brep_kernel/edit/

split.rs

//! Cut / split a body by a plane (Golovanov §6.4).
//!
//! The split reuses the ROBUST boolean rather than a bespoke classifier: the
//! plane is realised as two very large half-space TOOL boxes (one covering each
//! side of the plane), and each output piece is `Intersect(solid, tool)`. The
//! boolean machinery imprints the cut plane onto the solid and re-closes the
//! shell, so both pieces inherit the kernel's validated, watertight topology.

use crate::boolean::{boolean_operation, BooleanOperation, BooleanOptions};
use crate::spatial::Aabb;
use crate::topology::{make_box_brep, make_cylinder_brep, BrepSolid};
use crate::transform_topology::{transform_brep, AffineTransform};
use crate::{
    make_cone_brep, make_sphere_brep, make_torus_brep, AnalyticSurface, NurbsSurface, Vec3,
};
use serde::Deserialize;

/// Axis-aligned bounding box of a solid's vertices.
fn solid_aabb(solid: &BrepSolid) -> Aabb {
    let mut bounds = Aabb::empty();
    for vertex in &solid.vertices {
        bounds.include_point(vertex.point);
    }
    bounds
}

/// A boolean result counts as an empty piece when it carries no face geometry —
/// i.e. the half-space tool did not overlap the solid on that side.
fn is_empty_piece(solid: &BrepSolid) -> bool {
    solid.shells.is_empty() || solid.shells.iter().all(|shell| shell.faces.is_empty())
}

/// Build the affine placing a local, origin-centred cube so its local +Z axis
/// maps to `n`, +X to `u`, +Y to `v`, and its centre lands at `center`. The
/// columns of the rotation are `[u v n]` (a right-handed, det = +1 frame), so
/// the map is a proper rigid motion (no orientation reversal needed).
fn frame_transform(u: Vec3, v: Vec3, n: Vec3, center: Vec3) -> Result<AffineTransform, String> {
    AffineTransform::new([
        u.x, v.x, n.x, center.x, //
        u.y, v.y, n.y, center.y, //
        u.z, v.z, n.z, center.z, //
        0.0, 0.0, 0.0, 1.0,
    ])
}

/// Split `solid` into two pieces by the plane through `plane_point` with normal
/// `plane_normal`. Returns `(below, above)` where `below` is the piece on the
/// −n side of the plane and `above` the piece on the +n side.
///
/// Contract: when the plane does not actually divide the solid into two
/// non-degenerate pieces (it misses the body, or is tangent so one side is
/// empty), this returns `Err("split_solid_by_plane: plane does not intersect
/// the solid")` rather than a degenerate/empty piece.
pub fn split_solid_by_plane(
    solid: &BrepSolid,
    plane_point: Vec3,
    plane_normal: Vec3,
) -> Result<(BrepSolid, BrepSolid), String> {
    let n = plane_normal.normalized()?;
    // Orthonormal frame (n, u, v): u ⟂ n (unit), v = n × u (unit); [u v n] is
    // right-handed so the tool placement is a proper rotation.
    let u = n.perpendicular()?;
    let v = n.cross(u);

    let bounds = solid_aabb(solid);
    if !bounds.minimum.x.is_finite() {
        return Err("split_solid_by_plane: solid has no geometry".into());
    }
    let diagonal = bounds.diagonal();
    if diagonal <= 0.0 {
        return Err("split_solid_by_plane: solid is degenerate".into());
    }
    // A tool box 3× the solid diagonal on every side easily covers the body in
    // the plane's tangent directions.
    let length = 3.0 * diagonal;
    let half = 0.5 * length;

    // Centre the tool in the tangent (u, v) plane on the projection of the AABB
    // centre onto the cut plane, so the box brackets the whole solid regardless
    // of where `plane_point` sits within it. Along n it is offset by ±half so
    // the tool's cut face lands exactly on the plane.
    let center = bounds.minimum.add(bounds.maximum).scale(0.5);
    let center_on_plane = center.sub(n.scale(center.sub(plane_point).dot(n)));

    // Local cube centred at the local origin, spanning [-half, half]³.
    let cube = make_box_brep(Vec3::new(-half, -half, -half), length, length, length)?;

    // BELOW: tool centred at plane − n·half, so its +n face lies on the plane
    // and it extends distance `length` along −n, covering the −n side.
    let below_center = center_on_plane.sub(n.scale(half));
    let tool_below = transform_brep(&cube, frame_transform(u, v, n, below_center)?, false)?;

    // ABOVE: mirror to the +n side (centre at plane + n·half).
    let above_center = center_on_plane.add(n.scale(half));
    let tool_above = transform_brep(&cube, frame_transform(u, v, n, above_center)?, false)?;

    let options = BooleanOptions::default();
    let below = boolean_operation(solid, &tool_below, BooleanOperation::Intersect, &options);
    let above = boolean_operation(solid, &tool_above, BooleanOperation::Intersect, &options);

    match (below, above) {
        (Ok(below), Ok(above)) if !is_empty_piece(&below) && !is_empty_piece(&above) => {
            Ok((below, above))
        }
        _ => Err("split_solid_by_plane: plane does not intersect the solid".into()),
    }
}

// ---------------------------------------------------------------------------
// Generalized split by an analytic surface (Golovanov §6.4).
//
// The plane case above splits a body against two large half-space TOOL boxes.
// The analytic cases generalize that idea: an unbounded/bounded analytic
// surface (cylinder, cone, sphere, torus) is realised as ONE CLOSED SOLID
// region big enough to span the body wherever it matters, and the two output
// pieces are the boolean `Intersect` (inside the tool region) and `Subtract`
// (outside it) of the body against that region.  Because every cut runs
// through the validated boolean machinery, each piece inherits watertight
// topology, the cut surface is imprinted onto the body, and the two volumes
// sum to the original.
// ---------------------------------------------------------------------------

/// A closed analytic tool region used to cut a body.  Each variant is realised
/// as a closed solid (unbounded carriers are capped well beyond the body) whose
/// interior is one side of the analytic surface.
#[derive(Clone, Copy, Debug, Deserialize)]
#[serde(tag = "type", rename_all = "lowercase")]
pub enum SplitSurface {
    /// Infinite plane through `point` with `normal`; delegates to the plane path.
    Plane { point: Vec3, normal: Vec3 },
    /// Infinite cylinder about the axis line through `axis_point` along
    /// `axis_dir`, of the given `radius`.  Interior = inside the cylinder.
    Cylinder {
        axis_point: Vec3,
        axis_dir: Vec3,
        radius: f64,
    },
    /// Sphere centred at `center`.  Interior = inside the ball.
    Sphere { center: Vec3, radius: f64 },
    /// Single-nappe cone with its apex at `apex`, opening along `+axis_dir`,
    /// with the given `half_angle` (radians, apex half-angle).  Interior =
    /// inside the cone.
    Cone {
        apex: Vec3,
        axis_dir: Vec3,
        half_angle: f64,
    },
    /// Torus centred at `center` about `axis_dir`.  Interior = inside the tube.
    Torus {
        center: Vec3,
        axis_dir: Vec3,
        major_radius: f64,
        minor_radius: f64,
    },
}

/// Bounds + a sane margin/diagonal for a body, erroring on empty/degenerate
/// geometry the same way the plane path does.
fn solid_extent(solid: &BrepSolid) -> Result<(Aabb, f64), String> {
    let bounds = solid_aabb(solid);
    if !bounds.minimum.x.is_finite() {
        return Err("split_solid_by_surface: solid has no geometry".into());
    }
    let diagonal = bounds.diagonal();
    if diagonal <= 0.0 {
        return Err("split_solid_by_surface: solid is degenerate".into());
    }
    Ok((bounds, diagonal))
}

/// Build the closed tool solid for an analytic tool, sized to fully span the
/// body wherever the analytic surface passes through it.
fn build_tool_solid(solid: &BrepSolid, tool: &SplitSurface) -> Result<BrepSolid, String> {
    let (_, diagonal) = solid_extent(solid)?;
    let margin = diagonal.max(1.0);
    match *tool {
        SplitSurface::Plane { .. } => {
            Err("build_tool_solid: plane is handled by the plane path".into())
        }
        SplitSurface::Cylinder {
            axis_point,
            axis_dir,
            radius,
        } => {
            if radius <= 0.0 {
                return Err("split_solid_by_surface: cylinder radius must be positive".into());
            }
            let axis = axis_dir.normalized()?;
            // Extend the capped cylinder a full margin beyond the body's span
            // along the axis so its caps never cut the body.
            let (t_min, t_max) = axis_span(solid, axis_point, axis);
            let base = axis_point.add(axis.scale(t_min - margin));
            let height = (t_max - t_min) + 2.0 * margin;
            make_cylinder_brep(base, axis, radius, height)
        }
        SplitSurface::Sphere { center, radius } => {
            if radius <= 0.0 {
                return Err("split_solid_by_surface: sphere radius must be positive".into());
            }
            // A sphere is already a closed, bounded region.
            make_sphere_brep(center, radius, Vec3::new(0.0, 0.0, 1.0))
        }
        SplitSurface::Cone {
            apex,
            axis_dir,
            half_angle,
        } => {
            if !(half_angle > 0.0 && half_angle < std::f64::consts::FRAC_PI_2) {
                return Err("split_solid_by_surface: cone half-angle must be in (0, pi/2)".into());
            }
            let axis = axis_dir.normalized()?;
            // Distance of the farthest body point along +axis from the apex.
            let (_, d_max) = axis_span(solid, apex, axis);
            if d_max <= 0.0 {
                return Err(
                    "split_solid_by_surface: cone does not reach the solid (body is behind the apex)"
                        .into(),
                );
            }
            let big_h = d_max + margin;
            // Realise the nappe as a cone whose apex sits at `apex` and whose
            // base cap lands `big_h` past it along +axis: base at apex+axis·H,
            // built with axis pointing back to the apex so top(0-radius)=apex.
            let base = apex.add(axis.scale(big_h));
            let base_radius = big_h * half_angle.tan();
            make_cone_brep(base, axis.scale(-1.0), base_radius, 0.0, big_h)
        }
        SplitSurface::Torus {
            center,
            axis_dir,
            major_radius,
            minor_radius,
        } => {
            if minor_radius <= 0.0 || major_radius <= 0.0 {
                return Err("split_solid_by_surface: torus radii must be positive".into());
            }
            // A torus is already a closed, bounded region.
            make_torus_brep(center, axis_dir, major_radius, minor_radius)
        }
    }
}

/// Signed span `[min, max]` of the body's vertices projected onto the axis line
/// through `origin` along the unit direction `axis`.
fn axis_span(solid: &BrepSolid, origin: Vec3, axis: Vec3) -> (f64, f64) {
    let mut t_min = f64::INFINITY;
    let mut t_max = f64::NEG_INFINITY;
    for vertex in &solid.vertices {
        let t = vertex.point.sub(origin).dot(axis);
        t_min = t_min.min(t);
        t_max = t_max.max(t);
    }
    (t_min, t_max)
}

/// Split `solid` into pieces by an analytic tool surface (Golovanov §6.4).
///
/// For the `Plane` tool this is exactly `split_solid_by_plane`, returned as
/// `[below, above]`.  For a closed analytic tool region (cylinder / sphere /
/// cone / torus) the two pieces are `[inside, outside]` where `inside =
/// solid ∩ tool` and `outside = solid − tool`.  Both pieces are guaranteed
/// non-empty and valid; their volumes sum to the original.
///
/// Contract: when the tool does not actually divide the body into two
/// non-degenerate pieces (it misses the body, or wholly contains / is wholly
/// contained so one side is empty), this returns a clear `Err` rather than a
/// degenerate/empty piece.
pub fn split_solid_by_surface(
    solid: &BrepSolid,
    tool: &SplitSurface,
) -> Result<Vec<BrepSolid>, String> {
    if let SplitSurface::Plane { point, normal } = *tool {
        let (below, above) = split_solid_by_plane(solid, point, normal)?;
        return Ok(vec![below, above]);
    }

    let tool_solid = build_tool_solid(solid, tool)?;
    let options = BooleanOptions::default();
    let inside = boolean_operation(solid, &tool_solid, BooleanOperation::Intersect, &options);
    let outside = boolean_operation(solid, &tool_solid, BooleanOperation::Subtract, &options);

    match (inside, outside) {
        (Ok(inside), Ok(outside))
            if !is_empty_piece(&inside)
                && !is_empty_piece(&outside)
                && inside.validate().is_empty()
                && outside.validate().is_empty() =>
        {
            Ok(vec![inside, outside])
        }
        _ => Err("split_solid_by_surface: tool surface does not divide the solid".into()),
    }
}

/// Map a face's exact analytic carrier to the closed tool region that splits a
/// body by that surface.  Reuses the kernel's own analytic recognition so the
/// caller only has to hand over the selected face's surface (no host-side
/// geometry extraction).  Unrecognized / general-revolution carriers are
/// reported as unsupported (deferred), never approximated.
fn recognized_split_surface(surface: &NurbsSurface) -> Result<SplitSurface, String> {
    let analytic = surface
        .analytic()
        .ok_or("split_solid_by_face_surface: selected face is not an analytic surface")?;
    match analytic {
        AnalyticSurface::Plane {
            origin,
            u_dir,
            v_dir,
            ..
        } => {
            let normal = u_dir.cross(*v_dir).normalized()?;
            Ok(SplitSurface::Plane {
                point: *origin,
                normal,
            })
        }
        AnalyticSurface::RuledRevolution {
            frame,
            rho0,
            rho1,
            height,
        } => {
            // Cylinder when the two radii coincide, otherwise a cone/frustum.
            let scale = rho0.abs().max(rho1.abs()).max(1.0);
            if (rho0 - rho1).abs() <= 1e-9 * scale {
                Ok(SplitSurface::Cylinder {
                    axis_point: frame.origin,
                    axis_dir: frame.axis,
                    radius: 0.5 * (rho0 + rho1),
                })
            } else {
                // radius(axial) = rho0 + slope·axial, apex where radius = 0.
                let slope = (rho1 - rho0) / height;
                let axial_apex = -rho0 / slope;
                let apex = frame.origin.add(frame.axis.scale(axial_apex));
                // The nappe opens in the direction of increasing radius.
                let axis_dir = if slope >= 0.0 {
                    frame.axis
                } else {
                    frame.axis.scale(-1.0)
                };
                Ok(SplitSurface::Cone {
                    apex,
                    axis_dir,
                    half_angle: slope.abs().atan(),
                })
            }
        }
        AnalyticSurface::Sphere { frame, radius } => Ok(SplitSurface::Sphere {
            center: frame.origin,
            radius: *radius,
        }),
        AnalyticSurface::Torus {
            frame,
            major_radius,
            minor_radius,
        } => Ok(SplitSurface::Torus {
            center: frame.origin,
            axis_dir: frame.axis,
            major_radius: *major_radius,
            minor_radius: *minor_radius,
        }),
        AnalyticSurface::Revolution { .. } => Err(
            "split_solid_by_face_surface: general revolved surfaces are not supported as a cut tool"
                .into(),
        ),
    }
}

/// Split `solid` by the analytic carrier of a selected face `surface`
/// (Golovanov §6.4).  The face may be a plane, cylinder, cone, or sphere; the
/// carrier is extended to fully span the body.  Returns the two pieces
/// (`[below, above]` for a plane, `[inside, outside]` otherwise).  Errors on
/// non-analytic / general-revolution faces, or when the carrier does not
/// cleanly divide the body.
pub fn split_solid_by_face_surface(
    solid: &BrepSolid,
    surface: &NurbsSurface,
) -> Result<Vec<BrepSolid>, String> {
    let tool = recognized_split_surface(surface)?;
    split_solid_by_surface(solid, &tool)
}

#[cfg(test)]
mod tests {
    use super::*;
    use crate::{
        boolean_semantic_disagreement, make_box_brep, solid_mass_properties, BooleanOperation,
    };

    fn aabb(solid: &BrepSolid) -> (Vec3, Vec3) {
        let bounds = solid_aabb(solid);
        (bounds.minimum, bounds.maximum)
    }

    fn face_count(solid: &BrepSolid) -> usize {
        solid.shells.iter().map(|shell| shell.faces.len()).sum()
    }

    fn volume(solid: &BrepSolid) -> f64 {
        solid_mass_properties(solid).unwrap().volume
    }

    /// The `inside` piece must agree with `solid ∩ tool` and the `outside` piece
    /// with `solid − tool` at essentially every decidable sample point.
    fn assert_oracle_clean(
        solid: &BrepSolid,
        tool_solid: &BrepSolid,
        inside: &BrepSolid,
        outside: &BrepSolid,
    ) {
        let in_report = boolean_semantic_disagreement(
            solid,
            tool_solid,
            BooleanOperation::Intersect,
            inside,
            4000,
        )
        .unwrap();
        eprintln!(
            "  inside oracle: considered={} disagreements={} rate={:.6}",
            in_report.considered,
            in_report.disagreements.len(),
            in_report.disagreement_rate
        );
        // The kernel's own boolean correctness gate is `!is_flagged()`
        // (disagreement_rate <= DISAGREEMENT_THRESHOLD = 0.03).  The rare
        // residual disagreements here are grazing/near-boundary ray-cast noise,
        // not wrong topology; hold the pieces to well under 1% (~0).
        assert!(
            !in_report.is_flagged() && in_report.disagreement_rate < 0.01,
            "inside piece disagrees with solid∩tool (rate {}): {:?}",
            in_report.disagreement_rate,
            in_report.sample_disagreement()
        );
        let out_report = boolean_semantic_disagreement(
            solid,
            tool_solid,
            BooleanOperation::Subtract,
            outside,
            4000,
        )
        .unwrap();
        eprintln!(
            "  outside oracle: considered={} disagreements={} rate={:.6}",
            out_report.considered,
            out_report.disagreements.len(),
            out_report.disagreement_rate
        );
        assert!(
            !out_report.is_flagged() && out_report.disagreement_rate < 0.01,
            "outside piece disagrees with solid−tool (rate {}): {:?}",
            out_report.disagreement_rate,
            out_report.sample_disagreement()
        );
    }

    #[test]
    fn split_box_by_midplane_halves_it() {
        // Box(10³) centred at the origin.
        let box_solid = make_box_brep(Vec3::new(-5.0, -5.0, -5.0), 10.0, 10.0, 10.0).unwrap();

        let (below, above) =
            split_solid_by_plane(&box_solid, Vec3::default(), Vec3::new(1.0, 0.0, 0.0)).unwrap();

        // (1) Both pieces are valid, watertight solids.
        assert!(
            below.validate().is_empty(),
            "below invalid: {:?}",
            below.validate()
        );
        assert!(
            above.validate().is_empty(),
            "above invalid: {:?}",
            above.validate()
        );

        // (2) Each half is still a six-faced box (5 trimmed originals + 1 cut).
        assert_eq!(face_count(&below), 6);
        assert_eq!(face_count(&above), 6);

        // (3) Volumes: each ≈ 500, summing to ≈ 1000 (allow small boolean noise).
        let vol_below = solid_mass_properties(&below).unwrap().volume;
        let vol_above = solid_mass_properties(&above).unwrap().volume;
        assert!((vol_below - 500.0).abs() < 1e-3, "below volume {vol_below}");
        assert!((vol_above - 500.0).abs() < 1e-3, "above volume {vol_above}");
        assert!((vol_below + vol_above - 1000.0).abs() < 1e-3);

        // (4) The cut is flat on x = 0: the below piece fills x ∈ [-5, 0] and the
        //     above piece x ∈ [0, 5], so each gains a planar cut face on x = 0.
        let (below_min, below_max) = aabb(&below);
        assert!(
            (below_min.x - (-5.0)).abs() < 1e-6,
            "below min.x {}",
            below_min.x
        );
        assert!(below_max.x.abs() < 1e-6, "below max.x {}", below_max.x);
        let (above_min, above_max) = aabb(&above);
        assert!(above_min.x.abs() < 1e-6, "above min.x {}", above_min.x);
        assert!(
            (above_max.x - 5.0).abs() < 1e-6,
            "above max.x {}",
            above_max.x
        );

        // Explicit cut-face check: each piece has a face all of whose vertices lie
        // on x = 0. Coedges reference edges by id; each edge names its endpoints.
        let has_cut_face = |solid: &BrepSolid| -> bool {
            solid
                .shells
                .iter()
                .flat_map(|shell| &shell.faces)
                .any(|face| {
                    let mut points: Vec<Vec3> = Vec::new();
                    for coedge in face.loops.iter().flat_map(|lp| &lp.coedges) {
                        let Some(edge) = solid.edges.iter().find(|e| e.id == coedge.edge_id) else {
                            return false;
                        };
                        for vid in [edge.start_vertex_id, edge.end_vertex_id] {
                            if let Some(vx) = solid.vertices.iter().find(|vx| vx.id == vid) {
                                points.push(vx.point);
                            }
                        }
                    }
                    !points.is_empty() && points.iter().all(|p| p.x.abs() < 1e-6)
                })
        };
        assert!(has_cut_face(&below), "below missing cut face on x=0");
        assert!(has_cut_face(&above), "above missing cut face on x=0");
    }

    /// The generalized entry with a Plane tool must reproduce the plane path
    /// exactly (a new plane case still splits).
    #[test]
    fn generalized_plane_tool_still_splits() {
        let box_solid = make_box_brep(Vec3::new(-5.0, -5.0, -5.0), 10.0, 10.0, 10.0).unwrap();
        // Cut on y = 2 with a +y normal.
        let pieces = split_solid_by_surface(
            &box_solid,
            &SplitSurface::Plane {
                point: Vec3::new(0.0, 2.0, 0.0),
                normal: Vec3::new(0.0, 1.0, 0.0),
            },
        )
        .unwrap();
        assert_eq!(pieces.len(), 2);
        for piece in &pieces {
            assert!(piece.validate().is_empty(), "plane piece invalid");
        }
        let (below, above) = (&pieces[0], &pieces[1]);
        // below = y ∈ [-5, 2] (vol 700), above = y ∈ [2, 5] (vol 300).
        assert!(
            (volume(below) - 700.0).abs() < 1e-3,
            "below {}",
            volume(below)
        );
        assert!(
            (volume(above) - 300.0).abs() < 1e-3,
            "above {}",
            volume(above)
        );
        assert!((volume(below) + volume(above) - 1000.0).abs() < 1e-3);
    }

    #[test]
    fn split_cube_by_cylinder_two_valid_solids() {
        // Cube [-5,5]³, volume 1000.  A cylinder of radius 3 about the Z axis
        // passes fully through it (through the interior, capped beyond the box).
        let cube = make_box_brep(Vec3::new(-5.0, -5.0, -5.0), 10.0, 10.0, 10.0).unwrap();
        let tool = SplitSurface::Cylinder {
            axis_point: Vec3::default(),
            axis_dir: Vec3::new(0.0, 0.0, 1.0),
            radius: 3.0,
        };
        let pieces = split_solid_by_surface(&cube, &tool).unwrap();
        assert_eq!(pieces.len(), 2, "cylinder split should yield 2 pieces");
        let (inside, outside) = (&pieces[0], &pieces[1]);

        // (1) Both pieces valid, watertight.
        assert!(
            inside.validate().is_empty(),
            "inside invalid: {:?}",
            inside.validate()
        );
        assert!(
            outside.validate().is_empty(),
            "outside invalid: {:?}",
            outside.validate()
        );

        // (2) Volumes sum to the cube.  inside = the r=3 cylinder core of
        //     height 10 = π·9·10 ≈ 282.743; outside = the rest.
        let vol_in = volume(inside);
        let vol_out = volume(outside);
        let expected_core = std::f64::consts::PI * 9.0 * 10.0;
        assert!(
            (vol_in - expected_core).abs() < 1e-3,
            "core volume {vol_in}"
        );
        assert!(
            (vol_in + vol_out - 1000.0).abs() < 1e-6,
            "sum {}",
            vol_in + vol_out
        );

        // (3) Semantic oracle: inside == cube∩cyl, outside == cube−cyl.
        let tool_solid = build_tool_solid(&cube, &tool).unwrap();
        assert_oracle_clean(&cube, &tool_solid, inside, outside);
    }

    #[test]
    fn split_box_by_sphere_two_valid_solids() {
        // Box [-5,5]³, volume 1000.  A sphere of radius 4 centred at the origin
        // lies entirely inside → inside = the ball, outside = box with cavity.
        let box_solid = make_box_brep(Vec3::new(-5.0, -5.0, -5.0), 10.0, 10.0, 10.0).unwrap();
        let tool = SplitSurface::Sphere {
            center: Vec3::default(),
            radius: 4.0,
        };
        let pieces = split_solid_by_surface(&box_solid, &tool).unwrap();
        assert_eq!(pieces.len(), 2, "sphere split should yield 2 pieces");
        let (inside, outside) = (&pieces[0], &pieces[1]);

        assert!(
            inside.validate().is_empty(),
            "inside invalid: {:?}",
            inside.validate()
        );
        assert!(
            outside.validate().is_empty(),
            "outside invalid: {:?}",
            outside.validate()
        );

        let vol_in = volume(inside);
        let vol_out = volume(outside);
        let expected_ball = 4.0 / 3.0 * std::f64::consts::PI * 4.0_f64.powi(3);
        assert!(
            (vol_in - expected_ball).abs() < 1e-2,
            "ball volume {vol_in}"
        );
        assert!(
            (vol_in + vol_out - 1000.0).abs() < 1e-6,
            "sum {}",
            vol_in + vol_out
        );

        let tool_solid = build_tool_solid(&box_solid, &tool).unwrap();
        assert_oracle_clean(&box_solid, &tool_solid, inside, outside);
    }

    #[test]
    fn split_box_by_cone_two_valid_solids() {
        // Box [-5,5]³.  A cone apexed at (0,0,-6), opening +Z at 20°, cuts the
        // box interior: it enters through the bottom face as a tiny circle and
        // exits through the top face as an r≈4 circle, both within the box
        // cross-section — so it cleanly divides the body (like the cylinder).
        let box_solid = make_box_brep(Vec3::new(-5.0, -5.0, -5.0), 10.0, 10.0, 10.0).unwrap();
        let tool = SplitSurface::Cone {
            apex: Vec3::new(0.0, 0.0, -6.0),
            axis_dir: Vec3::new(0.0, 0.0, 1.0),
            half_angle: std::f64::consts::PI / 9.0, // 20°
        };
        let pieces = split_solid_by_surface(&box_solid, &tool).unwrap();
        assert_eq!(pieces.len(), 2, "cone split should yield 2 pieces");
        let (inside, outside) = (&pieces[0], &pieces[1]);

        assert!(
            inside.validate().is_empty(),
            "inside invalid: {:?}",
            inside.validate()
        );
        assert!(
            outside.validate().is_empty(),
            "outside invalid: {:?}",
            outside.validate()
        );

        let vol_in = volume(inside);
        let vol_out = volume(outside);
        assert!(vol_in > 0.0 && vol_out > 0.0, "both pieces non-empty");
        assert!(
            (vol_in + vol_out - 1000.0).abs() < 1e-6,
            "sum {}",
            vol_in + vol_out
        );

        let tool_solid = build_tool_solid(&box_solid, &tool).unwrap();
        assert_oracle_clean(&box_solid, &tool_solid, inside, outside);
    }

    #[test]
    fn split_by_selected_cylinder_face_recognizes_and_cuts() {
        // Take the side face of a real cylinder solid and use ITS surface as
        // the cut tool for a cube — exercises the analytic-recognition entry
        // the app uses when the user selects a cylindrical face.
        let cube = make_box_brep(Vec3::new(-5.0, -5.0, -5.0), 10.0, 10.0, 10.0).unwrap();
        let cyl = make_cylinder_brep(
            Vec3::new(0.0, 0.0, -8.0),
            Vec3::new(0.0, 0.0, 1.0),
            3.0,
            16.0,
        )
        .unwrap();
        // Face id 105 is the cylindrical side (see make_cylinder_brep).
        let side = cyl
            .shells
            .iter()
            .flat_map(|s| &s.faces)
            .find(|f| f.id == 105)
            .expect("cylinder side face");
        assert!(
            matches!(
                recognized_split_surface(&side.surface).unwrap(),
                SplitSurface::Cylinder { radius, .. } if (radius - 3.0).abs() < 1e-9
            ),
            "side face should recognize as an r=3 cylinder"
        );
        let pieces = split_solid_by_face_surface(&cube, &side.surface).unwrap();
        assert_eq!(pieces.len(), 2);
        for piece in &pieces {
            assert!(piece.validate().is_empty(), "face-split piece invalid");
        }
        let sum = volume(&pieces[0]) + volume(&pieces[1]);
        assert!((sum - 1000.0).abs() < 1e-6, "volumes sum {sum}");
        assert!(
            (volume(&pieces[0]) - std::f64::consts::PI * 9.0 * 10.0).abs() < 1e-3,
            "core volume {}",
            volume(&pieces[0])
        );
    }

    #[test]
    fn split_misses_body_errs() {
        // A cylinder whose axis and radius keep it clear of the cube entirely →
        // no split, clean Err (not a bad/empty solid).
        let cube = make_box_brep(Vec3::new(-5.0, -5.0, -5.0), 10.0, 10.0, 10.0).unwrap();
        let tool = SplitSurface::Cylinder {
            axis_point: Vec3::new(100.0, 0.0, 0.0),
            axis_dir: Vec3::new(0.0, 0.0, 1.0),
            radius: 1.0,
        };
        assert!(split_solid_by_surface(&cube, &tool).is_err());
    }
}