NOWN-DEVandClaude Opus 5.5
9e60080b10
kernel::sew refused a solid with a thin planar face away from the origin: a slab 30 x 2 mm and 0.00013 mm thick with a corner at (-300, -200, 5), turned 0.45 rad about x, failed with "sew: face 1: cannot attach a plane to a wire that is not on one plane", though its faces are flat to 1e-14 mm. truck's plane fit sums the cross products of a boundary's control points about a centre and takes the points' sum for that centre (it divides by the number of wires, not of points): eight times as far from the origin as a rectangle of four lines. The sum is the same about any centre, but its rounding grows with the square of the centre's distance, and on a thin face, whose normal is short, it turns the normal far enough for truck's own 1e-6 flatness test to fail: truck finds the slab's four thin faces 3.0e-7 to 2.1e-6 mm out of the planes it fitted. A planar face keeps truck's plane wherever truck gives one. Where truck refuses, the same fit is made on a copy of the boundary moved so that the mean of its control points is the origin, and the plane is moved back; a boundary that leaves its plane or has no area is refused as before. Co-authored-by: Claude Opus 5.5 <[email protected]>
831 lines
39 KiB
Rust
831 lines
39 KiB
Rust
//! Sewing a solid from face descriptions: each face is its boundary loops (lines, circular
|
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//! arcs and cubic Bézier chains, counter-clockwise about the outward normal; holes clockwise)
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//! and its surface (planar, revolved from a line, extruded from an arc, or ruled between two
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//! Bézier chains). Vertices and edges at the same places are shared, so the faces close into
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//! one shell without booleans — for solids whose faces are known exactly, such as folded
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//! sheet metal.
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use std::collections::HashMap;
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use std::sync::Arc;
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use mt::builder;
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use solidcraft_geom::Vec3;
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use truck_modeling as mt;
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use crate::body::{Body, Solid, p3, v3};
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use crate::{KernelError, Result, guard};
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/// Most control points of one Bézier chain edge.
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pub const MAX_CHAIN_POINTS: usize = 3 * 1024 + 1;
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/// A boundary edge.
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#[derive(Clone, Debug, PartialEq)]
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pub enum EdgeSpec {
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Line {
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a: Vec3,
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b: Vec3,
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},
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/// A circular arc from `a` to `b` through `mid`.
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Arc {
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a: Vec3,
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b: Vec3,
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mid: Vec3,
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},
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/// A chain of cubic Bézier pieces: 3n + 1 control points (n ≥ 1); the curve passes
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/// through `ctrl[0]`, `ctrl[3]`, … `ctrl[3n]`. For curves with no exact line, arc or conic
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/// form, such as a cut-out edge traced across a sheet metal bend.
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Chain {
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ctrl: Arc<[Vec3]>,
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},
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}
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impl EdgeSpec {
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fn ends(&self) -> (Vec3, Vec3) {
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match self {
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EdgeSpec::Line { a, b } | EdgeSpec::Arc { a, b, .. } => (*a, *b),
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EdgeSpec::Chain { ctrl } => (ctrl.first().copied().unwrap_or(Vec3::ZERO), ctrl.last().copied().unwrap_or(Vec3::ZERO)),
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}
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}
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/// The same edge, run the other way.
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pub fn reversed(&self) -> EdgeSpec {
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match self {
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EdgeSpec::Line { a, b } => EdgeSpec::Line { a: *b, b: *a },
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EdgeSpec::Arc { a, b, mid } => EdgeSpec::Arc { a: *b, b: *a, mid: *mid },
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EdgeSpec::Chain { ctrl } => EdgeSpec::Chain { ctrl: ctrl.iter().rev().copied().collect() },
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}
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}
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/// A point telling apart edges with the same ends, whichever way they run.
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fn mid_key(&self) -> Option<Key> {
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match self {
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EdgeSpec::Line { .. } => None,
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EdgeSpec::Arc { mid, .. } => Some(key(*mid)),
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EdgeSpec::Chain { ctrl } => {
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let n = ctrl.len().max(1) as f64;
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Some(key(ctrl.iter().fold(Vec3::ZERO, |s, p| s + *p) * (1.0 / n)))
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}
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}
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}
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fn valid(&self) -> bool {
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match self {
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EdgeSpec::Line { a, b } => a.is_finite() && b.is_finite(),
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EdgeSpec::Arc { a, b, mid } => a.is_finite() && b.is_finite() && mid.is_finite(),
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EdgeSpec::Chain { ctrl } => {
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ctrl.len() >= 4 && ctrl.len() <= MAX_CHAIN_POINTS && (ctrl.len() - 1) % 3 == 0 && ctrl.iter().all(|p| p.is_finite())
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}
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}
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}
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}
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/// A face's surface.
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#[derive(Clone, Debug, PartialEq)]
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pub enum SurfSpec {
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/// The plane of the boundary.
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Plane,
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/// The surface the line `a`→`b` sweeps turning `angle` about the axis.
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Revolved { a: Vec3, b: Vec3, axis_origin: Vec3, axis: Vec3, angle: f64 },
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/// The surface an arc sweeps moving along `dir`.
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Extruded { a: Vec3, b: Vec3, mid: Vec3, dir: Vec3 },
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/// The straight lines joining equal parameters of two Bézier chains with the same number
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/// of pieces, `a` and `b` running the same way; both chains lie on it as boundary edges.
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Ruled { a: EdgeSpec, b: EdgeSpec },
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}
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/// A face: boundary loops, surface, and a point on it with its outward normal (curved faces).
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#[derive(Clone, Debug, PartialEq)]
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pub struct FaceSpec {
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pub loops: Vec<Vec<EdgeSpec>>,
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pub surface: SurfSpec,
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pub probe: Option<(Vec3, Vec3)>,
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}
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type Key = (i64, i64, i64);
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fn key(p: Vec3) -> Key {
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let q = |x: f64| (x * 1e6).round() as i64;
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(q(p.x), q(p.y), q(p.z))
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}
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#[derive(Default)]
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struct Cache {
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verts: HashMap<Key, mt::Vertex>,
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edges: HashMap<(Key, Key, Option<Key>, usize), mt::Edge>,
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}
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impl Cache {
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fn vertex(&mut self, p: Vec3) -> mt::Vertex {
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self.verts.entry(key(p)).or_insert_with(|| builder::vertex(p3(p))).clone()
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}
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fn edge(&mut self, e: &EdgeSpec, sheet: usize) -> Result<mt::Edge> {
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let (a, b) = e.ends();
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let mid = e.mid_key();
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let (ka, kb) = (key(a), key(b));
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if let Some(found) = self.edges.get(&(ka, kb, mid, sheet)) {
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return Ok(found.clone());
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}
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if let Some(found) = self.edges.get(&(kb, ka, mid, sheet)) {
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return Ok(found.inverse());
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}
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let (va, vb) = (self.vertex(a), self.vertex(b));
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let made = match e {
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EdgeSpec::Line { .. } => builder::line(&va, &vb),
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EdgeSpec::Arc { mid, .. } => arc_edge(&va, &vb, *mid),
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EdgeSpec::Chain { .. } => {
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let curve = self.chain(e)?;
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mt::Edge::try_new(&va, &vb, mt::Curve::BSplineCurve(curve)).map_err(|e| KernelError::Failed(format!("sew: chain edge: {e}")))?
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}
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};
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self.edges.insert((ka, kb, mid, sheet), made.clone());
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Ok(made)
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}
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/// A Bézier chain as a cubic B-spline (triple inner knots) ending on the shared vertices.
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fn chain(&mut self, e: &EdgeSpec) -> Result<mt::BSplineCurve<mt::Point3>> {
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let EdgeSpec::Chain { ctrl } = e else { return Err(KernelError::Invalid("sew: not a Bézier chain".into())) };
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if !e.valid() {
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return Err(KernelError::Invalid("sew: a Bézier chain needs 3n + 1 finite control points".into()));
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}
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let n = (ctrl.len() - 1) / 3;
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let mut knots = vec![0.0; 4];
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for i in 1..n {
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knots.extend([i as f64; 3]);
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}
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knots.extend([n as f64; 4]);
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let mut pts: Vec<mt::Point3> = ctrl.iter().map(|p| p3(*p)).collect();
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let (a, b) = e.ends();
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if let Some(first) = pts.first_mut() {
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*first = self.vertex(a).point();
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}
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if let Some(last) = pts.last_mut() {
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*last = self.vertex(b).point();
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}
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mt::BSplineCurve::try_new(mt::KnotVec::from(knots), pts).map_err(|e| KernelError::Failed(format!("sew: chain curve: {e}")))
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}
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}
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/// Sew the faces into a closed solid.
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pub fn sew(faces: &[FaceSpec]) -> Result<Body> {
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sew_impl(faces, false, None).map(|(body, _)| body)
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}
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/// Separate boundary sheets at a shared geometric edge without moving it.
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/// Optional transient sources follow only unchanged produced face identities.
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/// Also reports the face each face of the body was built from (by its place in `faces`; `None`
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/// when that could not be followed).
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pub(crate) fn sew_touching_with_sources(faces: &[FaceSpec], sources: &[Option<crate::FaceSource>]) -> Result<(Body, Option<Vec<usize>>)> {
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if sources.len() != faces.len() {
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return Err(KernelError::Invalid("sew source alignment".into()));
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}
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sew_impl(faces, true, Some(sources))
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}
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type EdgeUse = (usize, usize, usize);
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fn touching_sheets(faces: &[FaceSpec]) -> Result<HashMap<EdgeUse, usize>> {
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type Use = (EdgeUse, Vec3, Vec3, Vec3);
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let mut uses: HashMap<(Key, Key), Vec<Use>> = HashMap::new();
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for (fi, face) in faces.iter().enumerate() {
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let Some(outer) = face.loops.first() else { continue };
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let normal = outer
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.iter()
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.fold(Vec3::ZERO, |n, e| {
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let (a, b) = e.ends();
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n + a.cross(b)
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})
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.normalized();
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for (li, lp) in face.loops.iter().enumerate() {
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for (ei, e) in lp.iter().enumerate() {
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if matches!(e, EdgeSpec::Line { .. }) && matches!(face.surface, SurfSpec::Plane) {
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let (a, b) = e.ends();
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let (ka, kb) = (key(a), key(b));
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let k = if ka < kb { (ka, kb) } else { (kb, ka) };
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if let Some(n) = normal {
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uses.entry(k).or_default().push(((fi, li, ei), a, b, n));
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}
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}
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}
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}
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}
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let mut sheets = HashMap::new();
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for group in uses.values().filter(|g| g.len() > 2) {
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if group.len() != 4 {
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return Err(KernelError::Invalid("sew: unsupported edge contact".into()));
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}
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let mut paired = std::collections::HashSet::new();
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for (i, (use_a, a, b, n)) in group.iter().enumerate() {
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if paired.contains(&i) {
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continue;
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}
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let t = (*b - *a).normalized().ok_or_else(|| KernelError::Invalid("sew: a degenerate contact".into()))?;
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// Pair the two faces bounding each material wedge, not the empty
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// wedge between them. Each pair uses the edge in opposite directions.
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let j = group
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.iter()
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.enumerate()
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.find_map(|(j, (_, c, d, m))| {
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(i != j
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&& !paired.contains(&j)
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&& key(*a) == key(*d)
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&& key(*b) == key(*c)
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&& n.cross(t).dot(*m) < -1e-8
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&& m.cross(-t).dot(*n) < -1e-8)
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.then_some(j)
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})
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.ok_or_else(|| KernelError::Invalid("sew: ambiguous edge contact".into()))?;
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let use_b = group.get(j).ok_or_else(|| KernelError::Invalid("sew: edge contact".into()))?.0;
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let sheet = paired.len() / 2;
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sheets.insert(*use_a, sheet);
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sheets.insert(use_b, sheet);
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paired.insert(i);
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paired.insert(j);
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}
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}
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Ok(sheets)
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}
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fn faces_connected(faces: &[mt::Face]) -> bool {
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let mut by_edge: HashMap<mt::EdgeID, Vec<usize>> = HashMap::new();
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for (i, f) in faces.iter().enumerate() {
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for e in f.edge_iter() {
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by_edge.entry(e.id()).or_default().push(i);
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}
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}
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let mut seen = std::collections::HashSet::new();
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let mut todo = vec![0];
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while let Some(i) = todo.pop() {
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if seen.insert(i)
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&& let Some(f) = faces.get(i)
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{
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for e in f.edge_iter() {
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if let Some(adjacent) = by_edge.get(&e.id()) {
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todo.extend(adjacent.iter().copied().filter(|j| !seen.contains(j)));
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}
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}
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}
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}
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seen.len() == faces.len()
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}
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/// Keep disconnected closed boundaries as distinct shells, preserving orientation.
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fn closed_components(faces: Vec<mt::Face>) -> Result<Vec<mt::Shell>> {
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const MAX_EDGE_USES: usize = 500_000;
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const MAX_COMPONENTS: usize = 1024;
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let fail = |s: &str| KernelError::Invalid(format!("sew: {s}"));
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let mut by_edge: HashMap<mt::EdgeID, Vec<usize>> = HashMap::new();
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let mut edge_uses = 0usize;
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for (i, face) in faces.iter().enumerate() {
|
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for edge in face.edge_iter() {
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edge_uses = edge_uses.saturating_add(1);
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if edge_uses > MAX_EDGE_USES {
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return Err(fail("edge budget exceeded"));
|
||
}
|
||
let uses = by_edge.entry(edge.id()).or_default();
|
||
if uses.len() >= 2 {
|
||
return Err(fail("nonmanifold edge contact"));
|
||
}
|
||
uses.push(i);
|
||
}
|
||
}
|
||
if by_edge.values().any(|uses| uses.len() != 2) {
|
||
return Err(fail("the faces do not close"));
|
||
}
|
||
let mut seen = vec![false; faces.len()];
|
||
let mut vertices = HashMap::new();
|
||
let mut components = Vec::new();
|
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for first in 0..faces.len() {
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if seen.get(first).copied().unwrap_or(true) {
|
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continue;
|
||
}
|
||
if components.len() >= MAX_COMPONENTS {
|
||
return Err(fail("component budget exceeded"));
|
||
}
|
||
let component = components.len();
|
||
let mut todo = vec![first];
|
||
if let Some(slot) = seen.get_mut(first) {
|
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*slot = true;
|
||
}
|
||
let mut indices = Vec::new();
|
||
while let Some(i) = todo.pop() {
|
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let face = faces.get(i).ok_or_else(|| fail("missing component face"))?;
|
||
indices.push(i);
|
||
for vertex in face.vertex_iter() {
|
||
if vertices.insert(vertex.id(), component).is_some_and(|previous| previous != component) {
|
||
return Err(fail("bodies touch only at a vertex"));
|
||
}
|
||
}
|
||
for edge in face.edge_iter() {
|
||
let adjacent = by_edge.get(&edge.id()).ok_or_else(|| fail("missing component edge"))?;
|
||
for j in adjacent {
|
||
let slot = seen.get_mut(*j).ok_or_else(|| fail("missing adjacent face"))?;
|
||
if !*slot {
|
||
*slot = true;
|
||
todo.push(*j);
|
||
}
|
||
}
|
||
}
|
||
}
|
||
indices.sort_unstable();
|
||
let component_faces =
|
||
indices.into_iter().map(|i| faces.get(i).cloned().ok_or_else(|| fail("missing component face"))).collect::<Result<Vec<_>>>()?;
|
||
components.push(component_faces.into());
|
||
}
|
||
Ok(components)
|
||
}
|
||
|
||
/// A contact's edge sheets can terminate in separate vertex fans. Give each fan
|
||
/// its own vertex at the same coordinates so the boundary remains a manifold.
|
||
fn split_vertex_fans(faces: Vec<mt::Face>) -> Result<Vec<mt::Face>> {
|
||
let mut by_vertex: HashMap<mt::VertexID, Vec<usize>> = HashMap::new();
|
||
let mut by_edge: HashMap<mt::EdgeID, Vec<usize>> = HashMap::new();
|
||
let mut vertices = HashMap::new();
|
||
for (i, f) in faces.iter().enumerate() {
|
||
for v in f.vertex_iter() {
|
||
vertices.insert(v.id(), v.clone());
|
||
by_vertex.entry(v.id()).or_default().push(i);
|
||
}
|
||
for e in f.edge_iter() {
|
||
by_edge.entry(e.id()).or_default().push(i);
|
||
}
|
||
}
|
||
let mut replacements: HashMap<(mt::VertexID, usize), mt::Vertex> = HashMap::new();
|
||
for (id, members) in &mut by_vertex {
|
||
members.sort_unstable();
|
||
members.dedup();
|
||
let mut seen = std::collections::HashSet::new();
|
||
let mut fans = Vec::new();
|
||
for start in members.iter().copied() {
|
||
if seen.contains(&start) {
|
||
continue;
|
||
}
|
||
let mut todo = vec![start];
|
||
let mut fan = Vec::new();
|
||
while let Some(i) = todo.pop() {
|
||
if !seen.insert(i) {
|
||
continue;
|
||
}
|
||
fan.push(i);
|
||
if let Some(f) = faces.get(i) {
|
||
for e in f.edge_iter().filter(|e| e.absolute_front().id() == *id || e.absolute_back().id() == *id) {
|
||
if let Some(adjacent) = by_edge.get(&e.id()) {
|
||
todo.extend(adjacent.iter().copied().filter(|j| !seen.contains(j)));
|
||
}
|
||
}
|
||
}
|
||
}
|
||
fans.push(fan);
|
||
}
|
||
if fans.len() > 1 {
|
||
let original = vertices.get(id).ok_or_else(|| KernelError::Failed("sew: missing contact vertex".into()))?;
|
||
for fan in fans {
|
||
let vertex = builder::vertex(original.point());
|
||
for i in fan {
|
||
replacements.insert((*id, i), vertex.clone());
|
||
}
|
||
}
|
||
}
|
||
}
|
||
let mut edges = HashMap::new();
|
||
for (i, f) in faces.iter().enumerate() {
|
||
for e in f.edge_iter() {
|
||
edges.entry(e.id()).or_insert_with(|| {
|
||
let (a, b) = (e.absolute_front(), e.absolute_back());
|
||
let a = replacements.get(&(a.id(), i)).unwrap_or(a);
|
||
let b = replacements.get(&(b.id(), i)).unwrap_or(b);
|
||
mt::Edge::new(a, b, e.curve())
|
||
});
|
||
}
|
||
}
|
||
faces
|
||
.into_iter()
|
||
.map(|f| {
|
||
let wires: Vec<mt::Wire> = f
|
||
.absolute_boundaries()
|
||
.iter()
|
||
.map(|w| {
|
||
w.edge_iter()
|
||
.map(|e| {
|
||
let rebuilt = edges.get(&e.id()).ok_or_else(|| KernelError::Failed("sew: missing contact edge".into()))?;
|
||
Ok(if e.front() == e.absolute_front() { rebuilt.clone() } else { rebuilt.inverse() })
|
||
})
|
||
.collect::<Result<Vec<_>>>()
|
||
.map(Into::into)
|
||
})
|
||
.collect::<Result<_>>()?;
|
||
let mut rebuilt = mt::Face::try_new(wires, f.surface()).map_err(|e| KernelError::Failed(format!("sew: contact face: {e}")))?;
|
||
if !f.orientation() {
|
||
rebuilt.invert();
|
||
}
|
||
Ok(rebuilt)
|
||
})
|
||
.collect()
|
||
}
|
||
|
||
fn sew_impl(faces: &[FaceSpec], touching: bool, sources: Option<&[Option<crate::FaceSource>]>) -> Result<(Body, Option<Vec<usize>>)> {
|
||
if faces.len() < 4 || faces.len() > 200_000 {
|
||
return Err(KernelError::Invalid("a solid needs 4…200000 faces".into()));
|
||
}
|
||
let mut edge_uses = 0usize;
|
||
for f in faces {
|
||
for l in &f.loops {
|
||
edge_uses = edge_uses.saturating_add(l.len().max(1));
|
||
if edge_uses > 500_000 {
|
||
return Err(KernelError::Invalid("sew: edge budget exceeded".into()));
|
||
}
|
||
for e in l {
|
||
let (a, b) = e.ends();
|
||
// Ends that weld to one vertex would make truck panic on a zero-length edge (#268).
|
||
if !e.valid() || !a.is_finite() || !b.is_finite() || a.dist(b) < 1e-9 || key(a) == key(b) {
|
||
return Err(KernelError::Invalid("sew: a degenerate edge".into()));
|
||
}
|
||
}
|
||
}
|
||
}
|
||
guard("sew", || {
|
||
let sheets = if touching { touching_sheets(faces)? } else { HashMap::new() };
|
||
let mut cache = Cache::default();
|
||
let mut out: Vec<mt::Face> = Vec::with_capacity(faces.len());
|
||
for (fi, f) in faces.iter().enumerate() {
|
||
let wires: Vec<mt::Wire> = f
|
||
.loops
|
||
.iter()
|
||
.enumerate()
|
||
.map(|(li, l)| {
|
||
l.iter()
|
||
.enumerate()
|
||
.map(|(ei, e)| cache.edge(e, sheets.get(&(fi, li, ei)).copied().unwrap_or(0)))
|
||
.collect::<Result<Vec<_>>>()
|
||
.map(Into::into)
|
||
})
|
||
.collect::<Result<_>>()?;
|
||
let face = match &f.surface {
|
||
SurfSpec::Plane => match builder::try_attach_plane(&wires) {
|
||
Ok(face) => face,
|
||
// truck's fit loses thin faces away from the origin: see `plane_about_the_mean`.
|
||
Err(e) => {
|
||
let plane = plane_about_the_mean(&wires).ok_or_else(|| KernelError::Failed(format!("sew: face {fi}: {e}")))?;
|
||
mt::Face::try_new(wires, mt::Surface::Plane(plane)).map_err(|e| KernelError::Failed(format!("sew: face {fi}: {e}")))?
|
||
}
|
||
},
|
||
SurfSpec::Revolved { a, b, axis_origin, axis, angle } => {
|
||
let k = axis.normalized().ok_or_else(|| KernelError::Invalid("sew: axis".into()))?;
|
||
let (va, vb) = (builder::vertex(p3(*a)), builder::vertex(p3(*b)));
|
||
let swept: mt::Shell = builder::rsweep(&builder::line(&va, &vb), p3(*axis_origin), v3(k), mt::Rad(*angle));
|
||
let tmp = swept.face_iter().next().cloned().ok_or_else(|| KernelError::Failed("sew: revolved surface".into()))?;
|
||
curved(tmp.oriented_surface(), wires, f.probe, fi)?
|
||
}
|
||
SurfSpec::Extruded { a, b, mid, dir } => {
|
||
let (va, vb) = (builder::vertex(p3(*a)), builder::vertex(p3(*b)));
|
||
let tmp: mt::Face = builder::tsweep(&arc_edge(&va, &vb, *mid), v3(*dir));
|
||
curved(tmp.oriented_surface(), wires, f.probe, fi)?
|
||
}
|
||
SurfSpec::Ruled { a, b } => {
|
||
let (ca, cb) = (cache.chain(a)?, cache.chain(b)?);
|
||
if ca.control_points().len() != cb.control_points().len() {
|
||
return Err(KernelError::Invalid("sew: ruled chains differ in pieces".into()));
|
||
}
|
||
let surface = mt::Surface::BSplineSurface(mt::BSplineSurface::homotopy(ca, cb));
|
||
curved(surface, wires, f.probe, fi)?
|
||
}
|
||
};
|
||
out.push(face);
|
||
}
|
||
let source_ids: HashMap<_, _> = out
|
||
.iter()
|
||
.enumerate()
|
||
.filter_map(|(i, f)| sources.and_then(|s| s.get(i)).and_then(Option::as_ref).map(|s| (f.id(), (f.orientation(), s))))
|
||
.collect();
|
||
if !sheets.is_empty() && !faces_connected(&out) {
|
||
return Err(KernelError::Invalid("sew: bodies touch only along an edge".into()));
|
||
}
|
||
if !sheets.is_empty() {
|
||
out = split_vertex_fans(out)?;
|
||
}
|
||
// Faces keep their identity into the solid (grouped into shells) and the body.
|
||
let built: HashMap<mt::FaceID, usize> = out.iter().enumerate().map(|(i, f)| (f.id(), i)).collect();
|
||
let shells = closed_components(out)?;
|
||
let solid = Solid::try_new(shells).map_err(|e| KernelError::Failed(format!("sew: the faces do not close: {e}")))?;
|
||
let from = solid.face_iter().map(|f| built.get(&f.id()).copied()).collect();
|
||
let body = Body::new(solid)?;
|
||
let mapped =
|
||
body.solid.face_iter().map(|f| source_ids.get(&f.id()).filter(|(o, _)| *o == f.orientation()).map(|(_, s)| (*s).clone())).collect();
|
||
Ok((body.with_face_sources(sources.map(|_| std::sync::Arc::new(mapped))), from))
|
||
})
|
||
}
|
||
|
||
/// Below this sagitta-to-half-chord ratio an arc is built as its exact rational quadratic from
|
||
/// its ends and midpoint. truck's three-point arc (circumcentre, then a turn about it) misses
|
||
/// its own ends on very flat arcs: one 12 mm long with a 0.08 µm sagitta (a 225 m radius) ends
|
||
/// about 1e-6 mm off its vertex, and a planar face holding it far from the origin could not be
|
||
/// given a plane (its wire's points no longer closed).
|
||
const FLAT_ARC: f64 = 1e-2;
|
||
|
||
/// The arc from `a` to `b` through `mid`: the exact rational quadratic for a flat arc, truck's
|
||
/// three-point arc otherwise (and should the curve be refused, which its exact ends make
|
||
/// impossible).
|
||
fn arc_edge(a: &mt::Vertex, b: &mt::Vertex, mid: Vec3) -> mt::Edge {
|
||
let (pa, pb) = (a.point(), b.point());
|
||
let (pa, pb) = (Vec3::new(pa.x, pa.y, pa.z), Vec3::new(pb.x, pb.y, pb.z));
|
||
flat_arc(pa, pb, mid)
|
||
.and_then(|curve| mt::Edge::try_new(a, b, mt::Curve::NurbsCurve(curve)).ok())
|
||
.unwrap_or_else(|| builder::circle_arc(a, b, p3(mid)))
|
||
}
|
||
|
||
/// A flat arc (see [`FLAT_ARC`]) through its midpoint `mid` as one rational quadratic: the middle
|
||
/// control point on the line from the chord's midpoint through `mid`, 2 / (1 − t²) as far, weight
|
||
/// (1 − t²) / (1 + t²), where t is the sagitta over the half chord. None for a deeper arc, or
|
||
/// when `mid` is not halfway along the chord.
|
||
fn flat_arc(a: Vec3, b: Vec3, mid: Vec3) -> Option<mt::NurbsCurve<mt::Vector4>> {
|
||
let m = (a + b) * 0.5;
|
||
let half = a.dist(b) / 2.0;
|
||
let chord = (b - a).normalized()?;
|
||
let bow = mid - m;
|
||
let t = bow.len() / half;
|
||
if !(half > 1e-9) || !(t < FLAT_ARC) || bow.dot(chord).abs() > 1e-9 * half.max(1.0) {
|
||
return None;
|
||
}
|
||
let w = (1.0 - t * t) / (1.0 + t * t);
|
||
let apex = m + bow * (2.0 / (1.0 - t * t));
|
||
let h = |p: Vec3, w: f64| mt::Vector4::new(p.x * w, p.y * w, p.z * w, w);
|
||
Some(mt::NurbsCurve::new(mt::BSplineCurve::new(mt::KnotVec::bezier_knot(2), vec![h(a, 1.0), h(apex, w), h(b, 1.0)])))
|
||
}
|
||
|
||
/// A curved face on `surf`, turned so its normal at the probe points outward.
|
||
fn curved(mut surf: mt::Surface, wires: Vec<mt::Wire>, probe: Option<(Vec3, Vec3)>, fi: usize) -> Result<mt::Face> {
|
||
use mt::{ParametricSurface3D, SearchParameter};
|
||
if let Some((p, outward)) = probe
|
||
&& let Some((u, v)) = surf.search_parameter(p3(p), None, 100)
|
||
{
|
||
let n = surf.normal(u, v);
|
||
if Vec3::new(n.x, n.y, n.z).dot(outward) < 0.0 {
|
||
surf = mt::Invertible::inverse(&surf);
|
||
}
|
||
}
|
||
mt::Face::try_new(wires, surf).map_err(|e| KernelError::Failed(format!("sew: face {fi}: {e}")))
|
||
}
|
||
|
||
/// The plane of a boundary that truck's fit (`builder::try_attach_plane`) refused: truck's fit
|
||
/// again, on the boundary moved so that the mean of its control points is the origin, and the
|
||
/// plane moved back. None when truck refuses that one too (the boundary is not flat within
|
||
/// truck's 1e-6, or has no area).
|
||
///
|
||
/// truck sums the cross products of consecutive control points about a centre, and takes the
|
||
/// points' sum for that centre (it divides by the number of wires, not of points): eight times as
|
||
/// far from the origin as a rectangle of four lines. The sum is the same about any centre; its
|
||
/// rounding is not. It grows with the square of the centre's distance, and on a thin face, whose
|
||
/// normal is short, turns the normal far enough for truck's own flatness test to fail: truck
|
||
/// finds a 0.00013 x 30 mm face 360 mm from the origin 2e-6 mm out of the plane it fitted. With
|
||
/// the centre at the origin the same face is 1e-14 mm out at most.
|
||
fn plane_about_the_mean(wires: &[mt::Wire]) -> Option<mt::Plane> {
|
||
let (mut sum, mut count) = (Vec3::ZERO, 0usize);
|
||
for p in wires.iter().flat_map(|w| w.edge_iter()).flat_map(|e| e.oriented_curve().lift_up().control_points().clone()) {
|
||
sum += Vec3::new(p.x / p.w, p.y / p.w, p.z / p.w);
|
||
count += 1;
|
||
}
|
||
let mean = sum * (1.0 / count.max(1) as f64);
|
||
if !mean.is_finite() {
|
||
return None;
|
||
}
|
||
let moved: Vec<mt::Wire> = wires.iter().map(|w| builder::transformed(w, mt::Matrix4::from_translation(v3(-mean)))).collect();
|
||
match builder::try_attach_plane(&moved).ok()?.surface() {
|
||
mt::Surface::Plane(plane) => Some(mt::Transformed::transformed(&plane, mt::Matrix4::from_translation(v3(mean)))),
|
||
_ => None,
|
||
}
|
||
}
|
||
|
||
#[cfg(test)]
|
||
mod tests {
|
||
use super::*;
|
||
|
||
fn quad(a: Vec3, b: Vec3, c: Vec3, d: Vec3) -> FaceSpec {
|
||
FaceSpec {
|
||
loops: vec![vec![EdgeSpec::Line { a, b }, EdgeSpec::Line { a: b, b: c }, EdgeSpec::Line { a: c, b: d }, EdgeSpec::Line { a: d, b: a }]],
|
||
surface: SurfSpec::Plane,
|
||
probe: None,
|
||
}
|
||
}
|
||
|
||
fn box_faces(origin: Vec3, size: Vec3) -> Vec<FaceSpec> {
|
||
let p = |x: f64, y: f64, z: f64| origin + Vec3::new(x * size.x, y * size.y, z * size.z);
|
||
let (a, b, c, d) = (p(0., 0., 0.), p(1., 0., 0.), p(1., 1., 0.), p(0., 1., 0.));
|
||
let (e, f, g, h) = (p(0., 0., 1.), p(1., 0., 1.), p(1., 1., 1.), p(0., 1., 1.));
|
||
vec![quad(a, d, c, b), quad(e, f, g, h), quad(a, b, f, e), quad(b, c, g, f), quad(c, d, h, g), quad(d, a, e, h)]
|
||
}
|
||
|
||
#[test]
|
||
fn disconnected_closed_faces_keep_every_material_component() {
|
||
let mut faces = box_faces(Vec3::ZERO, Vec3::new(2.0, 3.0, 4.0));
|
||
faces.extend(box_faces(Vec3::X * 10.0, Vec3::new(2.0, 3.0, 4.0)));
|
||
for reverse in [false, true] {
|
||
if reverse {
|
||
faces.reverse();
|
||
}
|
||
let body = sew(&faces).unwrap();
|
||
assert_eq!(body.shell_count(), 2);
|
||
assert!(body.validity().is_empty());
|
||
assert!((crate::measure(&body).unwrap().volume - 48.0).abs() < 1e-9);
|
||
let lumps = body.lumps().unwrap();
|
||
assert_eq!(lumps.len(), 2);
|
||
assert!(lumps.iter().all(|b| (crate::measure(b).unwrap().volume - 24.0).abs() < 1e-9));
|
||
let mesh = body.tessellate(0.01).unwrap();
|
||
assert!(mesh.contains(Vec3::new(1.0, 1.0, 1.0)));
|
||
assert!(mesh.contains(Vec3::new(11.0, 1.0, 1.0)));
|
||
assert!(!mesh.contains(Vec3::new(5.0, 1.0, 1.0)));
|
||
let imported = crate::step_import(&crate::step_export(&[&body], "sewn pieces").unwrap()).unwrap();
|
||
assert!(imported.warnings.is_empty());
|
||
let volume: f64 = imported.bodies.iter().map(|b| crate::measure(&b.body).unwrap().volume).sum();
|
||
assert!((volume - 48.0).abs() < 1e-6);
|
||
}
|
||
}
|
||
|
||
#[test]
|
||
fn sewing_preserves_inward_cavity_orientation_and_refuses_vertex_contact() {
|
||
let outer = box_faces(Vec3::ZERO, Vec3::new(2.0, 3.0, 4.0));
|
||
let mut inner = box_faces(Vec3::new(0.5, 0.75, 1.0), Vec3::new(1.0, 1.5, 2.0));
|
||
for face in &mut inner {
|
||
for lp in &mut face.loops {
|
||
lp.reverse();
|
||
for edge in lp {
|
||
if let EdgeSpec::Line { a, b } = edge {
|
||
std::mem::swap(a, b);
|
||
}
|
||
}
|
||
}
|
||
}
|
||
let cavity = sew(&outer.iter().chain(&inner).cloned().collect::<Vec<_>>()).unwrap();
|
||
assert_eq!(cavity.shell_count(), 2);
|
||
assert_eq!(cavity.lumps().unwrap().len(), 1);
|
||
assert!((crate::measure(&cavity).unwrap().volume - 21.0).abs() < 1e-9);
|
||
assert!(!cavity.tessellate(0.01).unwrap().contains(Vec3::new(1.0, 1.5, 2.0)));
|
||
let touching = box_faces(Vec3::new(2.0, 3.0, 4.0), Vec3::new(2.0, 3.0, 4.0));
|
||
assert!(sew(&outer.iter().chain(&touching).cloned().collect::<Vec<_>>()).unwrap_err().to_string().contains("vertex"));
|
||
let mut hostile = outer.clone();
|
||
hostile[0].loops = vec![Vec::new(); 500_001];
|
||
assert!(sew(&hostile).unwrap_err().to_string().contains("budget"));
|
||
}
|
||
|
||
#[test]
|
||
fn flat_arcs_far_from_the_origin_keep_their_ends_and_their_faces_planes() {
|
||
// A 12 x 30 x 2 slab 1000 mm out whose y = 0 side bows 0.00008 mm (a 225 m radius).
|
||
for (o, bow) in [(Vec3::new(1000.0, 500.0, 0.0), 8e-5), (Vec3::new(-1238.4, 4.0, 14.0), 8e-5), (Vec3::ZERO, 0.5)] {
|
||
let p = |x: f64, y: f64, z: f64| o + Vec3::new(x, y, z);
|
||
let (a, b, c, d) = (p(0., 0., 0.), p(12., 0., 0.), p(12., 30., 0.), p(0., 30., 0.));
|
||
let up = Vec3::new(0., 0., 2.);
|
||
let (e, f, g, h) = (a + up, b + up, c + up, d + up);
|
||
let (m0, m1) = (p(6., -bow, 0.), p(6., -bow, 2.));
|
||
let line = |a, b| EdgeSpec::Line { a, b };
|
||
let plane = |l: Vec<EdgeSpec>| FaceSpec { loops: vec![l], surface: SurfSpec::Plane, probe: None };
|
||
let wall = FaceSpec {
|
||
loops: vec![vec![EdgeSpec::Arc { a, b, mid: m0 }, line(b, f), EdgeSpec::Arc { a: f, b: e, mid: m1 }, line(e, a)]],
|
||
surface: SurfSpec::Extruded { a, b, mid: m0, dir: up },
|
||
probe: Some((p(6., -bow, 1.), Vec3::new(0., -1., 0.))),
|
||
};
|
||
let faces = vec![
|
||
plane(vec![line(a, d), line(d, c), line(c, b), EdgeSpec::Arc { a: b, b: a, mid: m0 }]),
|
||
plane(vec![EdgeSpec::Arc { a: e, b: f, mid: m1 }, line(f, g), line(g, h), line(h, e)]),
|
||
wall,
|
||
quad(b, c, g, f),
|
||
quad(c, d, h, g),
|
||
quad(d, a, e, h),
|
||
];
|
||
let body = sew(&faces).unwrap_or_else(|e| panic!("{o:?} {bow}: {e}"));
|
||
assert!(body.validity().is_empty(), "{o:?}");
|
||
// The circular segment added to the slab (the measure follows flat arcs by chords).
|
||
let r = (36.0 + bow * bow) / (2.0 * bow);
|
||
let half = (6.0 / r).asin();
|
||
let segment = r * r * (half - half.sin() * half.cos());
|
||
let want = (360.0 + segment) * 2.0;
|
||
let got = crate::measure(&body).unwrap().volume;
|
||
assert!((got - want).abs() < 1e-4 * want, "{o:?} {bow}: {got} vs {want}");
|
||
}
|
||
}
|
||
|
||
#[test]
|
||
fn a_sewn_box() {
|
||
let p = |x: f64, y: f64, z: f64| Vec3::new(x, y, z);
|
||
let (a, b, c, d) = (p(0., 0., 0.), p(2., 0., 0.), p(2., 3., 0.), p(0., 3., 0.));
|
||
let (e, f, g, h) = (p(0., 0., 4.), p(2., 0., 4.), p(2., 3., 4.), p(0., 3., 4.));
|
||
let faces = vec![quad(a, d, c, b), quad(e, f, g, h), quad(a, b, f, e), quad(b, c, g, f), quad(c, d, h, g), quad(d, a, e, h)];
|
||
let body = sew(&faces).unwrap();
|
||
let m = crate::measure(&body).unwrap();
|
||
assert!((m.volume - 24.0).abs() < 1e-9, "{}", m.volume);
|
||
assert_eq!(body.face_count(), 6);
|
||
assert!(sew(&faces[..5]).is_err());
|
||
}
|
||
|
||
/// A 4 × 3 × 2 box whose +x wall bulges out as the cubic (4,0) (5,0) (5,3) (4,3), given as a
|
||
/// chain of its two halves at the bottom (`z = 0`) and the top, the wall ruled between them.
|
||
fn bulged_box(bottom: EdgeSpec, top: EdgeSpec) -> Vec<FaceSpec> {
|
||
let p = |x: f64, y: f64, z: f64| Vec3::new(x, y, z);
|
||
let (a, b, c, d) = (p(0., 0., 0.), p(4., 0., 0.), p(4., 3., 0.), p(0., 3., 0.));
|
||
let (e, f, g, h) = (p(0., 0., 2.), p(4., 0., 2.), p(4., 3., 2.), p(0., 3., 2.));
|
||
let line = |a: Vec3, b: Vec3| EdgeSpec::Line { a, b };
|
||
let flat = |edges: Vec<EdgeSpec>| FaceSpec { loops: vec![edges], surface: SurfSpec::Plane, probe: None };
|
||
vec![
|
||
flat(vec![line(a, d), line(d, c), bottom.reversed(), line(b, a)]),
|
||
flat(vec![line(e, f), top.clone(), line(g, h), line(h, e)]),
|
||
quad(a, b, f, e),
|
||
quad(c, d, h, g),
|
||
quad(d, a, e, h),
|
||
FaceSpec {
|
||
loops: vec![vec![bottom.clone(), line(c, g), top.reversed(), line(f, b)]],
|
||
surface: SurfSpec::Ruled { a: bottom, b: top },
|
||
probe: Some((p(4.75, 1.5, 1.0), Vec3::X)),
|
||
},
|
||
]
|
||
}
|
||
|
||
/// The bulge's cubic split at its middle (de Casteljau), at height `z`.
|
||
fn bulge(z: f64) -> EdgeSpec {
|
||
let ctrl = [(4.0, 0.0), (4.5, 0.0), (4.75, 0.75), (4.75, 1.5), (4.75, 2.25), (4.5, 3.0), (4.0, 3.0)];
|
||
EdgeSpec::Chain { ctrl: ctrl.iter().map(|(x, y)| Vec3::new(*x, *y, z)).collect() }
|
||
}
|
||
|
||
#[test]
|
||
fn a_ruled_wall_between_bezier_chains_closes_the_solid() {
|
||
let body = sew(&bulged_box(bulge(0.0), bulge(2.0))).unwrap();
|
||
assert_eq!(body.face_count(), 6);
|
||
assert!(body.validity().is_empty(), "{:?}", body.validity());
|
||
// x = 4 + 3t(1 − t), y = 3(3t² − 2t³): the bulge adds ∫ (x − 4) dy = 54 ∫ t²(1 − t)² dt
|
||
// = 1.8 to the 4 × 3 section; the solid is that section 2 high.
|
||
let m = crate::measure(&body).unwrap();
|
||
assert!((m.volume - 27.6).abs() < 2e-3, "{}", m.volume);
|
||
assert!((m.bbox.max.x - 4.75).abs() < 1e-3, "{:?}", m.bbox);
|
||
}
|
||
|
||
#[test]
|
||
fn hostile_bezier_chains_are_refused() {
|
||
let chain = |ctrl: Vec<Vec3>| EdgeSpec::Chain { ctrl: ctrl.into() };
|
||
let EdgeSpec::Chain { ctrl } = bulge(2.0) else { panic!() };
|
||
// Not 3n + 1 control points; a control point that is not a number; too many pieces.
|
||
let mut nan = ctrl.to_vec();
|
||
nan[2].x = f64::NAN;
|
||
let long: Vec<Vec3> = (0..MAX_CHAIN_POINTS + 3).map(|i| Vec3::new(4.0, 3.0 * i as f64 / (MAX_CHAIN_POINTS + 2) as f64, 2.0)).collect();
|
||
for top in [chain(ctrl[..6].to_vec()), chain(ctrl[..3].to_vec()), chain(Vec::new()), chain(nan), chain(long)] {
|
||
assert!(sew(&bulged_box(bulge(0.0), top)).is_err());
|
||
}
|
||
// A ruled wall needs chains with the same number of pieces.
|
||
let whole = chain(vec![Vec3::new(4.0, 0.0, 2.0), Vec3::new(5.0, 0.0, 2.0), Vec3::new(5.0, 3.0, 2.0), Vec3::new(4.0, 3.0, 2.0)]);
|
||
let e = sew(&bulged_box(bulge(0.0), whole)).unwrap_err().to_string();
|
||
assert!(e.contains("ruled chains differ"), "{e}");
|
||
}
|
||
|
||
#[test]
|
||
fn thin_faces_away_from_the_origin_get_their_planes() {
|
||
// Slabs 30 x 2 mm and 0.00013 to 0.1 mm thick, away from the origin and turned off the
|
||
// axes. truck's plane fit sums the cross products of a boundary's points about a centre
|
||
// and takes the points' sum for it, eight times as far from the origin as a rectangle;
|
||
// on the thin faces its normal then comes out so far off that truck finds a
|
||
// 0.00013 x 30 mm face at (-300, -200, 5) 2e-6 mm out of its own plane and refuses it:
|
||
// `cannot attach a plane to a wire that is not on one plane`. Nine of these 45 slabs
|
||
// have such a face. (Thinner slabs meet another limit, at the origin too: a face
|
||
// 0.00003 mm wide and askew to the axes is sewn but gets no triangles.)
|
||
let turned = |about_z: f64, about_x: f64| {
|
||
let (sz, cz) = about_z.sin_cos();
|
||
let (sx, cx) = about_x.sin_cos();
|
||
// The x, y and z axes turned about x, then about z.
|
||
(Vec3::new(cz, sz, 0.0), Vec3::new(-sz * cx, cz * cx, sx), Vec3::new(sz * sx, -cz * sx, cx))
|
||
};
|
||
// A box on the corner `o` with the edges `u`, `v` and `w` (right-handed).
|
||
let skew_box = |o: Vec3, u: Vec3, v: Vec3, w: Vec3| {
|
||
let p = |x: f64, y: f64, z: f64| o + u * x + v * y + w * z;
|
||
let (a, b, c, d) = (p(0., 0., 0.), p(1., 0., 0.), p(1., 1., 0.), p(0., 1., 0.));
|
||
let (e, f, g, h) = (p(0., 0., 1.), p(1., 0., 1.), p(1., 1., 1.), p(0., 1., 1.));
|
||
vec![quad(a, d, c, b), quad(e, f, g, h), quad(a, b, f, e), quad(b, c, g, f), quad(c, d, h, g), quad(d, a, e, h)]
|
||
};
|
||
for o in [Vec3::new(-300.0, -200.0, 5.0), Vec3::new(2500.0, -1800.0, 40.0), Vec3::ZERO] {
|
||
for width in [1.3e-4, 1e-3, 0.1] {
|
||
for (about_z, about_x) in [(0.0, 0.0), (0.0, 0.45), (0.9, 0.0), (-0.65, 0.45), (2.2, 1.1)] {
|
||
let tag = format!("{o:?}, {width} wide, turned {about_z} and {about_x}");
|
||
let (u, v, w) = turned(about_z, about_x);
|
||
let body = sew(&skew_box(o, u * width, v * 2.0, w * 30.0)).unwrap_or_else(|e| panic!("{tag}: {e}"));
|
||
assert!(body.validity().is_empty() && body.shell_count() == 1 && body.face_count() == 6, "{tag}: {:?}", body.validity());
|
||
// (The measure sums about the origin: it is good to about 1e-14 of the
|
||
// distance cubed, which three metres out is more than the thinnest slabs hold.)
|
||
let (got, want) = (crate::measure(&body).unwrap().volume, width * 60.0);
|
||
assert!((got - want).abs() < 1e-5 * want + 1e-14 * o.len().powi(3) + 1e-9, "{tag}: {got} vs {want}");
|
||
}
|
||
}
|
||
}
|
||
// A boundary that leaves its plane is refused as before: one corner of a face lifted by
|
||
// a thousandth of a millimetre, on a cube and on a sliver.
|
||
for size in [Vec3::new(10.0, 10.0, 10.0), Vec3::new(10.0, 2e-4, 10.0)] {
|
||
let mut warped = box_faces(Vec3::new(500.0, 300.0, 0.0), size);
|
||
if let EdgeSpec::Line { b, .. } = &mut warped[1].loops[0][1] {
|
||
b.z += 1e-3;
|
||
}
|
||
if let EdgeSpec::Line { a, .. } = &mut warped[1].loops[0][2] {
|
||
a.z += 1e-3;
|
||
}
|
||
let e = sew(&warped).unwrap_err().to_string();
|
||
assert!(e.contains("face 1") && e.contains("not on one plane"), "{e}");
|
||
}
|
||
// So is one with no area.
|
||
let mut flat = box_faces(Vec3::ZERO, Vec3::new(10.0, 10.0, 10.0));
|
||
let p = Vec3::new(0.0, 0.0, 10.0);
|
||
flat[1] = quad(p, p + Vec3::X * 3.0, p + Vec3::X * 7.0, p + Vec3::X * 10.0);
|
||
assert!(sew(&flat).unwrap_err().to_string().contains("not on one plane"));
|
||
}
|
||
}
|