains it.

crates/doc/src/eval.rs

@@ -2276,17 +2276,24 @@ fn hole_feature_tools(vals: &BTreeMap<String, Value>, st: &ModelState, f: &Featu
 /// counterbore) is machined like the equivalent extrude cut, so the sheet keeps it as a cut-out
 /// or pocket of its flat pattern (#560). Returns the sheet bodies it machined; none, with the
 /// model as it was, when a tool that meets a sheet can't be kept that way (the ordinary cut then
-/// refuses it).
+/// refuses it). Pieces the hole parts from a sheet's base are named in `warning`.
-fn sheet_hole_cut(st: &mut ModelState, f: &Feature, tools: &[(Traced, Option<more::PrimitivePrism>)]) -> Result<Vec<String>> {
+fn sheet_hole_cut(
+    st: &mut ModelState,
+    f: &Feature,
+    tools: &[(Traced, Option<more::PrimitivePrism>)],
+    warning: &mut Option<String>,
+) -> Result<Vec<String>> {
     if st.sheets.is_empty() {
         return Ok(Vec::new());
     }
     let saved = (st.sheets.clone(), st.bodies.clone());
     let mut handled: Vec<String> = Vec::new();
+    // Noted only when every tool was machined here.
+    let mut parted = None;
     for (tool, prism) in tools {
         let tool = &tool.body;
         let done = match prism {
-            Some(prism) => match more::sheet_primitive_cut(f, st, tool, *prism, Operation::Cut, true) {
+            Some(prism) => match more::sheet_primitive_cut(f, st, tool, *prism, Operation::Cut, true, &mut parted) {
                 Ok(done) => done,
                 // Drilled along a panel (into a rim) the hole is no flat cut-out: a bore of
                 // that panel, when it stays inside it.
@@ -2322,6 +2329,9 @@ fn sheet_hole_cut(st: &mut ModelState, f: &Feature, tools: &[(Traced, Option<mor
             }
         }
     }
+    if let Some(note) = parted {
+        append_warning(warning, note);
+    }
     Ok(handled)
 }
 
@@ -4045,7 +4055,7 @@ fn eval_feature(doc: &Document, vals: &BTreeMap<String, Value>, f: &Feature, st:
             // Cuts through sheet metal become cut-outs of its flat pattern.
             if matches!(operation, Operation::Cut | Operation::Intersect) && matches!(f.kind, FeatureKind::Extrude { .. }) && !st.sheets.is_empty() {
                 let bodies: Vec<Body> = tools.iter().map(|t| t.body.clone()).collect();
-                let handled = more::sheet_cut(f, st, &bodies, targets, constructor.as_ref())?;
+                let handled = more::sheet_cut(f, st, &bodies, targets, constructor.as_ref(), warning)?;
                 if !handled.is_empty() {
                     return apply_beside_sheet_cut(st, f, tools, *operation, targets, &handled);
                 }
@@ -4055,7 +4065,7 @@ fn eval_feature(doc: &Document, vals: &BTreeMap<String, Value>, f: &Feature, st:
         FeatureKind::Hole { thread, diameter, .. } => {
             let (spots, dir) = hole_spots(st, f)?;
             let tools = hole_feature_tools(vals, st, f)?;
-            let handled = sheet_hole_cut(st, f, &tools)?;
+            let handled = sheet_hole_cut(st, f, &tools, warning)?;
             let tools: Vec<Traced> = tools.into_iter().map(|(tool, _)| tool).collect();
             if handled.is_empty() {
                 apply_traced(st, f, tools, Operation::Cut, &[])?;
@@ -4445,7 +4455,7 @@ fn eval_feature(doc: &Document, vals: &BTreeMap<String, Value>, f: &Feature, st:
             let corner = point(vals, corner)?;
             let b = kernel::box_solid(corner, corner + s)?;
             let b = if matches!(operation, Operation::NewBody | Operation::Join) { b.with_box_certificate(f.id)? } else { b };
-            let handled = more::sheet_primitive_cut(f, st, &b, more::PrimitivePrism::Box { lo: corner, hi: corner + s }, *operation, false)?;
+            let handled = more::sheet_primitive_cut(f, st, &b, more::PrimitivePrism::Box { lo: corner, hi: corner + s }, *operation, false, warning)?;
             let tools = vec![crate::lineage::box_tool(b)];
             if !handled.is_empty() {
                 return apply_beside_sheet_cut(st, f, tools, *operation, &[], &handled);
@@ -4457,7 +4467,7 @@ fn eval_feature(doc: &Document, vals: &BTreeMap<String, Value>, f: &Feature, st:
             let b = kernel::cylinder(base, *axis, radius, height)?;
             let b = if matches!(operation, Operation::NewBody | Operation::Join) { b.with_cylinder_certificate(f.id)? } else { b };
             let prism = more::PrimitivePrism::Cylinder { base, axis: *axis, radius, height };
-            let handled = more::sheet_primitive_cut(f, st, &b, prism, *operation, false)?;
+            let handled = more::sheet_primitive_cut(f, st, &b, prism, *operation, false, warning)?;
             let tools = vec![crate::lineage::cylinder_tool(b)];
             if !handled.is_empty() {
                 return apply_beside_sheet_cut(st, f, tools, *operation, &[], &handled);

crates/doc/src/eval_more.rs

@@ -764,6 +764,7 @@ pub(super) fn sheet_cut(
     tools: &[Body],
     targets: &[String],
     constructor: Option<&ExtrudeConstructor>,
+    warning: &mut Option<String>,
 ) -> Result<Vec<String>> {
     let FeatureKind::Extrude { sketch, profiles, operation, extent, .. } = &f.kind else { return Ok(Vec::new()) };
     if extent.taper.is_some() || !any_eligible_sheet(f, st, targets) {
@@ -780,7 +781,7 @@ pub(super) fn sheet_cut(
         .flat_map(|l| ss.sketch.link_curves(&l.id))
         .flat_map(|ci| ss.sketch.exact_segs(ci).unwrap_or_else(|| ss.sketch.segs(ci)))
         .collect();
-    sheet_prism_cut(f, st, &ss.plane, &regions, *operation, tools, targets, constructor, extent.to.is_some(), &text)
+    sheet_prism_cut(f, st, &ss.plane, &regions, *operation, tools, targets, constructor, extent.to.is_some(), &text, warning)
 }
 
 /// Whether a cut of `f` with these targets (else its participants, else its component's
@@ -812,6 +813,7 @@ pub(super) fn sheet_primitive_cut(
     prism: PrimitivePrism,
     operation: Operation,
     drill: bool,
+    warning: &mut Option<String>,
 ) -> Result<Vec<String>> {
     if !matches!(operation, Operation::Cut | Operation::Intersect) || !any_eligible_sheet(f, st, &[]) {
         return Ok(Vec::new());
@@ -836,7 +838,7 @@ pub(super) fn sheet_primitive_cut(
     let Some(normal) = normal else { return Ok(Vec::new()) };
     let Some((plane, region, interval)) = prism.along(normal) else { return Ok(Vec::new()) };
     let tools = kernel::extrude(&plane, std::slice::from_ref(&region), interval.0, interval.1)?;
-    sheet_prism_cut(f, st, &plane, std::slice::from_ref(&region), operation, &tools, &[], None, false, &[])
+    sheet_prism_cut(f, st, &plane, std::slice::from_ref(&region), operation, &tools, &[], None, false, &[], warning)
 }
 
 /// A hole's straight drill along a panel of a sheet (into its rim), kept as a bore of each
@@ -941,6 +943,7 @@ fn sheet_prism_cut(
     constructor: Option<&ExtrudeConstructor>,
     footprints_bound: bool,
     text: &[Seg2],
+    warning: &mut Option<String>,
 ) -> Result<Vec<String>> {
     let n = plane.normal();
     let mut work = sheet::FlatWork::new();
@@ -986,6 +989,7 @@ fn sheet_prism_cut(
         Vec::new()
     };
     let mut plans = Vec::new();
+    let mut notes = Vec::new();
     'sheets: for original in &st.sheets {
         if !sheet_eligible(f, st, targets, original) {
             continue;
@@ -1133,16 +1137,24 @@ fn sheet_prism_cut(
         if !modeled {
             super::sheet_boolean_unchanged(&mb.body, tools, operation)?;
             plans.push((sh.body.clone(), Some((sh, mb.body.clone()))));
-        } else if sh.flat_material()?.is_empty() {
-            // Empty exact material removes geometry and metadata together. Budget or
-            // topology errors propagate; they are never mistaken for an empty blank.
-            plans.push((sh.body.clone(), None));
         } else {
-            let body = sh.solid()?;
+            let material = sh.flat_material()?;
-            plans.push((sh.body.clone(), Some((sh, body))));
+            if material.is_empty() {
+                // Empty exact material removes geometry and metadata together. Budget or
+                // topology errors propagate; they are never mistaken for an empty blank.
+                plans.push((sh.body.clone(), None));
+            } else {
+                // Every piece the cut leaves stays; the ones it parts from the base are named.
+                notes.extend(parted_note(&sh, &material, original));
+                let body = sh.solid()?;
+                plans.push((sh.body.clone(), Some((sh, body))));
+            }
         }
     }
     let handled = plans.iter().map(|(name, _)| name.clone()).collect();
+    if !notes.is_empty() {
+        append_warning(warning, notes.join("; "));
+    }
     for (name, result) in plans {
         match result {
             Some((sh, body)) => {
@@ -1163,6 +1175,35 @@ fn sheet_prism_cut(
     Ok(handled)
 }
 
+/// A cut's note on the pieces it parted from the base of `sh` (see
+/// [`sheet::SheetBody::parted_from_base`]; `material` is the sheet's flat material after the cut,
+/// `before` the sheet before it): how many, their area and where they lie in the flat pattern.
+/// The pieces stay, as every piece a cut leaves does. None when nothing is parted, and when the
+/// pieces can't be worked out: the note is no reason for a cut to fail.
+fn parted_note(sh: &sheet::SheetBody, material: &[Region2], before: &sheet::SheetBody) -> Option<String> {
+    let pieces = sh.parted_from_base(material, before).ok().filter(|p| !p.is_empty())?;
+    let area: f64 = pieces.iter().map(Region2::area).sum();
+    let at: Vec<String> = pieces
+        .iter()
+        .take(4)
+        .map(|r| {
+            let c = r.interior_point();
+            format!("({:.1}, {:.1})", c.x, c.y)
+        })
+        .collect();
+    let at = at.join(", ");
+    let body = &sh.body;
+    Some(match pieces.len() {
+        1 => format!("1 piece of `{body}` is no longer joined to its base ({area:.2} mm², near {at} in the flat pattern); it is kept"),
+        n => {
+            let more = if n > 4 { format!(" and {} more", n - 4) } else { String::new() };
+            format!(
+                "{n} pieces of `{body}` are no longer joined to its base ({area:.2} mm² in all, near {at}{more} in the flat pattern); they are kept"
+            )
+        }
+    })
+}
+
 /// Outline loops (in `plane` coordinates) of the mesh triangles lying in the plane at distance
 /// `level` from `at` along `n`: the edges used by one of them only, chained.
 fn face_loops(mesh: &solidcraft_geom::Mesh, plane: &Plane, at: Vec3, n: Vec3, level: f64, tol: f64) -> Vec<Vec<Vec2>> {

crates/doc/src/sheet.rs

@@ -31,6 +31,8 @@ const MAX_FLAT_POINTS: usize = 16_384;
 const MAX_FLAT_SAMPLES: usize = 65_536;
 const MAX_FLAT_PIECES: usize = 4096;
 const MAX_FLAT_WORK: usize = 500_000_000;
+/// Pieces of flat material sharing less area than this (mm²) only touch.
+const TOUCH_AREA: f64 = 1e-6;
 
 /// Starts the warning a fold gives when its `fixed` point touches no material: a recompute keeps
 /// the side the point lies on, and the `sheet.fold` command refuses such a point (#263).
@@ -1696,6 +1698,84 @@ impl SheetBody {
         let regions = if cuts.is_empty() { regions } else { material_boolean(&regions, &cuts, kernel::BoolOp::Cut, &mut work)? };
         Ok(regions)
     }
+
+    /// The pieces of flat material that a cut parted from the base: `after` is this sheet's
+    /// [`Self::flat_material`] after the cut, `before` the sheet before it. A piece is parted when
+    /// it holds none of the base panel, lies in a piece that held some before the cut, and no
+    /// other piece surrounds it: a flange cut off along its bend (with any flange on it), the
+    /// part of a ring's inside that lies on a flange's edge, the tip of a flange beyond a cut
+    /// through a closed corner. A ring's island and a letter's counter, inside other material,
+    /// are not counted; nor are pieces an earlier cut parted, nor anything once no piece holds
+    /// the base.
+    pub(crate) fn parted_from_base(&self, after: &[Region2], before: &SheetBody) -> Result<Vec<Region2>> {
+        if after.len() < 2 {
+            return Ok(Vec::new());
+        }
+        let mut work = FlatWork::new();
+        work.charge(after.len().saturating_mul(after.len()))?;
+        let base = [planar_region(&self.base)?];
+        let holds_base = |piece: &Region2, work: &mut FlatWork| -> Result<bool> {
+            let common = material_boolean(std::slice::from_ref(piece), &base, kernel::BoolOp::Intersect, work)?;
+            Ok(common.iter().map(Region2::area).sum::<f64>() > TOUCH_AREA)
+        };
+        // The cheap test first: a piece inside another's outline is an island, whatever it holds.
+        let outlines: Vec<(Vec<Vec2>, Vec2, Vec2)> = after
+            .iter()
+            .map(|r| {
+                let pts = r.outer.polyline(1e-3);
+                let lo = pts.iter().fold(Vec2::new(f64::MAX, f64::MAX), |a, p| Vec2::new(a.x.min(p.x), a.y.min(p.y)));
+                let hi = pts.iter().fold(Vec2::new(f64::MIN, f64::MIN), |a, p| Vec2::new(a.x.max(p.x), a.y.max(p.y)));
+                (pts, lo, hi)
+            })
+            .collect();
+        let (mut open, mut islands) = (Vec::new(), Vec::new());
+        for (i, piece) in after.iter().enumerate() {
+            let p = piece.interior_point();
+            let inside = |(pts, lo, hi): &(Vec<Vec2>, Vec2, Vec2)| (lo.x..=hi.x).contains(&p.x) && (lo.y..=hi.y).contains(&p.y) && point_in(pts, p);
+            if outlines.iter().enumerate().any(|(j, o)| j != i && inside(o)) {
+                islands.push(piece);
+            } else {
+                open.push(piece);
+            }
+        }
+        let (mut joined, mut loose) = (false, Vec::new());
+        for piece in open {
+            if holds_base(piece, &mut work)? {
+                joined = true;
+            } else {
+                loose.push(piece);
+            }
+        }
+        if loose.is_empty() {
+            return Ok(Vec::new());
+        }
+        // The base may be an island itself (a cut all round it).
+        for piece in islands {
+            if joined {
+                break;
+            }
+            joined = holds_base(piece, &mut work)?;
+        }
+        if !joined {
+            return Ok(Vec::new());
+        }
+        // A cut only takes material away: each piece lies in the piece it was part of.
+        let mut held = Vec::new();
+        for piece in before.flat_material()? {
+            if holds_base(&piece, &mut work)? {
+                held.push(piece);
+            }
+        }
+        Ok(loose
+            .into_iter()
+            .filter(|piece| {
+                let p = piece.interior_point();
+                held.iter().any(|h| h.contains(p))
+            })
+            .cloned()
+            .collect())
+    }
+
     /// Outline loops of the flat pattern (flat coordinates): the pieces' edges, shared ones left out.
     pub fn outline(&self) -> Result<Vec<Vec<Vec2>>> {
         if self.flanges.len().saturating_mul(2).saturating_add(1) > MAX_FLAT_PIECES {
@@ -7389,4 +7469,49 @@ mod tests {
             holds_the_flat_material(&s, &what);
         }
     }
+
+    /// The 100 x 60 plate with a 20 mm flange on its y = 0 edge (2.5 mm, R 2.5, K 0.44): in the
+    /// flat the base starts at y = t + R = 5, the bend's zone is (π/2)·(R + K·t) long and the
+    /// flange's panel 20 − 5, so its far edge lies at y = 5 − (π/2)·3.6 − 15.
+    #[test]
+    fn a_cut_names_the_pieces_it_parts_from_the_base_and_no_others() {
+        use std::f64::consts::{FRAC_PI_2, PI};
+        let far = 5.0 - FRAC_PI_2 * (2.5 + 0.44 * 2.5) - 15.0;
+        let mut s = plate(100.0, 60.0);
+        s.add_flange(Vec3::new(50.0, 0.0, 2.5), 20.0, FRAC_PI_2, 2.5, "inside", false).unwrap();
+        let r = |x0: f64, y0: f64, x1: f64, y1: f64| rect(Vec2::new(x0, y0), Vec2::new(x1, y0), Vec2::new(x1, y1), Vec2::new(x0, y1));
+        let ring = |c: Vec2, ro: f64, ri: f64| Region2 { outer: Loop2::circle(c, ro), holes: vec![Loop2::circle(c, ri)] };
+        let parted = |before: &SheetBody, holes: &[Region2]| {
+            let mut after = before.clone();
+            after.holes.extend_from_slice(holes);
+            after.parted_from_base(&after.flat_material().unwrap(), before).unwrap()
+        };
+        // A slot across the flange beside its bend parts the rest of the flange: 100 × (−3 − far).
+        let slot = r(-5.0, -3.0, 105.0, -1.0);
+        let p = parted(&s, std::slice::from_ref(&slot));
+        assert!(p.len() == 1 && (p[0].area() - 100.0 * (-3.0 - far)).abs() < 1e-6, "{p:?}");
+        // So does a ring on the flange's far edge: the half of its inside on the flange, π·2²/2.
+        let p = parted(&s, &[ring(Vec2::new(50.0, far), 4.0, 2.0)]);
+        assert!(p.len() == 1 && (p[0].area() - 2.0 * PI).abs() < 1e-6, "{p:?}");
+        // A ring's island, on the base or on the flange, has material round it; a strip across the
+        // whole sheet leaves two halves that each keep their part of the base. None is named.
+        for holes in [ring(Vec2::new(50.0, 30.0), 10.0, 5.0), ring(Vec2::new(50.0, -9.0), 4.0, 2.0), r(45.0, -30.0, 55.0, 70.0)] {
+            assert!(parted(&s, std::slice::from_ref(&holes)).is_empty(), "{holes:?}");
+        }
+        // Pieces an earlier cut parted are not named again, nor when a later cut splits them.
+        let mut cut = s.clone();
+        cut.holes.push(slot);
+        for holes in [Region2 { outer: Loop2::circle(Vec2::new(30.0, 30.0), 4.0), holes: vec![] }, r(45.0, -30.0, 55.0, -2.0)] {
+            assert!(parted(&cut, std::slice::from_ref(&holes)).is_empty(), "{holes:?}");
+        }
+        // Nothing is named once no piece holds the base: a cut that takes the base and both bends
+        // of a sheet with flanges on two sides leaves the two flanges.
+        let mut two = plate(100.0, 60.0);
+        two.add_flanges(&[Vec3::new(50.0, 0.0, 2.5), Vec3::new(50.0, 60.0, 2.5)], 20.0, FRAC_PI_2, 2.5, "inside", false).unwrap();
+        let mut after = two.clone();
+        after.holes.push(r(-5.0, -3.0, 105.0, 63.0));
+        let material = after.flat_material().unwrap();
+        assert_eq!(material.len(), 2);
+        assert!(after.parted_from_base(&material, &two).unwrap().is_empty());
+    }
 }

crates/engine/src/cmd/sheet_tests.rs

@@ -4147,3 +4147,149 @@ fn perforate_supports_a_square_pattern_and_refuses_impossible_values() {
         assert!(s.execute("sheet.perforate", &bad).is_err(), "{bad} must be refused");
     }
 }
+
+/// A 100 x 60 tray with one 45° flange 40 high on its y = 0 edge (2.5 mm, R 2.5, K 0.44), and on
+/// it a return 10 high when asked. Returns the far edge of the last panel in the flat pattern:
+/// the base starts at the setback s = (t + R)·tan 22.5°, each bend's zone is (π/4)·(R + K·t) long,
+/// and a panel h high is h − s long, or h − 2s with a return on its far edge.
+fn tray_with_a_45_degree_flange(s: &mut Session, with_return: bool) -> f64 {
+    base(s, 100.0, 60.0);
+    run(s, "sheet.flange", json!({"edges": [[50, 0, 2.5]], "height": 40, "angle": 45}));
+    let (setback, ba) = (5.0 * (PI / 8.0).tan(), PI / 4.0 * (2.5 + 0.44 * 2.5));
+    if with_return {
+        run(s, "sheet.flange", json!({"edges": [[50, -27.5, 26.5]], "height": 10, "angle": 45}));
+        return setback - ba - (40.0 - 2.0 * setback) - ba - (10.0 - setback);
+    }
+    setback - ba - (40.0 - setback)
+}
+
+/// A point on that flange's inside face, the plane y + z = 2.5·√2 (tangent to the bend's inside
+/// radius, 2.5 about y = 5·tan 22.5°, z = 5).
+const FLANGE_FACE: [f64; 3] = [50.0, 2.5 * std::f64::consts::SQRT_2 - 15.0, 15.0];
+
+fn last_warning(s: &Session) -> String {
+    s.model.results.last().and_then(|r| r.warning.clone()).unwrap_or_default()
+}
+
+fn parted_note(area: f64, at: [f64; 2]) -> String {
+    format!("1 piece of `Body1` is no longer joined to its base ({area:.2} mm², near ({:.1}, {:.1}) in the flat pattern); it is kept", at[0], at[1])
+}
+
+fn flat_pieces(s: &Session) -> Vec<f64> {
+    s.model.state().sheets[0].flat_regions().unwrap().iter().map(solidcraft_geom::Region2::area).collect()
+}
+
+#[test]
+fn a_cut_that_parts_a_flange_from_the_base_keeps_it_and_says_so_folded_or_flat() {
+    // A slot across the flange beside its bend (flat y −3 to −1.5) leaves the flange's panel past
+    // it, with any return on it, joined to nothing: 100 × (−3 − far). Cut on the folded flange's
+    // face or in the unfolded sheet, the piece stays, and the cut names it in its reply and on the
+    // timeline, with the middle of the piece in the flat pattern.
+    for (with_return, unfolded) in [(false, false), (false, true), (true, false), (true, true)] {
+        let what = format!("return {with_return}, unfolded {unfolded}");
+        let mut s = Session::default();
+        let far = tray_with_a_45_degree_flange(&mut s, with_return);
+        let out = if unfolded {
+            run(&mut s, "sheet.unfold", json!({}));
+            rectangle_tool(&mut s, "Slot", [-5.0, -3.0], [105.0, -1.5]);
+            run(&mut s, "solid.extrude", json!({"sketch": "Slot", "through_all": true, "direction": "symmetric", "operation": "cut"}))
+        } else {
+            run(&mut s, "sketch.create", json!({"plane": {"face": FLANGE_FACE}, "name": "Slot"}));
+            run(&mut s, "sketch.rectangle.two_point", json!({"p0": [-5, -3], "p1": [105, -1.5]}));
+            run(&mut s, "sketch.finish", json!({}));
+            run(&mut s, "solid.extrude", json!({"sketch": "Slot", "through_all": true, "direction": "negative", "operation": "cut"}))
+        };
+        let note = parted_note(100.0 * (-3.0 - far), [50.0, (far - 3.0) / 2.0]);
+        assert!(last_warning(&s).contains(&note), "{what}: {}", last_warning(&s));
+        assert_eq!(out["warning"], json!(last_warning(&s)), "{what}: {out}");
+        // Both pieces stay, folded and flat: the base with its bend left, and the flange.
+        let pieces = flat_pieces(&s);
+        assert!(pieces.len() == 2 && pieces.iter().any(|a| (a - 100.0 * (-3.0 - far)).abs() < 1e-6), "{what}: {pieces:?}");
+        for command in if unfolded { ["sheet.refold", "sheet.unfold"] } else { ["sheet.unfold", "sheet.refold"] } {
+            run(&mut s, command, json!({}));
+            assert_eq!(flat(&mut s)["outline"].as_array().map(Vec::len), Some(2), "{what} {command}");
+            assert_eq!(flat_pieces(&s), pieces, "{what} {command}");
+            if command == "sheet.unfold" {
+                assert!((volume(&mut s) - pieces.iter().sum::<f64>() * 2.5).abs() < 1e-3, "{what}: {}", volume(&mut s));
+            }
+        }
+    }
+}
+
+#[test]
+fn a_ring_over_a_flanges_edge_names_the_piece_of_its_inside_on_the_flange_but_not_an_island() {
+    // A ring Ø16 / Ø10 cut on the folded flange's face, centred on its far edge: the half of its
+    // inside on the flange (π·5²/2, its centroid 4·5/3π inside the edge) has nothing round it,
+    // and is named. Centred on the flange, its inside is an island, and nothing is named.
+    for (y, named) in [(None, true), (Some(-20.0), false)] {
+        let mut s = Session::default();
+        let far = tray_with_a_45_degree_flange(&mut s, false);
+        let y = y.unwrap_or(far);
+        run(&mut s, "sketch.create", json!({"plane": {"face": FLANGE_FACE}, "name": "Ring"}));
+        run(&mut s, "sketch.circle.center", json!({"center": [50, y], "diameter": 16}));
+        run(&mut s, "sketch.circle.center", json!({"center": [50, y], "diameter": 10}));
+        run(&mut s, "sketch.finish", json!({}));
+        let out = run(
+            &mut s,
+            "solid.extrude",
+            json!({"sketch": "Ring", "profiles": [{"point": [56.5, y]}], "through_all": true, "direction": "negative", "operation": "cut"}),
+        );
+        let warning = out["warning"].as_str().unwrap_or_default().to_string();
+        let note = parted_note(12.5 * PI, [50.0, far + 20.0 / (3.0 * PI)]);
+        assert_eq!(warning.contains(&note), named, "{y}: {warning}");
+        assert!(named || !warning.contains("no longer joined"), "{y}: {warning}");
+        assert_eq!(flat_pieces(&s).len(), 2, "{y}");
+    }
+}
+
+#[test]
+fn cuts_that_split_a_sheet_or_cut_it_beside_the_base_name_only_the_pieces_they_part() {
+    // Unfolded, a strip across tray and flange leaves two pieces that each keep their part of
+    // the base: nothing to name. A box over the smaller piece's base and bend then leaves its
+    // flange panel, 26 × (−3 − far), named; a hole in the base after it names nothing again.
+    let mut s = Session::default();
+    let far = tray_with_a_45_degree_flange(&mut s, false);
+    run(&mut s, "sheet.unfold", json!({}));
+    rectangle_tool(&mut s, "Strip", [70.0, -60.0], [74.0, 70.0]);
+    let out = run(&mut s, "solid.extrude", json!({"sketch": "Strip", "through_all": true, "direction": "symmetric", "operation": "cut"}));
+    assert!(out["warning"].is_null() && last_warning(&s).is_empty(), "{out}");
+    rectangle_tool(&mut s, "Box", [72.0, -3.0], [101.0, 61.0]);
+    let out = run(&mut s, "solid.extrude", json!({"sketch": "Box", "through_all": true, "direction": "symmetric", "operation": "cut"}));
+    assert_eq!(out["warning"], json!(parted_note(26.0 * (-3.0 - far), [87.0, (far - 3.0) / 2.0])), "{out}");
+    run(&mut s, "sketch.create", json!({"plane": "XY", "name": "Hole"}));
+    run(&mut s, "sketch.circle.center", json!({"center": [30, 30], "diameter": 8}));
+    run(&mut s, "sketch.finish", json!({}));
+    let out = run(&mut s, "solid.extrude", json!({"sketch": "Hole", "through_all": true, "direction": "symmetric", "operation": "cut"}));
+    assert!(out["warning"].is_null(), "{out}");
+    run(&mut s, "sheet.refold", json!({}));
+    assert_eq!(flat(&mut s)["outline"].as_array().map(Vec::len), Some(2));
+    // Folded, a slot across the base beside the bend leaves the flange with a strip of the base;
+    // a plain plate cut in two halves. Neither names anything.
+    let mut s = Session::default();
+    tray_with_a_45_degree_flange(&mut s, false);
+    rectangle_tool(&mut s, "Slot", [-5.0, 3.0], [105.0, 6.0]);
+    let out = run(&mut s, "solid.extrude", json!({"sketch": "Slot", "through_all": true, "direction": "symmetric", "operation": "cut"}));
+    assert!(out["warning"].is_null() && flat_pieces(&s).len() == 2, "{out}");
+    let mut s = Session::default();
+    base(&mut s, 100.0, 60.0);
+    rectangle_tool(&mut s, "Strip", [45.0, -5.0], [55.0, 65.0]);
+    let out = run(&mut s, "solid.extrude", json!({"sketch": "Strip", "through_all": true, "direction": "symmetric", "operation": "cut"}));
+    assert!(out["warning"].is_null() && flat_pieces(&s).len() == 2, "{out}");
+}
+
+#[test]
+fn a_hole_that_parts_a_flange_from_the_base_names_it() {
+    // A 10 x 60 plate with a 90° flange 40 high on its y = 0 edge: the flange's panel runs from
+    // flat y = 5 − BA (world z = 5) for 35 mm. A Ø12 hole drilled into it at z = 15 (flat
+    // y = 5 − BA − 10) takes its whole width, and leaves the 25 mm below the hole's centre less
+    // the half disc there: 10 × 25 − ∫ √(36 − u²) du over |u| ≤ 5 = 250 − (5√11 + 36·asin(5/6)).
+    let mut s = Session::default();
+    base(&mut s, 10.0, 60.0);
+    run(&mut s, "sheet.flange", json!({"edges": [[5, 0, 2.5]], "height": 40}));
+    let out = run(&mut s, "solid.hole", json!({"position": [5, 0, 15], "diameter": 12}));
+    let area = 250.0 - (5.0 * 11f64.sqrt() + 36.0 * (5.0f64 / 6.0).asin());
+    let warning = out["warning"].as_str().unwrap_or_default();
+    assert!(warning.starts_with(&format!("1 piece of `Body1` is no longer joined to its base ({area:.2} mm², near (5.0, ")), "{warning}");
+    assert_eq!(out["warning"], json!(last_warning(&s)));
+    assert_eq!(flat_pieces(&s).len(), 2);
+}

docs/book/src/guide/sheet-metal.md

@@ -244,6 +244,10 @@ exactly (`cutout_shapes`): a round hole as `{"circle": {"center", "radius"}}`, a
 
 Cuts can leave separate material pieces, including the centre of a ring cut. These pieces
 remain one logical sheet group through Unfold / Refold and export as separate flat outlines.
+A cut that parts a piece from the base (a flange cut off along its bend, the part of a ring's
+inside on a flange's edge) keeps it too, folded or flat, and its warning says how many pieces
+are no longer joined to the base, their area and where they lie in the flat pattern. Islands
+inside other material (a ring's centre, a letter's counter) are not counted.
 Large profiles that exceed the geometry processing budget report an error instead of
 exporting a partial outline.