BREP_kernel 0.4.0

use super::*;

struct HealPlan {
    /// The two boundary-edge indices whose neighbours are the primary pair.
    primary: [usize; 2],
    /// The two lateral boundary-edge indices (end caps).
    lateral: [usize; 2],
    /// Triple point (recovered corner) for each lateral index.
    lateral_point: HashMap<usize, Vec3>,
}

/// Choose the unique opposite neighbour pair whose planes re-intersect through
/// the transition face's region.
fn plan_heal(planes: &[Plane; 4], f_center: Vec3, f_reach: f64) -> Result<HealPlan, String> {
    let mut candidates: Vec<HealPlan> = Vec::new();
    for start in 0..2usize {
        let primary = [start, start + 2];
        let lateral = [(start + 1) % 4, (start + 3) % 4];
        let Some(line) = intersect_planes(&planes[primary[0]], &planes[primary[1]]) else {
            continue;
        };
        let mut lateral_point = HashMap::default();
        let mut ok = true;
        for &lat in &lateral {
            match intersect_line_plane(&line, &planes[lat]) {
                Some(point) if point.sub(f_center).length() <= f_reach => {
                    lateral_point.insert(lat, point);
                }
                _ => {
                    ok = false;
                    break;
                }
            }
        }
        if !ok {
            continue;
        }
        candidates.push(HealPlan {
            primary,
            lateral,
            lateral_point,
        });
    }
    match candidates.len() {
        1 => Ok(candidates.pop().unwrap()),
        0 => Err(
            "delete_face_and_heal: the neighbours do not re-intersect cleanly \
                  (parallel planes, non-adjacent healing, or a multi-face gap) — refusing \
                  rather than emitting an invalid solid"
                .into(),
        ),
        _ => Err(
            "delete_face_and_heal: healing is ambiguous — both opposite neighbour \
                  pairs re-intersect through the deleted face"
                .into(),
        ),
    }
}

// `retrim_planar_face` moved to the shared re-trim home
// (`crate::offset_retrim`, offset-unification audit §10) — its body is
// unchanged and it is re-exported here so its nine direct-edit call sites keep
// the bare name they have always used.
pub(super) use crate::offset_retrim::retrim_planar_face;

/// Find, in a face's loops, the (loop index, coedge index) of the coedge that
/// references `edge_id`.
pub(super) fn locate_coedge(face: &FaceRecord, edge_id: u64) -> Option<(usize, usize)> {
    for (loop_index, loop_record) in face.loops.iter().enumerate() {
        for (coedge_index, coedge) in loop_record.coedges.iter().enumerate() {
            if coedge.edge_id == edge_id {
                return Some((loop_index, coedge_index));
            }
        }
    }
    None
}

pub(super) fn coedge_from_vertex(coedge: &CoedgeRecord, edges: &HashMap<u64, EdgeRecord>) -> Option<u64> {
    let edge = edges.get(&coedge.edge_id)?;
    Some(if coedge.forward {
        edge.start_vertex_id
    } else {
        edge.end_vertex_id
    })
}

pub(super) fn coedge_to_vertex(coedge: &CoedgeRecord, edges: &HashMap<u64, EdgeRecord>) -> Option<u64> {
    let edge = edges.get(&coedge.edge_id)?;
    Some(if coedge.forward {
        edge.end_vertex_id
    } else {
        edge.start_vertex_id
    })
}

/// Golovanov §6.12 — delete a transition face and heal the hole by extending
/// and re-intersecting its immediate neighbours. See the module docs for the
/// covered vs deferred cases. Returns a fresh solid that is guaranteed to
/// `validate()`, or a clear `Err` describing why the heal was refused.
pub fn delete_face_and_heal(solid: &BrepSolid, face_id: u64) -> Result<BrepSolid, String> {
    let mut solid = solid.clone();
    let scale = solid_model_scale(&solid);
    let tolerance = (scale * 1e-7).max(1e-9);

    let (shell_index, face_index) = find_face(&solid, face_id)
        .ok_or_else(|| format!("delete_face_and_heal: no face with id {face_id}"))?;

    // --- Read the transition face's boundary (immutable snapshot) ---------
    let boundary: Vec<(u64, bool)> = {
        let face = &solid.shells[shell_index].faces[face_index];
        if face.loops.len() != 1 {
            return Err(format!(
                "delete_face_and_heal: face {face_id} has {} loops; only a simple \
                 single-loop transition face is supported",
                face.loops.len()
            ));
        }
        face.loops[0]
            .coedges
            .iter()
            .map(|coedge| (coedge.edge_id, coedge.forward))
            .collect()
    };
    if boundary.len() != 4 {
        return Err(format!(
            "delete_face_and_heal: face {face_id} has {} boundary edges; only 4-sided \
             transition faces (a single chamfer/fillet edge) are supported \
             (deferred: multi-face gaps)",
            boundary.len()
        ));
    }
    let boundary_edge_ids: HashSet<u64> = boundary.iter().map(|(edge_id, _)| *edge_id).collect();
    if boundary_edge_ids.len() == 3 {
        // A CLOSED transition strip (a fillet/chamfer around a full rim):
        // loop = [seam+, rim_a, seam-, rim_b] — the seam doubled, two closed
        // rims. Heals by re-intersecting the two neighbours analytically.
        return heal_closed_transition(&solid, shell_index, face_index, &boundary);
    }
    if boundary_edge_ids.len() != 4 {
        return Err(
            "delete_face_and_heal: transition face uses an edge more than once \
                    (deferred: periodic/closed transition)"
                .into(),
        );
    }

    // Neighbour faces (one per boundary edge, in loop order).
    let mut neighbour_ids = [0u64; 4];
    for (index, (edge_id, _)) in boundary.iter().enumerate() {
        neighbour_ids[index] = other_face_of_edge(&solid, *edge_id, face_id)?;
    }
    let unique: HashSet<u64> = neighbour_ids.iter().copied().collect();
    if unique.len() != 4 {
        return Err(
            "delete_face_and_heal: the transition face touches a neighbour more \
                    than once (deferred: periodic/closed transition)"
                .into(),
        );
    }

    // Carriers of the neighbours: all-planar takes the closed-form planar
    // path below; any curved analytic neighbour routes to the mixed
    // open-chain heal (plane × cylinder/ruled-revolution re-intersection).
    let neighbour_planes: [Plane; 4] = {
        let mut planes: Vec<Option<Plane>> = Vec::with_capacity(4);
        for &neighbour_id in &neighbour_ids {
            let (ns, nf) = find_face(&solid, neighbour_id)
                .ok_or_else(|| format!("delete_face_and_heal: missing neighbour {neighbour_id}"))?;
            planes.push(
                plane_of_surface(
                    &solid.shells[ns].faces[nf].surface,
                    (scale * 1e-6).max(1e-7),
                    "delete_face_and_heal",
                )
                .ok(),
            );
        }
        if planes.iter().any(Option::is_none) {
            return heal_open_transition_mixed(
                &solid,
                shell_index,
                face_index,
                &boundary,
                &neighbour_ids,
            );
        }
        [
            planes[0].unwrap(),
            planes[1].unwrap(),
            planes[2].unwrap(),
            planes[3].unwrap(),
        ]
    };

    // Transition-face region gate (centre + reach), from its loop vertices.
    let transition_vertices: Vec<u64> = boundary
        .iter()
        .map(|(edge_id, forward)| {
            let edge = solid
                .edges
                .iter()
                .find(|edge| edge.id == *edge_id)
                .ok_or_else(|| format!("delete_face_and_heal: missing edge {edge_id}"))?;
            Ok(if *forward {
                edge.start_vertex_id
            } else {
                edge.end_vertex_id
            })
        })
        .collect::<Result<Vec<u64>, String>>()?;
    if transition_vertices.iter().collect::<HashSet<_>>().len() != 4 {
        return Err(
            "delete_face_and_heal: transition face has repeated corner vertices \
                    (deferred: degenerate transition)"
                .into(),
        );
    }
    let mut f_center = Vec3::default();
    for &vertex_id in &transition_vertices {
        f_center = f_center.add(edge_point(&solid, vertex_id)?);
    }
    f_center = f_center.scale(0.25);
    let mut f_reach = 0.0f64;
    for &vertex_id in &transition_vertices {
        f_reach = f_reach.max(edge_point(&solid, vertex_id)?.sub(f_center).length());
    }
    let f_reach = f_reach * 3.0 + tolerance;

    let plan = plan_heal(&neighbour_planes, f_center, f_reach)?;

    // --- New recovered corners (triple points) and the new sharp edge ------
    let mut next_id = max_topology_id(&solid) + 1;
    let mut alloc = || {
        let value = next_id;
        next_id += 1;
        value
    };

    let lateral_a = plan.lateral[0];
    let lateral_b = plan.lateral[1];
    let point_a = plan.lateral_point[&lateral_a];
    let point_b = plan.lateral_point[&lateral_b];
    if point_a.sub(point_b).length() <= tolerance {
        return Err(
            "delete_face_and_heal: recovered corners coincide — the neighbours \
                    do not bound a clean edge"
                .into(),
        );
    }
    let vertex_a = alloc();
    let vertex_b = alloc();
    let mut lateral_vertex: HashMap<usize, u64> = HashMap::default();
    lateral_vertex.insert(lateral_a, vertex_a);
    lateral_vertex.insert(lateral_b, vertex_b);

    // The new sharp edge S (start = corner A, end = corner B).
    let sharp_edge_id = alloc();
    let sharp_edge = EdgeRecord {
        id: sharp_edge_id,
        curve: make_line(point_a, point_b)?,
        t0: 0.0,
        t1: 1.0,
        start_vertex_id: vertex_a,
        end_vertex_id: vertex_b,
        degenerate: false,
        name: None,
    };

    // --- Collapse each transition corner onto its recovered corner ---------
    // Corner vertex `transition_vertices[i]` sits between neighbour[(i+3)%4]
    // and neighbour[i]; exactly one of those two is a lateral face, and the
    // corner collapses onto that lateral's recovered corner.
    let lateral_set: HashSet<usize> = plan.lateral.iter().copied().collect();
    let mut collapse: HashMap<u64, u64> = HashMap::default();
    for index in 0..4usize {
        let previous = (index + 3) % 4;
        let lateral_index = if lateral_set.contains(&previous) {
            previous
        } else if lateral_set.contains(&index) {
            index
        } else {
            return Err(
                "delete_face_and_heal: transition corner is not flanked by a \
                        lateral face (unexpected neighbour ordering)"
                    .into(),
            );
        };
        let target = lateral_vertex[&lateral_index];
        collapse.insert(transition_vertices[index], target);
    }
    let new_vertex_points: HashMap<u64, Vec3> = [(vertex_a, point_a), (vertex_b, point_b)]
        .into_iter()
        .collect();

    // Relocate every non-transition edge that ends on a collapsed corner.
    for edge in &mut solid.edges {
        if boundary_edge_ids.contains(&edge.id) {
            continue;
        }
        let start_target = collapse.get(&edge.start_vertex_id).copied();
        let end_target = collapse.get(&edge.end_vertex_id).copied();
        if start_target.is_none() && end_target.is_none() {
            continue;
        }
        if edge.curve.degree != 1 || edge.curve.control_points.len() != 2 {
            return Err(
                "delete_face_and_heal: a side edge meeting the transition face is \
                        not a straight line (deferred: curved neighbour edges)"
                    .into(),
            );
        }
        let mut start_point = edge.curve.control_points[0].point()?;
        let mut end_point = edge.curve.control_points[1].point()?;
        if let Some(target) = start_target {
            edge.start_vertex_id = target;
            start_point = new_vertex_points[&target];
        }
        if let Some(target) = end_target {
            edge.end_vertex_id = target;
            end_point = new_vertex_points[&target];
        }
        if start_point.sub(end_point).length() <= tolerance {
            return Err(
                "delete_face_and_heal: healing would collapse a side edge to zero \
                        length (deferred: degenerate transition)"
                    .into(),
            );
        }
        edge.curve = make_line(start_point, end_point)?;
        edge.t0 = 0.0;
        edge.t1 = 1.0;
    }

    // Index the (now relocated) edges for loop rewrites and pcurve rebuilds.
    let mut edges_by_id: HashMap<u64, EdgeRecord> = solid
        .edges
        .iter()
        .map(|edge| (edge.id, edge.clone()))
        .collect();
    edges_by_id.insert(sharp_edge_id, sharp_edge.clone());

    // --- Rewrite neighbour loops ------------------------------------------
    // Primary faces: replace their support coedge (on the deleted face's edge)
    // with a coedge on the new sharp edge S.
    for &primary_index in &plan.primary {
        let primary_edge = boundary[primary_index].0;
        let neighbour_id = neighbour_ids[primary_index];
        let (ns, nf) = find_face(&solid, neighbour_id)
            .ok_or_else(|| format!("delete_face_and_heal: missing neighbour {neighbour_id}"))?;
        let face = &mut solid.shells[ns].faces[nf];
        let (loop_index, coedge_index) = locate_coedge(face, primary_edge).ok_or_else(|| {
            format!(
                "delete_face_and_heal: neighbour {neighbour_id} does not use edge {primary_edge}"
            )
        })?;
        let coedges = &face.loops[loop_index].coedges;
        let count = coedges.len();
        let previous = &coedges[(coedge_index + count - 1) % count];
        let next = &coedges[(coedge_index + 1) % count];
        let required_from = coedge_to_vertex(previous, &edges_by_id).ok_or_else(|| {
            "delete_face_and_heal: could not resolve loop connectivity".to_string()
        })?;
        let required_to = coedge_from_vertex(next, &edges_by_id).ok_or_else(|| {
            "delete_face_and_heal: could not resolve loop connectivity".to_string()
        })?;
        let forward = if required_from == vertex_a && required_to == vertex_b {
            true
        } else if required_from == vertex_b && required_to == vertex_a {
            false
        } else {
            return Err(
                "delete_face_and_heal: new edge does not close the primary loop \
                        (unexpected connectivity)"
                    .into(),
            );
        };
        let new_coedge = CoedgeRecord {
            id: alloc(),
            edge_id: sharp_edge_id,
            forward,
            // Placeholder; retrim_planar_face recomputes every pcurve below.
            pcurve: make_line(Vec3::default(), Vec3::new(1.0, 0.0, 0.0))?,
        };
        face.loops[loop_index].coedges[coedge_index] = new_coedge;
    }

    // Lateral (cap) faces: drop the cap coedge; its two neighbours already
    // meet at the recovered corner.
    for &lateral_index in &plan.lateral {
        let lateral_edge = boundary[lateral_index].0;
        let neighbour_id = neighbour_ids[lateral_index];
        let (ns, nf) = find_face(&solid, neighbour_id)
            .ok_or_else(|| format!("delete_face_and_heal: missing neighbour {neighbour_id}"))?;
        let face = &mut solid.shells[ns].faces[nf];
        let (loop_index, coedge_index) = locate_coedge(face, lateral_edge).ok_or_else(|| {
            format!(
                "delete_face_and_heal: neighbour {neighbour_id} does not use edge {lateral_edge}"
            )
        })?;
        face.loops[loop_index].coedges.remove(coedge_index);
        if face.loops[loop_index].coedges.is_empty() {
            return Err("delete_face_and_heal: healing emptied a lateral face loop".into());
        }
    }

    // --- Prune the deleted face, its edges, and its corner vertices --------
    solid.shells[shell_index]
        .faces
        .retain(|face| face.id != face_id);
    solid
        .edges
        .retain(|edge| !boundary_edge_ids.contains(&edge.id));
    let removed_vertices: HashSet<u64> = transition_vertices.iter().copied().collect();
    solid.edges.push(sharp_edge);
    solid
        .vertices
        .retain(|vertex| !removed_vertices.contains(&vertex.id));
    solid.vertices.push(VertexRecord {
        id: vertex_a,
        point: point_a,
    });
    solid.vertices.push(VertexRecord {
        id: vertex_b,
        point: point_b,
    });

    // --- Re-trim every affected neighbour on its (extended) carrier --------
    let final_edges: HashMap<u64, EdgeRecord> = solid
        .edges
        .iter()
        .map(|edge| (edge.id, edge.clone()))
        .collect();
    for (index, &neighbour_id) in neighbour_ids.iter().enumerate() {
        let plane = neighbour_planes[index];
        let (ns, nf) = find_face(&solid, neighbour_id)
            .ok_or_else(|| format!("delete_face_and_heal: missing neighbour {neighbour_id}"))?;
        retrim_planar_face(
            &mut solid.shells[ns].faces[nf],
            &plane,
            &final_edges,
            scale,
            "delete_face_and_heal",
        )?;
    }

    // Genus is preserved by removing a genus-neutral transition face; the
    // Euler check inside validate() confirms it.
    let issues = solid.validate();
    if !issues.is_empty() {
        return Err(format!(
            "delete_face_and_heal: healed solid failed validation: {issues:?}"
        ));
    }
    Ok(solid)
}

/// Resolve the id of the face nearest a 3D point (used by the app: the picked
/// point lies on the selected face). Mirrors `resolve_edge_by_point`.
pub fn resolve_face_by_point(solid: &BrepSolid, point: Vec3) -> Result<u64, String> {
    let scale = solid_model_scale(&solid);
    let mut best: Option<(u64, f64)> = None;
    for shell in &solid.shells {
        for face in &shell.faces {
            let Ok(projection) = crate::project_point_to_surface(&face.surface, point) else {
                continue;
            };
            if best
                .map(|(_, known)| projection.distance < known)
                .unwrap_or(true)
            {
                best = Some((face.id, projection.distance));
            }
        }
    }
    match best {
        Some((face_id, distance)) if distance <= (scale * 1e-3).max(1e-4) => Ok(face_id),
        Some((_, distance)) => Err(format!(
            "delete_face_and_heal: no face within tolerance of the point (nearest {distance:.6})"
        )),
        None => Err("delete_face_and_heal: solid has no faces".into()),
    }
}

// ---------------------------------------------------------------------------
// Tests — the capability matrix `examples/delete_face_matrix_probe.rs` measures,
// pinned. The probe is the instrument; these are the assertions it justified.
//
// The three lanes `delete_face_and_heal` dispatches across are covered in
// `tests.rs` (all-planar), `closed_heal_tests.rs` (closed full rim) and
// `open_heal_tests.rs` (open mixed). What lives HERE is what those files left
// unpinned: the dispatch GATES that never reach a lane at all, the closed
// lane's carrier breadth, and the one measurement that decides whether the
// shared re-intersection seam can replace the planar closed form.
// ---------------------------------------------------------------------------
#[cfg(test)]
mod delete_face_tests {
    use super::*;
    use crate::{
        boolean_operation, chamfer_edge, fillet_edge, make_box_brep, make_cone_brep,
        make_cylinder_brep, make_sphere_brep, solid_mass_properties, BooleanOperation,
        BooleanOptions,
    };

    /// The closed rim edge of a body of revolution at height `z`.
    fn closed_rim_at(solid: &BrepSolid, z: f64) -> u64 {
        solid
            .edges
            .iter()
            .find(|edge| {
                !edge.degenerate
                    && edge.start_vertex_id == edge.end_vertex_id
                    && edge
                        .curve
                        .evaluate(0.5 * (edge.t0 + edge.t1))
                        .map(|point| (point.z - z).abs() < 1e-6)
                        .unwrap_or(false)
            })
            .expect("closed rim")
            .id
    }

    fn named_face(solid: &BrepSolid, name: &str) -> u64 {
        solid
            .shells
            .iter()
            .flat_map(|shell| &shell.faces)
            .find(|face| face.name.as_deref() == Some(name))
            .expect("named blend face")
            .id
    }

    fn volume(solid: &BrepSolid) -> f64 {
        solid_mass_properties(solid)
            .expect("mass properties")
            .volume
    }

    /// Blend a closed rim, delete the blend, and require the ORIGINAL body
    /// back: same face count, same volume, clean `validate()`. The blend is
    /// the only thing that changed, so anything else that moves is a bug.
    fn round_trip(
        sharp: &BrepSolid,
        rim: u64,
        blend: fn(&BrepSolid, u64, f64, Option<&str>) -> Result<BrepSolid, String>,
        size: f64,
    ) -> BrepSolid {
        let faces_before: usize = sharp.shells.iter().map(|shell| shell.faces.len()).sum();
        let volume_before = volume(sharp);
        let blended = blend(sharp, rim, size, Some("B1")).expect("blend");
        assert!(blended.validate().is_empty(), "{:?}", blended.validate());
        let strip = named_face(&blended, "B1");

        let healed = delete_face_and_heal(&blended, strip).expect("heal");
        assert!(
            healed.validate().is_empty(),
            "healed solid must validate: {:?}",
            healed.validate()
        );
        assert_eq!(
            healed
                .shells
                .iter()
                .map(|shell| shell.faces.len())
                .sum::<usize>(),
            faces_before,
            "face count must return to the pre-blend count"
        );
        let volume_after = volume(&healed);
        assert!(
            (volume_after - volume_before).abs() <= 1e-6 * volume_before.abs(),
            "expected the pre-blend volume {volume_before}, got {volume_after}"
        );
        healed
    }

    // --- closed lane: carrier breadth ------------------------------------

    /// A rim CHAMFER leaves a conical strip between the same two neighbours a
    /// rim fillet leaves a toroidal one between. `closed_heal_tests.rs` pins
    /// only the fillet; this pins that the strip's own carrier is irrelevant
    /// to the heal, which re-intersects the NEIGHBOURS.
    #[test]
    fn closed_heal_restores_the_cylinder_after_a_rim_chamfer() {
        let cylinder =
            make_cylinder_brep(Vec3::default(), Vec3::new(0.0, 0.0, 1.0), 4.0, 6.0).unwrap();
        let rim = closed_rim_at(&cylinder, 6.0);
        let healed = round_trip(&cylinder, rim, chamfer_edge, 1.0);
        // The re-sharpened rim is back at the top, radius 4.
        assert!(healed.edges.iter().any(|edge| {
            let Ok(point) = edge.curve.evaluate(0.5 * (edge.t0 + edge.t1)) else {
                return false;
            };
            (point.z - 6.0).abs() < 1e-6 && (point.x.hypot(point.y) - 4.0).abs() < 1e-6
        }));
    }

    /// A cone frustum's wall is a TAPERED ruled revolution — the closed form
    /// the rim rebind uses is `axial / height`, which is only the identity for
    /// a cylinder. Pins that the taper is carried.
    #[test]
    fn closed_heal_restores_the_cone_frustum_after_a_rim_fillet() {
        let cone =
            make_cone_brep(Vec3::default(), Vec3::new(0.0, 0.0, 1.0), 5.0, 2.5, 6.0).unwrap();
        let rim = closed_rim_at(&cone, 6.0);
        let healed = round_trip(&cone, rim, fillet_edge, 0.8);
        assert!(healed.edges.iter().any(|edge| {
            let Ok(point) = edge.curve.evaluate(0.5 * (edge.t0 + edge.t1)) else {
                return false;
            };
            (point.z - 6.0).abs() < 1e-6 && (point.x.hypot(point.y) - 2.5).abs() < 1e-6
        }));
    }

    /// An upper half-ball: a flat disk whose only neighbour is the spherical
    /// dome, meeting along the great-circle equator.
    fn upper_half_ball(radius: f64) -> BrepSolid {
        let sphere = make_sphere_brep(Vec3::default(), radius, Vec3::new(0.0, 0.0, 1.0)).unwrap();
        let box_up = make_box_brep(
            Vec3::new(-2.0 * radius, -2.0 * radius, 0.0),
            4.0 * radius,
            4.0 * radius,
            2.0 * radius,
        )
        .unwrap();
        let options = BooleanOptions {
            merge_coplanar_faces: true,
            ..BooleanOptions::default()
        };
        boolean_operation(&sphere, &box_up, BooleanOperation::Intersect, &options).unwrap()
    }

    /// A SPHERE neighbour. `intersect_analytic_pair` answers Sphere×Plane with
    /// the exact equator circle, but the rim rebind used to refuse anything
    /// that was not a `RuledRevolution` — the gate was narrower than the
    /// intersector behind it. Measured by the matrix probe as
    /// `ERR curved neighbour is not a ruled revolution` before this landed.
    #[test]
    fn closed_heal_rebinds_a_sphere_neighbour_after_a_rim_fillet() {
        let ball = upper_half_ball(5.0);
        let rim = closed_rim_at(&ball, 0.0);
        let healed = round_trip(&ball, rim, fillet_edge, 0.8);
        // The recovered rim is the great circle: radius 5 in the plane z = 0.
        assert!(healed.edges.iter().any(|edge| {
            let Ok(point) = edge.curve.evaluate(0.5 * (edge.t0 + edge.t1)) else {
                return false;
            };
            point.z.abs() < 1e-6 && (point.x.hypot(point.y) - 5.0).abs() < 1e-6
        }));
        // Every point of every edge still sits on the ball or its base plane —
        // the check that catches a seam meridian replaced by its chord.
        for edge in &healed.edges {
            if edge.degenerate {
                continue;
            }
            for step in 0..=8 {
                let t = edge.t0 + (edge.t1 - edge.t0) * f64::from(step) / 8.0;
                let point = edge.curve.evaluate(t).unwrap();
                let on_sphere = (point.length() - 5.0).abs() < 1e-6;
                let on_base = point.z.abs() < 1e-6 && point.length() <= 5.0 + 1e-6;
                assert!(
                    on_sphere || on_base,
                    "edge {} left both carriers at t={t}: {point:?}",
                    edge.id
                );
            }
        }
    }

    /// The same neighbour pair with a CONICAL strip instead of a toroidal one.
    #[test]
    fn closed_heal_rebinds_a_sphere_neighbour_after_a_rim_chamfer() {
        let ball = upper_half_ball(5.0);
        let rim = closed_rim_at(&ball, 0.0);
        round_trip(&ball, rim, chamfer_edge, 0.8);
    }

    /// A TORUS neighbour, the other carrier `intersect_plane_quadric` answers
    /// and the rim rebind used to refuse. Half a torus cut by the plane
    /// through its tube: `Plane × Torus` returns TWO closed circles (inner and
    /// outer rim), so this also pins that the heal picks the branch the strip
    /// surrounded rather than the first one offered.
    #[test]
    fn closed_heal_rebinds_a_torus_neighbour_after_a_rim_fillet() {
        let torus =
            crate::make_torus_brep(Vec3::default(), Vec3::new(0.0, 0.0, 1.0), 5.0, 2.0).unwrap();
        let box_up = make_box_brep(Vec3::new(-20.0, -20.0, 0.0), 40.0, 40.0, 20.0).unwrap();
        let options = BooleanOptions {
            merge_coplanar_faces: true,
            ..BooleanOptions::default()
        };
        let half =
            boolean_operation(&torus, &box_up, BooleanOperation::Intersect, &options).unwrap();
        // Half a torus: V = pi^2 * R * r^2.
        let expected = std::f64::consts::PI.powi(2) * 5.0 * 4.0;
        assert!((volume(&half) - expected).abs() <= 1e-6 * expected);
        let rim = closed_rim_at(&half, 0.0);
        let healed = round_trip(&half, rim, fillet_edge, 0.4);
        assert!((volume(&healed) - expected).abs() <= 1e-6 * expected);
    }

    // --- dispatch gates: the refusals that never reach a lane --------------

    #[test]
    fn refuses_a_face_that_does_not_exist() {
        let cube = make_box_brep(Vec3::default(), 1.0, 1.0, 1.0).unwrap();
        let error = delete_face_and_heal(&cube, 999_999).unwrap_err();
        assert!(
            error.contains("no face with id 999999"),
            "unexpected refusal: {error}"
        );
    }

    /// A drilled plate's top face has TWO loops (outer boundary + the hole).
    /// Healing a multi-loop face is a different problem from healing a
    /// transition strip; the gate must say so rather than heal the outer loop
    /// and leave the hole dangling.
    #[test]
    fn refuses_a_multi_loop_face_naming_the_loop_count() {
        let plate = make_box_brep(Vec3::default(), 20.0, 20.0, 4.0).unwrap();
        let drill = make_cylinder_brep(
            Vec3::new(10.0, 10.0, -1.0),
            Vec3::new(0.0, 0.0, 1.0),
            3.0,
            6.0,
        )
        .unwrap();
        let drilled = boolean_operation(
            &plate,
            &drill,
            BooleanOperation::Subtract,
            &BooleanOptions::default(),
        )
        .unwrap();
        let top = resolve_face_by_point(&drilled, Vec3::new(2.0, 2.0, 4.0)).unwrap();
        let error = delete_face_and_heal(&drilled, top).unwrap_err();
        assert!(
            error.contains("2 loops") && error.contains("single-loop"),
            "refusal must name the loop count: {error}"
        );
    }

    /// A 3-sided face is a CORNER transition: healing it recovers a vertex,
    /// not an edge, and that is a different algorithm (heal-tail plan §3.3,
    /// k = 3). The gate must name the side count so the refusal is actionable.
    #[test]
    fn refuses_a_face_that_is_not_four_sided() {
        let cube = make_box_brep(Vec3::default(), 10.0, 10.0, 10.0).unwrap();
        let profile = [
            make_line(Vec3::new(8.0, 0.0, 10.0), Vec3::new(0.0, 8.0, 10.0)).unwrap(),
            make_line(Vec3::new(0.0, 8.0, 10.0), Vec3::new(20.0, 20.0, 10.0)).unwrap(),
            make_line(Vec3::new(20.0, 20.0, 10.0), Vec3::new(8.0, 0.0, 10.0)).unwrap(),
        ];
        let cutter =
            crate::extrude_profile_brep(&profile, Vec3::new(0.0, 0.0, -1.0), 8.0).unwrap();
        let cut = boolean_operation(
            &cube,
            &cutter,
            BooleanOperation::Subtract,
            &BooleanOptions::default(),
        )
        .unwrap();
        let triangle = cut
            .shells
            .iter()
            .flat_map(|shell| &shell.faces)
            .find(|face| face.loops.len() == 1 && face.loops[0].coedges.len() == 3)
            .expect("3-sided cut face")
            .id;
        let error = delete_face_and_heal(&cut, triangle).unwrap_err();
        assert!(
            error.contains("3 boundary edges") && error.contains("4-sided"),
            "refusal must name the side count: {error}"
        );
    }

    // --- the shared re-intersection seam, measured -------------------------

    /// Can `offset_reintersect::reintersect_carriers` — the shared "these two
    /// carriers used to meet through a face that moved, where do they meet
    /// now" service — replace the all-planar closed form in `plan_heal`?
    ///
    /// MEASURED, not predicted: it ANSWERS — but only through the MARCHED
    /// lane, and that is the whole answer.
    ///
    /// `intersect_analytic_pair` declines Plane×Plane **by design**
    /// (`geometry/analytic_surface/intersect.rs:173-179`, with the reason in a
    /// comment there), so the shared seam falls straight through its exact
    /// lane for the commonest delete-face case there is and traces the line
    /// instead. What comes back is a `fit_polyline` of a traced polyline,
    /// residual-gated but an approximation; `plan_heal` returns the exact
    /// `intersect_planes` line. Swapping the seam in for the closed form would
    /// therefore replace an exact edge with a fitted one on every chamfered
    /// box in the corpus — strictly less exact, and not bit-identical.
    ///
    /// (A prediction this test refuted, recorded so it is not made twice: the
    /// march was expected to find NOTHING, on the grounds that it clamps to
    /// each surface's stored domain — `intersect/surface_surface_intersection.rs:111-117`
    /// — and a blend trims its neighbours back. It does clamp; but `chamfer_edge`
    /// leaves the neighbour CARRIERS at their original extents and only rewrites
    /// the trim loops, so the patches still overlap. Carrier coverage after a
    /// blend is a property of the blend, not something a general re-intersection
    /// may assume either way.)
    #[test]
    fn the_shared_reintersect_seam_declines_the_chamfered_cube_primaries() {
        let cube = make_box_brep(Vec3::default(), 1.0, 1.0, 1.0).unwrap();
        let edge = cube
            .edges
            .iter()
            .find(|edge| {
                edge.curve
                    .evaluate(0.5 * (edge.t0 + edge.t1))
                    .map(|point| (point.x - 1.0).abs() < 1e-9 && (point.z - 1.0).abs() < 1e-9)
                    .unwrap_or(false)
            })
            .expect("top-right cube edge")
            .id;
        let chamfered = chamfer_edge(&cube, edge, 0.2, Some("C1")).unwrap();
        let strip = named_face(&chamfered, "C1");

        // The two PRIMARY neighbours: the faces the chamfer's opposite
        // boundary edges border — the ones whose re-intersection is the
        // recovered sharp edge.
        let top = resolve_face_by_point(&chamfered, Vec3::new(0.4, 0.5, 1.0)).unwrap();
        let right = resolve_face_by_point(&chamfered, Vec3::new(1.0, 0.5, 0.4)).unwrap();
        assert_ne!(top, strip);
        assert_ne!(right, strip);
        let surface_of = |id: u64| {
            chamfered
                .shells
                .iter()
                .flat_map(|shell| &shell.faces)
                .find(|face| face.id == id)
                .map(|face| face.surface.clone())
                .expect("face")
        };

        // Seeded on the very boundary the heal is replacing — the strongest
        // seed set there is, so a refusal here is not a seeding accident.
        let mut seeds: Vec<Vec3> = Vec::new();
        for edge in &chamfered.edges {
            for step in 0..=4 {
                let t = edge.t0 + (edge.t1 - edge.t0) * f64::from(step) / 4.0;
                if let Ok(point) = edge.curve.evaluate(t) {
                    seeds.push(point);
                }
            }
        }
        let policy = MarchPolicy {
            tolerance: 1e-7,
            residual_tolerance: 1e-5,
            seeds,
        };
        let found = reintersect_carriers(&surface_of(top), &surface_of(right), &policy)
            .expect("the seam answers this pair");
        assert!(
            matches!(found.lane, RimLane::Marched),
            "plane x plane has no closed form, so the answer must come from the \
             marched lane; got the analytic one"
        );
        assert_eq!(found.sections.len(), 1, "one line, traced");
        // It is the right line, to within a fit residual — which is exactly the
        // exactness the closed form does not spend.
        let section = &found.sections[0];
        let [s0, s1] = section.curve.domain().unwrap();
        let mut worst = 0.0f64;
        for step in 0..=16 {
            let point = section
                .curve
                .evaluate(s0 + (s1 - s0) * f64::from(step) / 16.0)
                .unwrap();
            worst = worst.max((point.x - 1.0).abs().max((point.z - 1.0).abs()));
        }
        assert!(worst <= 1e-5, "the marched line drifts {worst} off x=1,z=1");

        // And the operation heals them anyway, through the closed form.
        let healed = delete_face_and_heal(&chamfered, strip).unwrap();
        assert!(healed.validate().is_empty());
        assert!((volume(&healed) - 1.0).abs() < 1e-9);
    }
}