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OneCAD/apps/solvecraft-cli/src/seams.rs
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//! Seam-normalised topology of Fusion's measurements.
//!
//! Fusion splits a closed surface along seams: a full cylinder can be two half faces, and a
//! closed curve crossing a seam becomes two edges with a vertex on the seam. SolveCraft's merged
//! counts already count each closed surface patch once and ignore seam edges and vertices, so
//! the oracle normalises Fusion's side the same way from its face, edge and vertex lists:
//! - faces cut from one periodic surface (cylinder, cone, sphere, torus) and separated only by
//! seam edges count once;
//! - a seam edge lies on that surface and on no other face's surface: it is dropped;
//! - a vertex left with exactly two edges is no corner (a solid's corners have three or more):
//! the two edges join, and a curve that closes on itself keeps one vertex.
use std::collections::HashMap;
use serde_json::Value;
type V3 = [f64; 3];
const TOL: f64 = 1e-4;
fn v3(v: &Value) -> Option<V3> {
let a = v.as_array()?;
Some([a.first()?.as_f64()?, a.get(1)?.as_f64()?, a.get(2)?.as_f64()?])
}
fn sub(a: V3, b: V3) -> V3 {
[a[0] - b[0], a[1] - b[1], a[2] - b[2]]
}
fn add(a: V3, b: V3) -> V3 {
[a[0] + b[0], a[1] + b[1], a[2] + b[2]]
}
fn mul(a: V3, s: f64) -> V3 {
[a[0] * s, a[1] * s, a[2] * s]
}
fn dot(a: V3, b: V3) -> f64 {
a[0] * b[0] + a[1] * b[1] + a[2] * b[2]
}
fn cross(a: V3, b: V3) -> V3 {
[a[1] * b[2] - a[2] * b[1], a[2] * b[0] - a[0] * b[2], a[0] * b[1] - a[1] * b[0]]
}
fn len(a: V3) -> f64 {
dot(a, a).sqrt()
}
fn unit(a: V3) -> Option<V3> {
let l = len(a);
(l > 1e-12).then(|| mul(a, 1.0 / l))
}
#[derive(Clone, Copy, Debug, PartialEq)]
enum Surf {
Plane { p: V3, n: V3 },
Cylinder { o: V3, a: V3, r: f64 },
Cone { o: V3, a: V3, r: f64, tan: f64 },
Sphere { c: V3, r: f64 },
Torus { c: V3, a: V3, big: f64, small: f64 },
Other,
}
impl Surf {
fn of(f: &Value) -> Surf {
let g = |k: &str| v3(&f[k]);
let n = |k: &str| f[k].as_f64();
let s = match f["type"].as_str().unwrap_or_default() {
"plane" => g("centroid").zip(g("plane_normal_outward").and_then(unit)).map(|(p, n)| Surf::Plane { p, n }),
"cylinder" => (|| Some(Surf::Cylinder { o: g("axis_origin")?, a: unit(g("axis")?)?, r: n("radius_mm")? }))(),
"cone" => {
(|| Some(Surf::Cone { o: g("axis_origin")?, a: unit(g("axis")?)?, r: n("radius_mm")?, tan: n("half_angle_deg")?.to_radians().tan() }))(
)
}
"sphere" => (|| Some(Surf::Sphere { c: g("center")?, r: n("radius_mm")? }))(),
"torus" => (|| Some(Surf::Torus { c: g("center")?, a: unit(g("axis")?)?, big: n("major_radius_mm")?, small: n("minor_radius_mm")? }))(),
_ => None,
};
s.unwrap_or(Surf::Other)
}
fn periodic(&self) -> bool {
matches!(self, Surf::Cylinder { .. } | Surf::Cone { .. } | Surf::Sphere { .. } | Surf::Torus { .. })
}
/// Whether the point lies on the surface; `None` when that can't be told (free-form faces).
fn contains(&self, p: V3) -> Option<bool> {
let radial = |o: V3, a: V3| {
let d = sub(p, o);
let t = dot(d, a);
(t, len(sub(d, mul(a, t))))
};
Some(match *self {
Surf::Plane { p: q, n } => dot(sub(p, q), n).abs() < TOL,
Surf::Cylinder { o, a, r } => (radial(o, a).1 - r).abs() < TOL,
Surf::Cone { o, a, r, tan } => {
let (t, rho) = radial(o, a);
(rho - (r + t * tan)).abs() < TOL || (rho - (r - t * tan)).abs() < TOL
}
Surf::Sphere { c, r } => (len(sub(p, c)) - r).abs() < TOL,
Surf::Torus { c, a, big, small } => {
let (t, rho) = radial(c, a);
((rho - big).hypot(t) - small).abs() < TOL
}
Surf::Other => return None,
})
}
fn same(&self, o: &Surf) -> bool {
let close = |a: f64, b: f64| (a - b).abs() < TOL;
let pt = |a: V3, b: V3| len(sub(a, b)) < TOL;
let par = |a: V3, b: V3| len(cross(a, b)) < TOL;
// Same axis line: parallel, and either origin on the other's axis.
let axis = |o1: V3, a1: V3, o2: V3, a2: V3| par(a1, a2) && len(cross(sub(o2, o1), a1)) < TOL;
match (*self, *o) {
(Surf::Cylinder { o: o1, a: a1, r: r1 }, Surf::Cylinder { o: o2, a: a2, r: r2 }) => axis(o1, a1, o2, a2) && close(r1, r2),
(Surf::Cone { o: o1, a: a1, r: r1, tan: t1 }, Surf::Cone { .. }) => {
// Same cone: the other's frame circle lies on this one, same opening angle.
let Surf::Cone { o: o2, a: a2, r: r2, tan: t2 } = *o else { return false };
axis(o1, a1, o2, a2) && close(t1, t2) && {
let t = dot(sub(o2, o1), a1) * dot(a1, a2).signum();
close(r2, r1 + t * t1) || close(r2, r1 - t * t1)
}
}
(Surf::Sphere { c: c1, r: r1 }, Surf::Sphere { c: c2, r: r2 }) => pt(c1, c2) && close(r1, r2),
(Surf::Torus { c: c1, a: a1, big: b1, small: s1 }, Surf::Torus { c: c2, a: a2, big: b2, small: s2 }) => {
pt(c1, c2) && par(a1, a2) && close(b1, b2) && close(s1, s2)
}
_ => false,
}
}
}
/// Points along an edge from Fusion's edge list.
fn edge_points(e: &Value) -> Vec<V3> {
let (s, t) = (v3(&e["start"]), v3(&e["end"]));
let mut pts: Vec<V3> = s.into_iter().chain(t).collect();
let (c, r, a) = (v3(&e["center"]), e["radius_mm"].as_f64(), v3(&e["axis"]).and_then(unit));
match (e["type"].as_str().unwrap_or_default(), s, t) {
("line", Some(s), Some(t)) => pts.push(mul(add(s, t), 0.5)),
("arc", Some(s), Some(t)) => {
if let (Some(c), Some(r)) = (c, r)
&& let Some(m) = unit(add(sub(s, c), sub(t, c)))
{
let long = e["length_mm"].as_f64().is_some_and(|l| l > std::f64::consts::PI * r);
pts.push(add(c, mul(m, if long { -r } else { r })));
}
}
("circle", Some(s), _) => {
if let (Some(c), Some(a)) = (c, a) {
let d = sub(s, c);
for th in [2.0 * std::f64::consts::FRAC_PI_3, 4.0 * std::f64::consts::FRAC_PI_3] {
pts.push(add(c, add(mul(d, th.cos()), mul(cross(a, d), th.sin()))));
}
}
}
_ => {}
}
pts
}
fn key(p: V3) -> [i64; 3] {
p.map(|x| (x * 1e6).round() as i64)
}
fn find(p: &mut [usize], mut i: usize) -> usize {
while let Some(&q) = p.get(i) {
if q == i {
break;
}
i = q;
}
i
}
/// Faces, edges and vertices of one Fusion body after merging seam splits; `None` when the
/// lists are missing.
pub fn normalised(body: &Value) -> Option<(usize, usize, usize)> {
let faces = body["face_list"].as_array()?;
let edges = body["edge_list"].as_array()?;
let surfs: Vec<Surf> = faces.iter().map(Surf::of).collect();
// Group faces cut from one periodic surface.
let mut group: Vec<usize> = (0..surfs.len()).collect();
for i in 0..surfs.len() {
for j in 0..i {
if surfs[i].periodic() && surfs[i].same(&surfs[j]) {
group[i] = group[j];
break;
}
}
}
let size = |g: usize| group.iter().filter(|x| **x == g).count();
// Seam edges: on a split group's surface and on no other face's surface.
let mut seams_in: HashMap<usize, usize> = HashMap::new();
let mut seam = vec![false; edges.len()];
for (ei, e) in edges.iter().enumerate() {
let pts = edge_points(e);
if pts.is_empty() {
continue;
}
let on = |s: &Surf| pts.iter().map(|p| s.contains(*p)).try_fold(true, |acc, x| Some(acc && x?));
let carriers: Vec<Option<bool>> = surfs.iter().map(on).collect();
if carriers.contains(&None) {
continue;
}
let groups: Vec<usize> = (0..surfs.len()).filter(|f| carriers[*f] == Some(true)).map(|f| group[f]).collect();
if let Some(&g) = groups.first()
&& groups.iter().all(|x| *x == g)
&& surfs[g].periodic()
&& size(g) > 1
{
seam[ei] = true;
*seams_in.entry(g).or_insert(0) += 1;
}
}
let mut face_count = 0;
for g in 0..surfs.len() {
let k = size(g);
if k > 0 {
face_count += k.saturating_sub(seams_in.get(&g).copied().unwrap_or(0)).max(1);
}
}
// Vertex degrees over the remaining edges; a closed edge counts once at its vertex.
let mut ends: Vec<(usize, Option<[i64; 3]>, Option<[i64; 3]>)> = Vec::new();
for (ei, e) in edges.iter().enumerate() {
if seam[ei] {
continue;
}
let (s, t) = (v3(&e["start"]).map(key), v3(&e["end"]).map(key));
let t = if t == s { None } else { t };
ends.push((ends.len(), s, t));
}
// A seam between two closed curves (a closed face's seam whose surface we can't evaluate):
// an open edge whose ends each meet only a closed edge. At a real vertex three edges meet.
let closed_at = |v: &[i64; 3], ends: &[(usize, Option<[i64; 3]>, Option<[i64; 3]>)]| {
let closed = ends.iter().filter(|(_, s, t)| t.is_none() && s.as_ref() == Some(v)).count();
let open = ends.iter().filter(|(_, s, t)| t.is_some() && (s.as_ref() == Some(v) || t.as_ref() == Some(v))).count();
closed == 1 && open == 1
};
let loop_seams: Vec<usize> =
ends.iter().filter(|(_, s, t)| matches!((s, t), (Some(s), Some(t)) if closed_at(s, &ends) && closed_at(t, &ends))).map(|e| e.0).collect();
ends.retain(|e| !loop_seams.contains(&e.0));
for (k, e) in ends.iter_mut().enumerate() {
e.0 = k;
}
let mut deg: HashMap<[i64; 3], Vec<usize>> = HashMap::new();
for (i, s, t) in &ends {
for v in [s, t].into_iter().flatten() {
deg.entry(*v).or_default().push(*i);
}
}
let mut ep: Vec<usize> = (0..ends.len()).collect();
let mut merged: Vec<[i64; 3]> = Vec::new();
for (v, es) in &deg {
// Two open edges meeting: one curve split at a seam.
if let [i, j] = es[..]
&& i != j
&& ends.get(i).is_some_and(|e| e.2.is_some())
&& ends.get(j).is_some_and(|e| e.2.is_some())
{
let (ri, rj) = (find(&mut ep, i), find(&mut ep, j));
if let Some(x) = ep.get_mut(ri) {
*x = rj;
}
merged.push(*v);
}
}
let mut real: HashMap<usize, bool> = HashMap::new();
for (i, s, t) in &ends {
let r = find(&mut ep, *i);
let has_real = [s, t].into_iter().flatten().any(|v| !merged.contains(v)) || (s.is_none() && t.is_none());
*real.entry(r).or_insert(false) |= has_real;
}
let closed = real.values().filter(|r| !**r).count();
let vertices = deg.keys().filter(|v| !merged.contains(v)).count() + closed;
Some((face_count, real.len(), vertices))
}
#[cfg(test)]
mod tests {
use super::*;
use serde_json::json;
/// A cylinder (r 5, height 10) split by Fusion into two halves along two seams.
#[test]
fn split_cylinder_counts_once() {
let cyl = json!({"type": "cylinder", "axis_origin": [0, 0, 0], "axis": [0, 0, 1], "radius_mm": 5.0});
let plane = |z: f64, n: f64| json!({"type": "plane", "centroid": [0, 0, z], "plane_normal_outward": [0, 0, n]});
let arc = |z: f64, s: [f64; 3], t: [f64; 3]| json!({"type": "arc", "start": s, "end": t, "center": [0, 0, z], "radius_mm": 5.0, "axis": [0, 0, 1], "length_mm": 15.707963});
let line = |x: f64| json!({"type": "line", "start": [x, 0, 0], "end": [x, 0, 10]});
let body = json!({
"face_list": [cyl.clone(), cyl, plane(0.0, -1.0), plane(10.0, 1.0)],
"edge_list": [line(5.0), line(-5.0), arc(0.0, [5.0, 0.0, 0.0], [-5.0, 0.0, 0.0]), arc(0.0, [-5.0, 0.0, 0.0], [5.0, 0.0, 0.0]), arc(10.0, [5.0, 0.0, 10.0], [-5.0, 0.0, 10.0]), arc(10.0, [-5.0, 0.0, 10.0], [5.0, 0.0, 10.0])],
});
assert_eq!(normalised(&body), Some((3, 2, 2)));
}
/// Oracle 35: a fillet (free-form face, surface unknown) between two cylinders is bounded by
/// two closed contact curves joined by its seam arc. The arc goes; the curves and circles stay.
#[test]
fn seam_between_closed_curves_on_an_unknown_surface() {
let circle =
|s: [f64; 3], c: [f64; 3], a: [f64; 3]| json!({"type": "circle", "start": s, "end": s, "center": c, "radius_mm": 1.0, "axis": a});
let lp = |p: [f64; 3]| json!({"type": "nurbs", "start": p, "end": p});
let (p, q) = ([0.0, -10.833333333, 10.374916332], [0.0, -10.0, 12.449899598]);
let body = json!({
"face_list": [{"type": "nurbs"}],
"edge_list": [
{"type": "arc", "start": p, "end": q, "center": [0.0, -13.0, 12.449899598], "radius_mm": 3.0, "axis": [1, 0, 0]},
circle([-40.0, 0.0, 15.0], [-40.0, 0.0, 0.0], [-1.0, 0.0, 0.0]),
circle([-10.0, 0.0, 35.0], [0.0, 0.0, 35.0], [0.0, 0.0, 1.0]),
circle([40.0, 0.0, 15.0], [40.0, 0.0, 0.0], [1.0, 0.0, 0.0]),
lp(p),
lp(q),
],
});
assert_eq!(normalised(&body), Some((1, 5, 5)));
}
/// A closed curve split into two edges at a seam vertex joins again (Fusion part 61's keyway).
#[test]
fn degree_two_vertices_join() {
let n = |s: [f64; 3], t: [f64; 3]| json!({"type": "nurbs", "start": s, "end": t});
let body = json!({"face_list": [], "edge_list": [n([0.0, 0.0, 0.0], [1.0, 0.0, 0.0]), n([1.0, 0.0, 0.0], [0.0, 0.0, 0.0])]});
assert_eq!(normalised(&body), Some((0, 1, 1)));
}
}
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