fix: a lip swept flush around a rounded rim joins the body it sits on (#1164)

fix: a lip swept flush around a rounded rim joins the body it sits on.

crates/kernel/src/outline.rs

@@ -0,0 +1,563 @@
+//! Union of bodies touching back to back over part of a planar face, imprinted along the
+//! outline of the contact itself.
+//!
+//! [`crate::coplanar::imprint_union`] splits each body's face along the other's sides, extended
+//! to whole planes and cylinders. Where a side's surface runs on into the contact (the inner
+//! wall of a lip swept round a corner, whose straight part is tangent to its round part), the
+//! two bodies' pieces don't match and the faces can't be glued. Here each face in the plane is
+//! divided only by the other body's edges in the plane, as far as they run across it: both
+//! bodies' faces in the plane are lines and circular arcs, every edge is cut where the other's
+//! edges cross or touch it, the other's edges lying inside a face are copied into it, and the
+//! face is rebuilt as the regions those edges bound. The common regions are then the same faces
+//! in both bodies, and [`crate::coplanar::glue`] takes them away.
+
+use std::collections::HashMap;
+use std::f64::consts::TAU;
+
+use mt::{BoundedCurve, ParametricCurve};
+use solidcraft_geom::{Vec2, Vec3};
+use truck_modeling as mt;
+
+use crate::body::{Body, from_p3};
+use crate::history::History;
+use crate::record::Rebuild;
+use crate::{KernelError, Result, guard, record};
+
+/// Most edges of a body's faces in the plane the outline imprint takes on.
+const MAX_EDGES: usize = 2000;
+
+/// A frame in the plane, `x × y` its normal.
+#[derive(Clone, Copy)]
+struct Frame {
+    o: Vec3,
+    x: Vec3,
+    y: Vec3,
+}
+
+impl Frame {
+    /// The plane `n · p = d` (`n` a unit normal).
+    fn new(n: Vec3, d: f64) -> Frame {
+        let x = n.any_perp();
+        Frame { o: n * d, x, y: n.cross(x) }
+    }
+
+    fn normal(&self) -> Vec3 {
+        self.x.cross(self.y)
+    }
+
+    /// The same plane seen from its other side.
+    fn flipped(&self) -> Frame {
+        Frame { o: self.o, x: self.x, y: -self.y }
+    }
+
+    fn local(&self, p: Vec3) -> Vec2 {
+        let v = p - self.o;
+        Vec2::new(v.dot(self.x), v.dot(self.y))
+    }
+
+    fn world(&self, q: Vec2) -> Vec3 {
+        self.o + self.x * q.x + self.y * q.y
+    }
+}
+
+/// A line or circular arc in the plane, in the direction of the edge it is.
+#[derive(Clone, Copy, Debug)]
+enum Piece {
+    Line {
+        a: Vec2,
+        b: Vec2,
+    },
+    /// From the angle `t0` about `c`, turning by `sweep` (counter-clockwise when positive).
+    Arc {
+        c: Vec2,
+        r: f64,
+        t0: f64,
+        sweep: f64,
+    },
+}
+
+/// A fixed direction for counting crossings, clear of the axes and of round angles.
+const RAY: (f64, f64) = (0.951_056_516_295_153_6, 0.309_016_994_374_947_45);
+
+impl Piece {
+    fn at(&self, s: f64) -> Vec2 {
+        match *self {
+            Piece::Line { a, b } => a.lerp(b, s),
+            Piece::Arc { c, r, t0, sweep } => c + Vec2::from_angle(t0 + sweep * s) * r,
+        }
+    }
+
+    fn len(&self) -> f64 {
+        match *self {
+            Piece::Line { a, b } => a.dist(b),
+            Piece::Arc { r, sweep, .. } => r * sweep.abs(),
+        }
+    }
+
+    /// Where the angle `t` lies along the arc (0 at its start, 1 at its end), if it does.
+    fn arc_fraction(t0: f64, sweep: f64, t: f64) -> Option<f64> {
+        let turned = if sweep >= 0.0 { (t - t0).rem_euclid(TAU) } else { (t0 - t).rem_euclid(TAU) };
+        let span = sweep.abs();
+        if turned <= span {
+            Some(turned / span)
+        } else if span >= TAU - 1e-12 {
+            Some(0.0)
+        } else {
+            None
+        }
+    }
+
+    /// Distance from `p` to the piece.
+    fn dist(&self, p: Vec2) -> f64 {
+        match *self {
+            Piece::Line { a, b } => {
+                let d = b - a;
+                let l2 = d.len2();
+                let s = if l2 > 0.0 { ((p - a).dot(d) / l2).clamp(0.0, 1.0) } else { 0.0 };
+                p.dist(a + d * s)
+            }
+            Piece::Arc { c, r, t0, sweep } => match Self::arc_fraction(t0, sweep, (p - c).angle()) {
+                Some(_) => ((p - c).len() - r).abs(),
+                None => p.dist(self.at(0.0)).min(p.dist(self.at(1.0))),
+            },
+        }
+    }
+
+    /// How many times the ray from `p` along [`RAY`] crosses the piece.
+    fn crossings(&self, p: Vec2) -> usize {
+        let dir = Vec2::new(RAY.0, RAY.1);
+        match *self {
+            Piece::Line { a, b } => {
+                let e = b - a;
+                let den = dir.cross(e);
+                if den.abs() < 1e-300 {
+                    return 0;
+                }
+                let w = a - p;
+                let t = w.cross(e) / den;
+                let s = w.cross(dir) / den;
+                usize::from(t > 0.0 && (0.0..1.0).contains(&s))
+            }
+            Piece::Arc { c, r, t0, sweep } => {
+                // p + t·dir on the circle: t² + 2t(w·dir) + |w|² − r² = 0, w = p − c.
+                let w = p - c;
+                let bq = w.dot(dir);
+                let disc = bq * bq - (w.len2() - r * r);
+                if !(disc > 0.0) {
+                    return 0;
+                }
+                let root = disc.sqrt();
+                [-bq - root, -bq + root]
+                    .into_iter()
+                    .filter(|t| *t > 0.0)
+                    .filter(|t| Self::arc_fraction(t0, sweep, (p + dir * *t - c).angle()).is_some_and(|f| f < 1.0 || sweep.abs() >= TAU - 1e-12))
+                    .count()
+            }
+        }
+    }
+
+    /// The unit direction from the piece's start (`end` false) or end (`end` true) toward a
+    /// point a little along it: the direction it leaves or enters its vertex, with its bend.
+    fn leaving(&self, end: bool) -> Option<Vec2> {
+        let len = self.len();
+        let s = if len > 0.0 { (1e-3 / len).min(0.25) } else { 0.25 };
+        let (v, q) = if end { (self.at(1.0), self.at(1.0 - s)) } else { (self.at(0.0), self.at(s)) };
+        (q - v).normalized()
+    }
+}
+
+/// The edge `e` (in its own direction) as a line or arc in the frame's plane; `None` when it is
+/// off the plane or neither.
+fn piece_of(e: &mt::Edge, fr: &Frame, tol: f64) -> Option<Piece> {
+    let c = e.oriented_curve();
+    let (t0, t1) = c.range_tuple();
+    let n = fr.normal();
+    let pts: Vec<Vec3> = (0..=8).map(|k| from_p3(c.subs(t0 + (t1 - t0) * k as f64 / 8.0))).collect();
+    if pts.iter().any(|p| (*p - fr.o).dot(n).abs() > tol) {
+        return None;
+    }
+    let q: Vec<Vec2> = pts.iter().map(|p| fr.local(*p)).collect();
+    let (&a, &b, &m) = (q.first()?, q.last()?, q.get(4)?);
+    let closed = a.dist(b) <= tol;
+    if !closed {
+        let line = Piece::Line { a, b };
+        if q.iter().all(|p| line.dist(*p) <= tol) {
+            return Some(line);
+        }
+    }
+    // The circle through three of the points.
+    let (p1, p2, p3) = if closed { (a, *q.get(3)?, *q.get(6)?) } else { (a, m, b) };
+    let (u, v) = (p2 - p1, p3 - p1);
+    let den = 2.0 * u.cross(v);
+    if den.abs() < 1e-300 {
+        return None;
+    }
+    let centre = p1 + Vec2::new(v.y * u.len2() - u.y * v.len2(), u.x * v.len2() - v.x * u.len2()) * (1.0 / den);
+    let r = (a - centre).len();
+    if !(r > tol) || q.iter().any(|p| ((*p - centre).len() - r).abs() > tol) {
+        return None;
+    }
+    let start = (a - centre).angle();
+    let ccw = (a - centre).cross(*q.get(1)? - centre) > 0.0;
+    let sweep = if closed {
+        if ccw { TAU } else { -TAU }
+    } else if ccw {
+        ((b - centre).angle() - start).rem_euclid(TAU)
+    } else {
+        -((start - (b - centre).angle()).rem_euclid(TAU))
+    };
+    // The samples run along it in order (a rational arc is not even in angle).
+    let mut last = -1e-9;
+    for p in q.iter().skip(1).take(7) {
+        let f = Piece::arc_fraction(start, sweep, (*p - centre).angle())?;
+        if f < last {
+            return None;
+        }
+        last = f;
+    }
+    Some(Piece::Arc { c: centre, r, t0: start, sweep })
+}
+
+/// Where two pieces cross or touch (each point within `tol` of both).
+fn meetings(p: &Piece, q: &Piece, tol: f64) -> Vec<Vec2> {
+    let mut out: Vec<Vec2> = Vec::new();
+    let line_circle = |a: Vec2, b: Vec2, c: Vec2, r: f64, out: &mut Vec<Vec2>| {
+        let Some(dir) = (b - a).normalized() else { return };
+        let foot = a + dir * (c - a).dot(dir);
+        let h = (c - foot).len();
+        if h > r + tol {
+            return;
+        }
+        if (h - r).abs() <= tol {
+            out.push(foot);
+        } else {
+            let k = (r * r - h * h).max(0.0).sqrt();
+            out.extend([foot - dir * k, foot + dir * k]);
+        }
+    };
+    match (*p, *q) {
+        (Piece::Line { a, b }, Piece::Line { a: c, b: d }) => {
+            let (e, f) = (b - a, d - c);
+            let den = e.cross(f);
+            if den.abs() > 1e-12 * e.len() * f.len() {
+                let s = (c - a).cross(f) / den;
+                out.push(a + e * s);
+            }
+        }
+        (Piece::Line { a, b }, Piece::Arc { c, r, .. }) | (Piece::Arc { c, r, .. }, Piece::Line { a, b }) => line_circle(a, b, c, r, &mut out),
+        (Piece::Arc { c: c1, r: r1, .. }, Piece::Arc { c: c2, r: r2, .. }) => {
+            let d = c1.dist(c2);
+            if d > tol && d <= r1 + r2 + tol && d + tol >= (r1 - r2).abs() {
+                let a = (r1 * r1 - r2 * r2 + d * d) / (2.0 * d);
+                let h = (r1 * r1 - a * a).max(0.0).sqrt();
+                let u = (c2 - c1) * (1.0 / d);
+                let base = c1 + u * a;
+                if h <= tol {
+                    out.push(base);
+                } else {
+                    out.extend([base + u.perp() * h, base - u.perp() * h]);
+                }
+            }
+        }
+    }
+    // The ends of either lying on the other (a T, or where overlapping pieces part).
+    for (x, y) in [(p, q), (q, p)] {
+        for end in [x.at(0.0), x.at(1.0)] {
+            if y.dist(end) <= tol {
+                out.push(end);
+            }
+        }
+    }
+    out.retain(|m| p.dist(*m) <= tol && q.dist(*m) <= tol);
+    out
+}
+
+/// The edges of `body`'s faces in the plane of `fr` that face along its normal, once each, in
+/// their absolute direction, with their pieces. `None` when one is neither a line nor an arc.
+fn plane_edges(body: &Body, faces: &[usize], fr: &Frame, tol: f64) -> Option<Vec<(mt::Edge, Piece)>> {
+    let fs: Vec<&mt::Face> = body.solid.face_iter().collect();
+    let mut seen = std::collections::HashSet::new();
+    let mut out = Vec::new();
+    for f in faces.iter().filter_map(|i| fs.get(*i)) {
+        for e in f.edge_iter() {
+            if !seen.insert(e.id()) {
+                continue;
+            }
+            let abs = if e.orientation() { e.clone() } else { e.inverse() };
+            out.push((abs.clone(), piece_of(&abs, fr, tol)?));
+            if out.len() > MAX_EDGES {
+                return None;
+            }
+        }
+    }
+    Some(out)
+}
+
+/// Points where the edges of `own` are to be cut so that every piece of them lies inside,
+/// outside or along the edges of `other` (in world coordinates).
+fn cuts(own: &[(mt::Edge, Piece)], other: &[(mt::Edge, Piece)], fr: &Frame, tol: f64) -> Vec<Vec3> {
+    let mut out = Vec::new();
+    for (_, p) in own {
+        for (_, q) in other {
+            for m in meetings(p, q, tol) {
+                if m.dist(p.at(0.0)) > tol && m.dist(p.at(1.0)) > tol {
+                    out.push(fr.world(m));
+                }
+            }
+        }
+    }
+    out
+}
+
+/// One edge use in a face being rebuilt: the edge as the face uses it, its piece in that
+/// direction, its ends, and its reverse use when it is a copy used both ways.
+struct Use {
+    edge: mt::Edge,
+    piece: Piece,
+    from: mt::VertexID,
+    to: mt::VertexID,
+    twin: Option<usize>,
+}
+
+/// Does the point lie inside the region bounded by `pieces` (closed loops, holes included)?
+fn inside(pieces: &[Piece], p: Vec2) -> bool {
+    pieces.iter().map(|x| x.crossings(p)).sum::<usize>() % 2 == 1
+}
+
+/// The loops of uses, each next use the one leaving the vertex furthest clockwise from the way
+/// the last one came in: each loop runs round one region with it on the left.
+fn loops(uses: &[Use]) -> Option<Vec<Vec<usize>>> {
+    let mut out_of: HashMap<mt::VertexID, Vec<usize>> = HashMap::new();
+    for (i, u) in uses.iter().enumerate() {
+        out_of.entry(u.from).or_default().push(i);
+    }
+    let mut used = vec![false; uses.len()];
+    let mut out = Vec::new();
+    for start in 0..uses.len() {
+        if used.get(start).copied().unwrap_or(true) {
+            continue;
+        }
+        let mut lp = vec![start];
+        if let Some(x) = used.get_mut(start) {
+            *x = true;
+        }
+        let mut cur = start;
+        loop {
+            let u = uses.get(cur)?;
+            let back = u.piece.leaving(true)?;
+            let next = out_of
+                .get(&u.to)?
+                .iter()
+                .copied()
+                .filter(|k| Some(*k) != u.twin)
+                .filter_map(|k| {
+                    let d = uses.get(k)?.piece.leaving(false)?;
+                    // Counter-clockwise from the way back, in (0, 2π].
+                    let turn = back.cross(d).atan2(back.dot(d));
+                    Some((k, if turn <= 0.0 { turn + TAU } else { turn }))
+                })
+                .max_by(|x, y| x.1.total_cmp(&y.1))
+                .map(|(k, _)| k)?;
+            if next == start {
+                break;
+            }
+            if used.get(next).copied().unwrap_or(true) || lp.len() > uses.len() {
+                return None;
+            }
+            if let Some(x) = used.get_mut(next) {
+                *x = true;
+            }
+            lp.push(next);
+            cur = next;
+        }
+        out.push(lp);
+    }
+    Some(out)
+}
+
+/// The signed area a loop bounds (positive counter-clockwise).
+fn area(uses: &[Use], lp: &[usize]) -> f64 {
+    let pts: Vec<Vec2> = lp.iter().filter_map(|i| uses.get(*i)).flat_map(|u| (0..16).map(move |k| u.piece.at(k as f64 / 16.0))).collect();
+    (0..pts.len()).map(|i| pts.get(i).zip(pts.get((i + 1) % pts.len())).map(|(a, b)| a.cross(*b)).unwrap_or(0.0)).sum::<f64>() * 0.5
+}
+
+/// `body` with its faces `faces` (in the plane of `fr`, facing along its normal) divided by those
+/// edges of `other` that run inside them: each such edge is copied into the face, and the face
+/// is rebuilt as the regions its own edges and the copies bound. History over `[body]`. `None`
+/// when a face can't be rebuilt so.
+fn divided(body: &Body, faces: &[usize], other: &[(mt::Edge, Piece)], fr: &Frame, tol: f64) -> Result<Option<Body>> {
+    let fs: Vec<&mt::Face> = body.solid.face_iter().collect();
+    // Each face's own edge uses, in the direction it runs them (counter-clockwise about the
+    // frame's normal round its outside).
+    let mut own: Vec<(usize, Vec<(mt::Edge, Piece)>)> = Vec::new();
+    for &fi in faces {
+        let Some(f) = fs.get(fi) else { continue };
+        let mut es = Vec::new();
+        for w in f.boundaries() {
+            for e in w.edge_iter() {
+                let Some(p) = piece_of(e, fr, tol) else { return Ok(None) };
+                es.push((e.clone(), p));
+            }
+        }
+        own.push((fi, es));
+    }
+    let all_own: Vec<Piece> = own.iter().flat_map(|(_, es)| es.iter().map(|(_, p)| *p)).collect();
+    // The vertices the copies end on: the faces' own where they meet, else new ones shared.
+    let mut pool: Vec<mt::Vertex> = own.iter().flat_map(|(_, es)| es.iter().flat_map(|(e, _)| [e.front().clone(), e.back().clone()])).collect();
+    let mut vertex = |p: Vec3| -> mt::Vertex {
+        if let Some(v) = pool.iter().find(|v| from_p3(v.point()).dist(p) <= tol) {
+            return v.clone();
+        }
+        let v = mt::Vertex::new(crate::body::p3(p));
+        pool.push(v.clone());
+        v
+    };
+    let mut copies: HashMap<usize, Vec<(mt::Edge, Piece)>> = HashMap::new();
+    for (e, p) in other {
+        // Along the faces' own edges: nothing to add.
+        if [0.25, 0.5, 0.75].iter().all(|s| all_own.iter().any(|o| o.dist(p.at(*s)) <= tol * 10.0)) {
+            continue;
+        }
+        let mid = p.at(0.5);
+        let Some((fi, _)) = own.iter().find(|(_, es)| inside(&es.iter().map(|(_, x)| *x).collect::<Vec<_>>(), mid)) else { continue };
+        let (v0, v1) = (vertex(from_p3(e.front().point())), vertex(from_p3(e.back().point())));
+        // On the face's own vertices, which lie within `tol` of the edge's ends.
+        let copy = mt::Edge::new_unchecked(&v0, &v1, e.curve());
+        let Some(cp) = piece_of(&copy, fr, tol) else { return Ok(None) };
+        copies.entry(*fi).or_default().push((copy, cp));
+    }
+    if copies.is_empty() {
+        return Ok(None);
+    }
+    let mut rebuilt: HashMap<usize, Vec<mt::Face>> = HashMap::new();
+    for (fi, es) in &own {
+        let Some(cs) = copies.get(fi) else { continue };
+        let Some(f) = fs.get(*fi) else { continue };
+        let mut uses: Vec<Use> =
+            es.iter().map(|(e, p)| Use { edge: e.clone(), piece: *p, from: e.front().id(), to: e.back().id(), twin: None }).collect();
+        for (e, p) in cs {
+            let k = uses.len();
+            let back = e.inverse();
+            let Some(bp) = piece_of(&back, fr, tol) else { return Ok(None) };
+            uses.push(Use { edge: e.clone(), piece: *p, from: e.front().id(), to: e.back().id(), twin: Some(k + 1) });
+            uses.push(Use { from: back.front().id(), to: back.back().id(), edge: back, piece: bp, twin: Some(k) });
+        }
+        let Some(lps) = loops(&uses) else { return Ok(None) };
+        let (outer, holes): (Vec<(Vec<usize>, f64)>, Vec<(Vec<usize>, f64)>) = lps
+            .into_iter()
+            .map(|lp| {
+                let a = area(&uses, &lp);
+                (lp, a)
+            })
+            .partition(|(_, a)| *a > 0.0);
+        let pieces_of = |lp: &[usize]| -> Vec<Piece> { lp.iter().filter_map(|i| uses.get(*i)).map(|u| u.piece).collect() };
+        let mut groups: Vec<(Vec<usize>, f64, Vec<Vec<usize>>)> = outer.into_iter().map(|(lp, a)| (lp, a, Vec::new())).collect();
+        for (hole, _) in holes {
+            let Some(p) = hole.first().and_then(|i| uses.get(*i)).map(|u| u.piece.at(0.5)) else { return Ok(None) };
+            let Some(g) = groups.iter_mut().filter(|(lp, _, _)| inside(&pieces_of(lp), p)).min_by(|x, y| x.1.total_cmp(&y.1)) else {
+                return Ok(None);
+            };
+            g.2.push(hole);
+        }
+        let wire = |lp: &[usize]| -> mt::Wire { lp.iter().filter_map(|i| uses.get(*i)).map(|u| u.edge.clone()).collect::<Vec<_>>().into() };
+        let mut made = Vec::new();
+        for (lp, _, hs) in &groups {
+            let wires: Vec<mt::Wire> = std::iter::once(wire(lp)).chain(hs.iter().map(|h| wire(h))).collect();
+            // The loops run round the face as its normal sees them; a face turned against its
+            // surface stores them the other way.
+            let nf = if f.orientation() {
+                mt::Face::try_new(wires, f.surface())
+            } else {
+                mt::Face::try_new(wires.iter().map(|w| w.inverse()).collect(), f.surface()).map(|mut x| {
+                    x.invert();
+                    x
+                })
+            };
+            made.push(nf.map_err(|x| KernelError::Failed(format!("rebuilding a face of the contact: {x}")))?);
+        }
+        rebuilt.insert(*fi, made);
+    }
+    let mut rec = Rebuild::default();
+    let mut index = 0;
+    let mut shells = Vec::new();
+    for sh in body.solid.boundaries() {
+        let mut faces = Vec::new();
+        for f in sh.face_iter() {
+            match rebuilt.get(&index) {
+                Some(made) => {
+                    for nf in made {
+                        rec.whole(nf, f);
+                        faces.push(nf.clone());
+                    }
+                }
+                None => {
+                    rec.whole(f, f);
+                    faces.push(f.clone());
+                }
+            }
+            index += 1;
+        }
+        shells.push(mt::Shell::from(faces));
+    }
+    let Ok(solid) = mt::Solid::try_new(shells) else { return Ok(None) };
+    let split = Body {
+        solid: std::sync::Arc::new(solid),
+        size: 0.0,
+        volume: Some(std::sync::Arc::new(std::sync::Mutex::new(None))),
+        coarse_missing: None,
+        mesh: None,
+        color: body.color,
+        paint: None,
+        splits: body.splits.clone(),
+        face_sources: None,
+        history: None,
+        regularization_protected: true,
+        display_of: None,
+    };
+    Ok(Some(record::rebuilt_body(split, &[&body.solid], &rec)))
+}
+
+/// Union of bodies touching back to back over part of a planar face whose edges there are lines
+/// and circular arcs (a lip swept along a rim, flush with a round side): imprinted on each other
+/// along the outline of the contact and glued. `None` when that does not give a result
+/// `accept`ed.
+pub(crate) fn outline_union(a: &Body, b: &Body, accept: &dyn Fn(&Body) -> bool) -> Option<Body> {
+    let size = a.size().max(b.size());
+    let tol = (size * 1e-7).max(1e-9) * 10.0;
+    let back: Vec<(Vec3, f64)> = crate::coplanar::coincident_planes(a, b).into_iter().filter(|(_, _, same)| !*same).map(|(n, d, _)| (n, d)).collect();
+    if back.is_empty() {
+        return None;
+    }
+    let run = || -> Result<Option<Body>> {
+        let (mut a2, mut ha): (Body, Option<History>) = (a.clone(), crate::boolean_record::kept(a, 0, 1));
+        let (mut b2, mut hb): (Body, Option<History>) = (b.clone(), crate::boolean_record::kept(b, 0, 1));
+        for (n, d) in &back {
+            // a's faces face along n in the plane; b's the other way.
+            let fa = Frame::new(*n, *d);
+            let fb = fa.flipped();
+            let in_a = |x: &Body| crate::coplanar::faces_in(x, *n, *d, tol);
+            let in_b = |x: &Body| crate::coplanar::faces_in(x, -*n, -*d, tol);
+            let (Some(ea), Some(eb)) = (plane_edges(&a2, &in_a(&a2), &fa, tol), plane_edges(&b2, &in_b(&b2), &fa, tol)) else { return Ok(None) };
+            let a3 = crate::splitface::split_edges_at(&a2, &cuts(&ea, &eb, &fa, tol))?;
+            ha = crate::boolean_record::through(&a3, 0, ha.as_ref());
+            let b3 = crate::splitface::split_edges_at(&b2, &cuts(&eb, &ea, &fa, tol))?;
+            hb = crate::boolean_record::through(&b3, 0, hb.as_ref());
+            // Each side's edges as the other side's frame sees them.
+            let (Some(eb), Some(ea)) = (plane_edges(&b3, &in_b(&b3), &fa, tol), plane_edges(&a3, &in_a(&a3), &fb, tol)) else { return Ok(None) };
+            let a4 = divided(&a3, &in_a(&a3), &eb, &fa, tol)?.unwrap_or(a3);
+            let b4 = divided(&b3, &in_b(&b3), &ea, &fb, tol)?.unwrap_or(b3);
+            ha = crate::boolean_record::through(&a4, 0, ha.as_ref());
+            hb = crate::boolean_record::through(&b4, 0, hb.as_ref());
+            (a2, b2) = (a4, b4);
+        }
+        let Some(r) = crate::coplanar::glue(&a2, &b2) else { return Ok(None) };
+        let r = r?;
+        let (ha, hb) = (crate::boolean_record::placed(ha, 0, 2), crate::boolean_record::placed(hb, 1, 2));
+        let h = crate::boolean_record::of_pair(&r, &ha, &hb);
+        Ok(Some(r.with_checked_history(h, &record::counts(&[a, b]))))
+    };
+    match guard("outline union", run) {
+        Ok(Some(r)) if accept(&r) => Some(r),
+        _ => None,
+    }
+}