BREP_kernel 0.5.0

use super::*;

/// General OPEN-edge rolling-ball fillet or chamfer: §4.9 march +
/// §6.9 surgery with transverse edges on the two end faces.
pub fn blend_open_edge(
    solid: &BrepSolid,
    edge_id: u64,
    radius: f64,
    chamfer: bool,
    name: Option<&str>,
) -> Result<BrepSolid, String> {
    if !(radius > 0.0) || !radius.is_finite() {
        return Err("blend: radius must be positive".into());
    }
    blend_open_edge_impl(solid, edge_id, &|_| radius, chamfer, name)
}

pub(super) fn blend_open_edge_impl(
    solid: &BrepSolid,
    edge_id: u64,
    radius_at: &dyn Fn(f64) -> f64,
    chamfer: bool,
    name: Option<&str>,
) -> Result<BrepSolid, String> {
    let edge = solid
        .edges
        .iter()
        .find(|edge| edge.id == edge_id)
        .ok_or_else(|| format!("blend: edge {edge_id} not found"))?;
    if edge.start_vertex_id == edge.end_vertex_id {
        return Err("blend: blend_open_edge requires an open edge".into());
    }
    let (first_face, first_loop, first_coedge) = locate_mate(solid, edge_id, None)?;
    let (second_face, second_loop, second_coedge) =
        locate_mate(solid, edge_id, Some((first_face.id, first_loop)))?;
    let mid_radius = radius_at(edge.t0 + (edge.t1 - edge.t0) * 0.5);
    let (rho1, rho2) = signed_radii(
        edge,
        first_face,
        first_coedge,
        second_face,
        second_coedge,
        mid_radius,
    )?;
    let first_mate = BlendMate {
        face: first_face,
        coedge: first_coedge,
        loop_index: first_loop,
        rho: rho1,
    };
    let second_mate = BlendMate {
        face: second_face,
        coedge: second_coedge,
        loop_index: second_loop,
        rho: rho2,
    };
    // End topology: boundary edges of both mates at each end vertex, the
    // single face across the corner, and the support crossings.  When a
    // prior fillet has already consumed one of the end corners, the support
    // crossing can land at the very rim of the marched rows (the prior
    // blend's transverse arc meets our contact line right at its base).
    // March with a growing overshoot until every crossing lands strictly
    // inside the fitted-row domain so the surgery can trim cleanly.
    let debug = std::env::var("BREP_DEBUG_BLEND_MARCH").is_ok();
    if debug {
        let sp = edge.curve.evaluate(edge.t0);
        let ep = edge.curve.evaluate(edge.t1);
        eprintln!(
            "OPEN edge {} v{}->v{} first_face {} second_face {} p0={:?} p1={:?}",
            edge.id,
            edge.start_vertex_id,
            edge.end_vertex_id,
            first_face.id,
            second_face.id,
            sp,
            ep
        );
    }
    let compute = |overshoot_fraction: f64| -> Result<(FittedRows, Vec<EndSurgery>, bool), String> {
        // The open-edge surgery locates its ends by support crossings, not by
        // the marched vertex stations, so the snapped indices are unused here.
        let (stations, _) = march_open_stations(
            edge,
            &first_mate,
            &second_mate,
            radius_at,
            overshoot_fraction,
        )?;
        let parameters = station_parameters(&stations);
        let rows = fit_open_rows(&stations, &parameters, chamfer)?;
        let mut ends = Vec::with_capacity(2);
        let mut in_range = true;
        for (vertex, at_start) in [(edge.start_vertex_id, true), (edge.end_vertex_id, false)] {
            let (end, side_in_range) = resolve_free_end(
                solid,
                edge_id,
                &first_mate,
                &second_mate,
                &rows,
                vertex,
                at_start,
            )?;
            if debug {
                eprintln!(
                    "  [os {overshoot_fraction:.2}] end v{vertex} at_start={at_start} end_face={} first_boundary={}(t={:.4}) second_boundary={}(t={:.4}) cr={:.4} cs={:.4} in_range={side_in_range}",
                    end.end_face_id,
                    end.first_edge_id,
                    end.first_edge_parameter,
                    end.second_edge_id,
                    end.second_edge_parameter,
                    end.cr_parameter,
                    end.cs_parameter,
                );
            }
            in_range &= side_in_range;
            ends.push(end);
        }
        Ok((rows, ends, in_range))
    };

    // Radius-aware seeded first attempt (occt-filleting-system-study §6(b)
    // lesson 7): OCCT floors corner extensions at 1.5·max_radius
    // (`ExtentTwoCorner`) instead of probing blindly.  Convert that floor to
    // an overshoot fraction of THIS edge: the contact rails sit r·tan(α/2)
    // from the edge (α = sign-adjusted angle between the mates' raw normals
    // at mid-edge — the march's own `cos_alpha`), so seed with 1.5× the
    // widest end radius's rail offset over the edge arc length, clamped to
    // the ladder's proven [0.08, 0.45] envelope.  Deterministic; `None` when
    // it degenerates or merely reproduces the ladder's first rung.
    let seeded_fraction: Option<f64> = (|| {
        let span = edge.t1 - edge.t0;
        let mut length = 0.0f64;
        let mut previous = edge.curve.evaluate(edge.t0).ok()?;
        for index in 1..=16 {
            let t = edge.t0 + span * index as f64 / 16.0;
            let point = edge.curve.evaluate(t).ok()?;
            length += point.sub(previous).length();
            previous = point;
        }
        if !(length > 0.0) || !length.is_finite() {
            return None;
        }
        let mid_t = edge.t0 + span * 0.5;
        let uv1 = edge_uv_on_face(first_mate.coedge, edge, mid_t).ok()?;
        let uv2 = edge_uv_on_face(second_mate.coedge, edge, mid_t).ok()?;
        let n1 = raw_normal(&first_mate.face.surface, uv1[0], uv1[1]).ok()?;
        let n2 = raw_normal(&second_mate.face.surface, uv2[0], uv2[1]).ok()?;
        let cos_alpha =
            (rho1.signum() * rho2.signum() * n1.dot(n2)).clamp(-1.0, 1.0);
        // tan(α/2) = √((1−cosα)/(1+cosα)); the tangent-offset factor from
        // the edge to each rail (box: α = π/2 → offset = r).
        let tan_half = ((1.0 - cos_alpha).max(0.0) / (1.0 + cos_alpha).max(1e-9)).sqrt();
        let end_radius = radius_at(edge.t0).abs().max(radius_at(edge.t1).abs());
        let fraction = (1.5 * end_radius * tan_half / length).clamp(0.08, 0.45);
        if !fraction.is_finite() || (fraction - 0.08).abs() < 1e-12 {
            return None;
        }
        Some(fraction)
    })();

    // Retry with a growing overshoot; keep the first attempt whose crossings
    // are all in range, else fall back to the widest march tried.  The seeded
    // attempt is accepted ONLY when its crossings land in range — otherwise
    // the blind ladder below runs exactly as before (including its
    // fallback-to-first-Ok semantics), so the seed can improve the first
    // landing but never change the fallback behaviour.
    let mut chosen: Option<(FittedRows, Vec<EndSurgery>)> = None;
    let mut last_error: Option<String> = None;
    if let Some(fraction) = seeded_fraction {
        match compute(fraction) {
            Ok((rows, ends, true)) => chosen = Some((rows, ends)),
            Ok(_) => {}
            Err(error) => last_error = Some(error),
        }
    }
    if chosen.is_none() {
        for &overshoot_fraction in &[0.08f64, 0.16, 0.28, 0.45] {
            match compute(overshoot_fraction) {
                Ok((rows, ends, in_range)) => {
                    let fallback = chosen.is_none();
                    if in_range {
                        chosen = Some((rows, ends));
                        break;
                    } else if fallback {
                        chosen = Some((rows, ends));
                    }
                }
                Err(error) => last_error = Some(error),
            }
        }
    }
    let (rows, ends) = chosen.ok_or_else(|| {
        last_error.unwrap_or_else(|| "blend: open march failed at every overshoot".into())
    })?;

    let [start_end, finish_end] = match <[EndSurgery; 2]>::try_from(ends) {
        Ok(pair) => pair,
        Err(_) => return Err("blend: open surgery needs exactly two ends".into()),
    };
    // A crossing that only resolved on a looser rung of the tolerance ladder
    // builds something master refused outright, so it must earn its answer
    // (see [`SpokeCrossings`]).
    let mut crossings = SpokeCrossings::default();
    crossings.note(start_end.escalated || finish_end.escalated);
    let mut result = solid.clone();
    let mut take_id = fresh_id_source(solid);
    build_open_surgery(
        solid,
        &mut result,
        &mut take_id,
        edge,
        &first_mate,
        &second_mate,
        rows,
        [EndPlan::Free(start_end), EndPlan::Free(finish_end)],
        name,
    )?;
    prune_orphan_vertices(&mut result);
    crossings.gate(result)
}

/// A fresh id allocator seeded past the vertex, edge, face, loop and coedge IDs.
/// Solid and shell IDs are outside this allocation domain. Shared by
/// a whole group of stripes so their vertices, edges and coedges cannot
/// collide.
pub(in crate::blend) fn fresh_id_source(solid: &BrepSolid) -> impl FnMut() -> u64 {
    let mut next_id = solid
        .vertices
        .iter()
        .map(|vertex| vertex.id)
        .chain(solid.edges.iter().map(|edge| edge.id))
        .chain(
            solid
                .shells
                .iter()
                .flat_map(|shell| &shell.faces)
                .flat_map(|face| {
                    face.loops
                        .iter()
                        .map(|loop_record| loop_record.id)
                        .chain(face.loops.iter().flat_map(|loop_record| {
                            loop_record.coedges.iter().map(|coedge| coedge.id)
                        }))
                        .chain(std::iter::once(face.id))
                }),
        )
        .max()
        .unwrap_or(0)
        + 1;
    move || {
        let id = next_id;
        next_id += 1;
        id
    }
}

/// Sew ONE stripe into `result`.
///
/// `solid` is the ORIGINAL topology every stripe was marched against (the
/// row-coincidence detection reads it); `result` is the shared evolving
/// solid, and `take_id` the shared id allocator — a group of stripes meeting
/// at a corner must create their rim vertices and cross-section arcs from one
/// counter, and must see each other's work.
///
/// Each end is either free (terminate on the face across the corner) or a
/// corner stop; see [`EndPlan`].  Pruning orphaned vertices is the caller's
/// job, once, after every stripe of the group is in.
pub(in crate::blend) fn build_open_surgery(
    solid: &BrepSolid,
    result: &mut BrepSolid,
    take_id: &mut dyn FnMut() -> u64,
    edge: &EdgeRecord,
    first: &BlendMate,
    second: &BlendMate,
    rows: FittedRows,
    ends: [EndPlan; 2],
    name: Option<&str>,
) -> Result<SewnStripe, String> {
    let [start_end, finish_end] = ends;

    // Trim the support rows to the crossing window.
    let trim_row = |row: &NurbsCurve, a: f64, b: f64| -> Result<NurbsCurve, String> {
        let (_, tail) = row.split(a)?;
        let (middle, _) = tail.split(b)?;
        Ok(middle)
    };
    let kind = |plan: &EndPlan| match plan {
        EndPlan::Free(_) => "free",
        EndPlan::Corner(_) => "corner",
        EndPlan::Miter(_) => "miter",
        EndPlan::Cap(_) => "cap",
    };
    let describe_trim = |error: String| {
        format!(
            "{error} (edge {} rows trimmed for a {} start at cr {:.6}/cs {:.6} and a {} finish \
             at cr {:.6}/cs {:.6})",
            edge.id,
            kind(&start_end),
            start_end.cr_parameter(),
            start_end.cs_parameter(),
            kind(&finish_end),
            finish_end.cr_parameter(),
            finish_end.cs_parameter()
        )
    };
    let cr = trim_row(&rows.cr, start_end.cr_parameter(), finish_end.cr_parameter())
        .map_err(describe_trim)?;
    let cr_pcurve = trim_row(
        &rows.cr_pcurve,
        start_end.cr_parameter(),
        finish_end.cr_parameter(),
    )?;
    let cs = trim_row(&rows.cs, start_end.cs_parameter(), finish_end.cs_parameter())
        .map_err(describe_trim)?;
    let cs_pcurve = trim_row(
        &rows.cs_pcurve,
        start_end.cs_parameter(),
        finish_end.cs_parameter(),
    )?;

    let cr_domain = cr.domain()?;
    let cs_domain = cs.domain()?;
    let old_start = edge.start_vertex_id;
    let old_finish = edge.end_vertex_id;

    // Classify each of the four support crossings.  A crossing that lands at
    // the FAR endpoint of the boundary edge it meets (the end away from the
    // corner) means a prior fillet already consumed that whole boundary: the
    // new blend reuses the existing vertex there and the boundary edge is
    // deleted (its role is taken over by the new transverse curve on the
    // prior blend face).  An interior crossing is the pristine case — a fresh
    // vertex with the boundary trimmed to it.
    let classify =
        |boundary_id: u64, boundary_param: f64, corner: u64| -> Result<RimResolution, String> {
            let boundary = result
                .edges
                .iter()
                .find(|candidate| candidate.id == boundary_id)
                .ok_or("blend: end boundary edge missing during surgery")?;
            let span = (boundary.t1 - boundary.t0).abs().max(1e-12);
            let far_vertex = if boundary.start_vertex_id == corner {
                Some((boundary.end_vertex_id, boundary.t1))
            } else if boundary.end_vertex_id == corner {
                Some((boundary.start_vertex_id, boundary.t0))
            } else {
                None
            };
            if let Some((far_id, _far_t)) = far_vertex {
                // A consumed boundary is a COINCIDENCE — a prior fillet's rim
                // vertex is exactly where this rail crosses — and the operands
                // were healed before the march, so it holds to solver
                // precision.  It is not "near the far end": a fillet whose
                // radius is 1e-3 short of the face's width crosses 1e-3 from
                // the far vertex and must keep that sliver, or the face is
                // snapped a full 1e-3 out of true (the oversized-radius limit
                // cases and issue 1177 measure exactly that).  Measured in
                // model units, never in the boundary's parameter — a unit
                // parameter on a 20-long edge would call 2e-3 a coincidence.
                let far_point = result
                    .vertices
                    .iter()
                    .find(|candidate| candidate.id == far_id)
                    .map(|candidate| candidate.point)
                    .ok_or("blend: consumed boundary far vertex missing")?;
                let near_point = result
                    .vertices
                    .iter()
                    .find(|candidate| candidate.id == corner)
                    .map(|candidate| candidate.point)
                    .ok_or("blend: boundary corner vertex missing")?;
                let crossing = boundary.curve.evaluate_extended(boundary_param)?;
                let extent = far_point.sub(near_point).length();
                let consumed_band = (1e-6 * (1.0 + extent)).max(1e-7);
                let _ = span;
                if crossing.sub(far_point).length() <= consumed_band {
                    // Sanity: the reused vertex must exist.
                    if !result
                        .vertices
                        .iter()
                        .any(|candidate| candidate.id == far_id)
                    {
                        return Err("blend: consumed boundary far vertex missing".into());
                    }
                    return Ok(RimResolution::Consumed(far_id));
                }
            }
            Ok(RimResolution::Fresh)
        };
    // A CORNER end has no boundary to classify: the ball's tangency vertex is
    // the rim, and the boundary edge that used to reach the sharp corner is
    // the neighbouring stripe's own blended edge, which that stripe replaces.
    let resolve_side = |plan: &EndPlan,
                        side_first: bool,
                        corner: u64|
     -> Result<RimResolution, String> {
        if let Some(vertex) = plan.planned_rim(side_first) {
            return Ok(RimResolution::Corner(vertex));
        }
        match plan {
            EndPlan::Free(free) => classify(
                if side_first {
                    free.first_edge_id
                } else {
                    free.second_edge_id
                },
                if side_first {
                    free.first_edge_parameter
                } else {
                    free.second_edge_parameter
                },
                corner,
            ),
            EndPlan::Corner(_) | EndPlan::Miter(_) | EndPlan::Cap(_) => {
                Err("blend: planned end without rim vertices".into())
            }
        }
    };
    let start_first = resolve_side(&start_end, true, old_start)?;
    let start_second = resolve_side(&start_end, false, old_start)?;
    let finish_first = resolve_side(&finish_end, true, old_finish)?;
    let finish_second = resolve_side(&finish_end, false, old_finish)?;

    // Manifold pairing: the blend's use of the first support row must oppose
    // F1's use of the blended edge (see the blend-loop construction below).
    let first_use_forward = first.coedge.forward;
    let blend_cr_forward = !first_use_forward;

    // Curve-level coincidence (OCCT PR #1449 lesson 3): when BOTH of a mate's
    // crossings are endpoint-consumed AND the trimmed support row retraces the
    // existing edge joining the two far vertices, that mate face is FULLY
    // consumed — the surgery sews the blend face straight onto the existing
    // edge and drops the zero-width face, instead of creating a coincident
    // fresh support edge that would leave a sliver strip (the r = face-width
    // class).  Each side is detected independently; any ambiguity keeps the
    // pristine path (fail-safe).  `row_traversed_from_start`: the blend loop
    // walks cr in station order iff `blend_cr_forward`, and cs in the
    // OPPOSITE order (see the two loop branches below).
    // A stripe with a CORNER end has no boundary edges at that end to be
    // coincident with, so the detection only runs on stripes that are free at
    // both ends.  (Fail-safe: not detecting a coincidence keeps the pristine
    // path, which is what a corner stop wants anyway.)
    let (sew_first, sew_second) = match (start_end.free(), finish_end.free()) {
        (Some(start_free), Some(finish_free)) => (
            detect_row_coincidence(
                solid,
                first,
                edge.id,
                start_free.first_edge_id,
                finish_free.first_edge_id,
                start_first.is_consumed(),
                start_first.existing().unwrap_or(0),
                finish_first.is_consumed(),
                finish_first.existing().unwrap_or(0),
                &cr,
                blend_cr_forward,
            )?,
            detect_row_coincidence(
                solid,
                second,
                edge.id,
                start_free.second_edge_id,
                finish_free.second_edge_id,
                start_second.is_consumed(),
                start_second.existing().unwrap_or(0),
                finish_second.is_consumed(),
                finish_second.existing().unwrap_or(0),
                &cs,
                !blend_cr_forward,
            )?,
        ),
        _ => (None, None),
    };
    // One face hosting both sides (the blended edge used twice by one face)
    // cannot be dropped for one side while the other still splices into it —
    // ambiguous, keep the pristine path for both.
    let (sew_first, sew_second): (Option<RowSew>, Option<RowSew>) =
        if first.face.id == second.face.id {
            (None, None)
        } else {
            (sew_first, sew_second)
        };

    // Resolve the four rim vertices: reuse the existing vertex for a consumed
    // side, else create a fresh vertex at the support-row endpoint.
    let mut resolve = |rim: &RimResolution, point: Result<Vec3, String>| -> Result<u64, String> {
        match rim.existing() {
            Some(id) => Ok(id),
            None => {
                let id = take_id();
                result.vertices.push(VertexRecord { id, point: point? });
                Ok(id)
            }
        }
    };
    let w1a = resolve(&start_first, cr.evaluate(cr_domain[0]))?;
    let w1b = resolve(&finish_first, cr.evaluate(cr_domain[1]))?;
    let w2a = resolve(&start_second, cs.evaluate(cs_domain[0]))?;
    let w2b = resolve(&finish_second, cs.evaluate(cs_domain[1]))?;

    // Support edges: a sewn side reuses the EXISTING coincident edge (no
    // fresh edge — OCCT's `SetExistingEdge` move); a pristine side gets the
    // fitted row as a fresh edge.
    let cr_edge_id = match &sew_first {
        Some(sew) => sew.edge_id,
        None => {
            let id = take_id();
            result.edges.push(EdgeRecord {
                id,
                curve: cr.clone(),
                t0: cr_domain[0],
                t1: cr_domain[1],
                start_vertex_id: w1a,
                end_vertex_id: w1b,
                degenerate: false,
                name: None,
            });
            id
        }
    };
    let cs_edge_id = match &sew_second {
        Some(sew) => sew.edge_id,
        None => {
            let id = take_id();
            result.edges.push(EdgeRecord {
                id,
                curve: cs.clone(),
                t0: cs_domain[0],
                t1: cs_domain[1],
                start_vertex_id: w2a,
                end_vertex_id: w2b,
                degenerate: false,
                name: None,
            });
            id
        }
    };
    // The edge closing each end of the blend face: the §6.9 transverse curve
    // on the end face for a free end, or — at a corner — the end
    // cross-section arc the corner patch was already given, committed by the
    // caller and merely referenced here.
    let mut commit_end_edge = |plan: &EndPlan,
                               first_rim: u64,
                               second_rim: u64|
     -> Result<Option<u64>, String> {
        match plan {
            EndPlan::Corner(_) | EndPlan::Miter(_) | EndPlan::Cap(_) => Ok(None),
            EndPlan::Free(free) => {
                let id = take_id();
                let domain = free.transverse_curve.domain()?;
                result.edges.push(EdgeRecord {
                    id,
                    curve: free.transverse_curve.clone(),
                    t0: domain[0],
                    t1: domain[1],
                    start_vertex_id: first_rim,
                    end_vertex_id: second_rim,
                    degenerate: false,
                    name: None,
                });
                Ok(Some(id))
            }
        }
    };
    let transverse_a_id = commit_end_edge(&start_end, w1a, w2a)?;
    let transverse_b_id = commit_end_edge(&finish_end, w1b, w2b)?;

    // Replace the blended edge in each PRISTINE mate's loop — the blend
    // face's loop direction is forced by manifold pairing with F1's use of
    // the blended edge (`first_use_forward`, captured above).  A sewn mate is
    // dropped whole below; nothing to splice.
    for (mate, new_edge_id, pcurve_forward, sewn) in [
        (first, cr_edge_id, &cr_pcurve, sew_first.is_some()),
        (second, cs_edge_id, &cs_pcurve, sew_second.is_some()),
    ] {
        if sewn {
            continue;
        }
        let face = result
            .shells
            .iter_mut()
            .flat_map(|shell| &mut shell.faces)
            .find(|face| face.id == mate.face.id)
            .ok_or("blend: mate face lost during surgery")?;
        let loop_record = &mut face.loops[mate.loop_index];
        let position = loop_record
            .coedges
            .iter()
            .position(|coedge| coedge.edge_id == edge.id)
            .ok_or("blend: edge coedge lost during surgery")?;
        let old_forward = loop_record.coedges[position].forward;
        loop_record.coedges[position] = CoedgeRecord {
            id: loop_record.coedges[position].id,
            edge_id: new_edge_id,
            forward: old_forward,
            pcurve: if old_forward {
                pcurve_forward.clone()
            } else {
                pcurve_forward.reversed()?
            },
        };
    }

    // A capped end's legs: on each mate, the leg runs from the rail's rim
    // vertex to the sharp vertex, where the continuing edge still starts.
    // It goes between the rail coedge and that continuing coedge, with the
    // sense that walks rim -> vertex when the rail ends at the rim.
    for (plan, at_start) in [(&start_end, true), (&finish_end, false)] {
        let EndPlan::Cap(cap) = plan else {
            continue;
        };
        for (mate, rail_edge_id, leg, rim) in [
            (first, cr_edge_id, &cap.first_leg, if at_start { w1a } else { w1b }),
            (second, cs_edge_id, &cap.second_leg, if at_start { w2a } else { w2b }),
        ] {
            let face = result
                .shells
                .iter_mut()
                .flat_map(|shell| &mut shell.faces)
                .find(|face| face.id == mate.face.id)
                .ok_or("blend: mate face lost during cap splice")?;
            let loop_record = &mut face.loops[mate.loop_index];
            let count = loop_record.coedges.len();
            let rail_at = loop_record
                .coedges
                .iter()
                .position(|coedge| coedge.edge_id == rail_edge_id)
                .ok_or("blend: rail coedge lost during cap splice")?;
            // Which side of the rail coedge is this end?  The rail coedge
            // traverses rim-to-rim; the capped end is at its traversal END
            // when walking forward means station order and this is the
            // finish end, etc.  Decide by geometry: the neighbour whose
            // traversal touches the sharp vertex.
            let rail_forward = loop_record.coedges[rail_at].forward;
            let end_is_traversal_end = if rail_forward { !at_start } else { at_start };
            let (insert_at, forward, pcurve) = if end_is_traversal_end {
                // rail ... rim -> [leg rim->vertex] -> continuing edge
                (rail_at + 1, true, leg.1.clone())
            } else {
                // continuing edge -> [leg vertex->rim] -> rim ... rail
                (rail_at, false, leg.1.reversed()?)
            };
            let _ = (count, rim);
            loop_record.coedges.insert(
                insert_at,
                CoedgeRecord {
                    id: take_id(),
                    edge_id: leg.0,
                    forward,
                    pcurve,
                },
            );
        }
    }

    // Drop consumed boundary edges from the mate loop they share with the
    // blended edge: the fresh support coedge already begins at the reused far
    // vertex, so removing the fully-covered boundary keeps the loop closed.
    // A SEWN mate's whole loop collapses (the face is dropped below), so its
    // consumed boundaries are only recorded for deletion, never spliced.
    let mut consumed_edges: Vec<u64> = Vec::new();
    let start_free = start_end.free();
    let finish_free = finish_end.free();
    for (mate, sewn, sides) in [
        (
            first,
            sew_first.is_some(),
            [
                (&start_first, start_free.map(|free| free.first_edge_id)),
                (&finish_first, finish_free.map(|free| free.first_edge_id)),
            ],
        ),
        (
            second,
            sew_second.is_some(),
            [
                (&start_second, start_free.map(|free| free.second_edge_id)),
                (&finish_second, finish_free.map(|free| free.second_edge_id)),
            ],
        ),
    ] {
        for (cross, boundary_id) in sides {
            if !cross.is_consumed() {
                continue;
            }
            let Some(boundary_id) = boundary_id else {
                continue;
            };
            if !sewn {
                let face = result
                    .shells
                    .iter_mut()
                    .flat_map(|shell| &mut shell.faces)
                    .find(|face| face.id == mate.face.id)
                    .ok_or("blend: mate face lost during surgery")?;
                face.loops[mate.loop_index]
                    .coedges
                    .retain(|coedge| coedge.edge_id != boundary_id);
            }
            if !consumed_edges.contains(&boundary_id) {
                consumed_edges.push(boundary_id);
            }
        }
    }
    // Lesson 7: zero-span leftovers of a collapsing loop go with their face.
    for sew in [&sew_first, &sew_second].into_iter().flatten() {
        for id in &sew.collapsed_edges {
            if !consumed_edges.contains(id) {
                consumed_edges.push(*id);
            }
        }
    }

    // Locate the corner junction on each end face BEFORE trimming (the two
    // boundary coedges that meet at the old corner vertex, stepping over the
    // pole between them where the end face's apex IS that vertex) — edge ids
    // alone are ambiguous on two-coedge cap loops, so the meeting must be at
    // the corner.
    // (end, transverse_id, corner, first_consumed, second_consumed) -> plan.
    // Only FREE ends appear here: a corner stop rebuilds nothing on a third
    // face, because the corner patch is what closes it.
    let mut end_plans = Vec::with_capacity(2);
    for (end, transverse_id, corner, first_consumed, second_consumed) in [
        (
            start_end.free(),
            transverse_a_id,
            old_start,
            start_first.is_consumed(),
            start_second.is_consumed(),
        ),
        (
            finish_end.free(),
            transverse_b_id,
            old_finish,
            finish_first.is_consumed(),
            finish_second.is_consumed(),
        ),
    ] {
        let (Some(end), Some(transverse_id)) = (end, transverse_id) else {
            continue;
        };
        let face = result
            .shells
            .iter()
            .flat_map(|shell| &shell.faces)
            .find(|face| face.id == end.end_face_id)
            .ok_or("blend: end face lost during surgery")?;
        // Key on stable coedge ids (not indices) so processing one end can't
        // invalidate another that shares this face.
        let Some(located) = locate_end_corner(
            &result,
            face,
            corner,
            end.first_edge_id,
            end.second_edge_id,
        ) else {
            return Err("blend: end-face corner (adjacent boundary coedges) not found".into());
        };
        // The apex the transverse curve cuts off goes with the boundaries the
        // blend consumes.
        for pole in &located.pole_edge_ids {
            if !consumed_edges.contains(pole) {
                consumed_edges.push(*pole);
            }
        }
        end_plans.push((
            end.end_face_id,
            transverse_id,
            end.transverse_end_pcurve.clone(),
            located,
            first_consumed,
            second_consumed,
        ));
    }

    // Trim the boundary edges at their support crossings.  A consumed side is
    // deleted instead of trimmed; a CORNER side touches no boundary at all.
    for (rim_resolution, boundary, corner, rim) in [
        (
            &start_first,
            start_free.map(|free| (free.first_edge_id, free.first_edge_parameter)),
            old_start,
            w1a,
        ),
        (
            &start_second,
            start_free.map(|free| (free.second_edge_id, free.second_edge_parameter)),
            old_start,
            w2a,
        ),
        (
            &finish_first,
            finish_free.map(|free| (free.first_edge_id, free.first_edge_parameter)),
            old_finish,
            w1b,
        ),
        (
            &finish_second,
            finish_free.map(|free| (free.second_edge_id, free.second_edge_parameter)),
            old_finish,
            w2b,
        ),
    ] {
        if !rim_resolution.trims_boundary() {
            continue;
        }
        let Some((boundary_id, boundary_param)) = boundary else {
            continue;
        };
        trim_edge_at(result, boundary_id, boundary_param, corner, rim)?;
    }

    // Rebuild each end face's corner: drop the consumed boundary coedge(s) and
    // splice in the transverse coedge between the (trimmed) boundaries.
    for (end_face, transverse_id, transverse_end_pcurve, located, first_consumed, second_consumed) in
        end_plans
    {
        let forward = located.x_is_first;
        let pcurve = if forward {
            transverse_end_pcurve
        } else {
            transverse_end_pcurve.reversed()?
        };
        let (x_consumed, y_consumed) = if located.x_is_first {
            (first_consumed, second_consumed)
        } else {
            (second_consumed, first_consumed)
        };
        let transverse_coedge = CoedgeRecord {
            id: take_id(),
            edge_id: transverse_id,
            forward,
            pcurve,
        };
        splice_end_corner(
            result,
            end_face,
            &located,
            transverse_coedge,
            x_consumed,
            y_consumed,
        )?;
    }

    // Blend face: cr fwd -> TB -> cs rev -> TA rev in (t, z) space.
    let mid_u = (cr_domain[0] + cr_domain[1]) * 0.5;
    let blend_normal = raw_normal(&rows.surface, mid_u, 0.0)?;
    let station_uv = cr_pcurve.evaluate(mid_u)?;
    let n1 = raw_normal(&first.face.surface, station_uv.x, station_uv.y)?;
    let out1 = if first.face.same_sense {
        n1
    } else {
        n1.scale(-1.0)
    };
    let same_sense = blend_normal.dot(out1) >= 0.0;
    let loop_id = take_id();
    // Traversal senses of the blend's support coedges.  A fresh support edge
    // is parameterized in station order, so the sense is the loop's walking
    // direction (`blend_cr_forward` for cr, its opposite for cs); a SEWN
    // side's sense comes from the detection (the existing edge's own
    // parameter direction relative to that same walk — equal to the dropped
    // face's old sense, preserving manifold pairing with the survivor).  The
    // pcurves always follow the LOOP's walking direction and are unchanged.
    let cr_forward = sew_first
        .as_ref()
        .map_or(blend_cr_forward, |sew| sew.forward);
    let cs_forward = sew_second
        .as_ref()
        .map_or(!blend_cr_forward, |sew| sew.forward);
    // The two end slots of the blend loop.  `natural_forward` is the sense the
    // loop walks a transverse edge stored first-rim -> second-rim; a CORNER
    // arc was already committed in the walk direction (so the corner patch can
    // take it the other way round), so it is always used forward.
    // A slot is one coedge for a free end (the transverse curve) or a corner
    // end (the section arc), and one or two for a miter end (the seam, then
    // the sibling's section when the seam left the sibling first).  A corner
    // arc was committed in the walk direction; a miter edge records its own
    // sense along the walk.
    let mut end_slot = |plan: &EndPlan,
                        free_edge_id: Option<u64>,
                        natural_forward: bool|
     -> Result<Vec<CoedgeRecord>, String> {
        match plan {
            EndPlan::Corner(end) => Ok(vec![CoedgeRecord {
                id: take_id(),
                edge_id: end.arc_edge_id,
                forward: true,
                pcurve: end.arc_blend_pcurve.clone(),
            }]),
            EndPlan::Cap(end) => Ok(vec![CoedgeRecord {
                id: take_id(),
                edge_id: end.arc_edge_id,
                forward: true,
                pcurve: end.arc_blend_pcurve.clone(),
            }]),
            EndPlan::Miter(end) => end
                .edges
                .iter()
                .map(|(edge_id, forward, pcurve)| {
                    Ok(CoedgeRecord {
                        id: take_id(),
                        edge_id: *edge_id,
                        forward: *forward,
                        pcurve: pcurve.clone(),
                    })
                })
                .collect(),
            EndPlan::Free(free) => {
                let edge_id =
                    free_edge_id.ok_or("blend: free end without its transverse edge")?;
                Ok(vec![if natural_forward {
                    CoedgeRecord {
                        id: take_id(),
                        edge_id,
                        forward: true,
                        pcurve: free.transverse_blend_pcurve.clone(),
                    }
                } else {
                    CoedgeRecord {
                        id: take_id(),
                        edge_id,
                        forward: false,
                        pcurve: free.transverse_blend_pcurve.reversed()?,
                    }
                }])
            }
        }
    };
    let start_slot = end_slot(&start_end, transverse_a_id, !blend_cr_forward)?;
    let finish_slot = end_slot(&finish_end, transverse_b_id, blend_cr_forward)?;
    let coedges = if blend_cr_forward {
        let mut coedges = vec![CoedgeRecord {
            id: take_id(),
            edge_id: cr_edge_id,
            forward: cr_forward,
            pcurve: crate::sweep_topology::parameter_line(
                cr_domain[0],
                0.0,
                cr_domain[1],
                0.0,
            )?,
        }];
        coedges.extend(finish_slot);
        coedges.push(CoedgeRecord {
            id: take_id(),
            edge_id: cs_edge_id,
            forward: cs_forward,
            pcurve: cs_blend_pcurve_reversed(&cs_domain)?,
        });
        coedges.extend(start_slot);
        coedges
    } else {
        let mut coedges = vec![CoedgeRecord {
            id: take_id(),
            edge_id: cr_edge_id,
            forward: cr_forward,
            pcurve: crate::sweep_topology::parameter_line(
                cr_domain[1],
                0.0,
                cr_domain[0],
                0.0,
            )?,
        }];
        coedges.extend(start_slot);
        coedges.push(CoedgeRecord {
            id: take_id(),
            edge_id: cs_edge_id,
            forward: cs_forward,
            pcurve: crate::sweep_topology::parameter_line(
                cs_domain[0],
                1.0,
                cs_domain[1],
                1.0,
            )?,
        });
        coedges.extend(finish_slot);
        coedges
    };
    let blend_face_id = take_id();
    let mut blend_face = FaceRecord {
        id: blend_face_id,
        surface: rows.surface,
        same_sense,
        loops: vec![LoopRecord {
            id: loop_id,
            coedges,
        }],
        name: name.map(|value| value.to_string()),
    };
    if rows.exact_extrusion {
        transpose_face(&mut blend_face)?;
    }
    let shell_index = result
        .shells
        .iter()
        .position(|shell| shell.faces.iter().any(|face| face.id == first.face.id))
        .ok_or("blend: mate shell lost during surgery")?;
    // Drop the fully-consumed mate faces (lesson 3): their loops collapsed
    // between the sewn edge and the blend; the consumed boundaries and
    // lesson-7 leftovers are deleted below, the sewn edge lives on shared by
    // the blend face and the surviving neighbour.
    for (mate, sew) in [(first, &sew_first), (second, &sew_second)] {
        if sew.is_some() {
            for shell in &mut result.shells {
                shell.faces.retain(|face| face.id != mate.face.id);
            }
        }
    }
    result.shells[shell_index].faces.push(blend_face);

    result.edges.retain(|candidate| candidate.id != edge.id);
    // Delete the boundary edges a prior fillet's corner had left behind that
    // this blend fully consumed.
    result
        .edges
        .retain(|candidate| !consumed_edges.contains(&candidate.id));
    Ok(SewnStripe {
        cr_edge_id,
        cs_edge_id,
        blend_face_id,
    })
}

/// Swap the two parameters of a face: the surface's control net, every
/// coedge pcurve, and the sense (S_u × S_v changes sign).  The face's
/// geometry is untouched; only its chart is.  Used to hand an exact
/// cylinder patch built with its section along v to the analytic recogniser,
/// which wants the circle along u.
pub(in crate::blend) fn transpose_face(face: &mut FaceRecord) -> Result<(), String> {
    let surface = &face.surface;
    let rows_u = surface.control_points.len();
    let rows_v = surface.control_points.first().map(|row| row.len()).unwrap_or(0);
    let mut transposed = vec![Vec::with_capacity(rows_u); rows_v];
    for row in &surface.control_points {
        for (j, point) in row.iter().enumerate() {
            transposed[j].push(*point);
        }
    }
    face.surface = NurbsSurface::new(
        surface.degree_v,
        surface.degree_u,
        surface.knots_v.clone(),
        surface.knots_u.clone(),
        transposed,
    )?;
    for loop_record in &mut face.loops {
        for coedge in &mut loop_record.coedges {
            for control in &mut coedge.pcurve.control_points {
                std::mem::swap(&mut control.x, &mut control.y);
            }
        }
    }
    face.same_sense = !face.same_sense;
    Ok(())
}

/// Drop every vertex no longer referenced by an edge — the sharp corners the
/// blends replaced, and anything freed by a consumed boundary.  Run ONCE after
/// a whole group of stripes is in: a corner vertex is still referenced by the
/// selected edges that have not been sewn yet.
pub(in crate::blend) fn prune_orphan_vertices(result: &mut BrepSolid) {
    let used: rustc_hash::FxHashSet<u64> = result
        .edges
        .iter()
        .flat_map(|candidate| [candidate.start_vertex_id, candidate.end_vertex_id])
        .collect();
    result
        .vertices
        .retain(|candidate| used.contains(&candidate.id));
}

fn cs_blend_pcurve_reversed(cs_domain: &[f64; 2]) -> Result<NurbsCurve, String> {
    crate::sweep_topology::parameter_line(cs_domain[1], 1.0, cs_domain[0], 1.0)
}

// BREP private tests: 9cca6ef52feb16d7