fix: axis or tangent plane on a drill tip no longer fails with "no face at NaN" (#567) (#655)

The nearest point on a triangle with a zero-length edge (a cone's tip) is no longer NaN, so an axis or tangent plane on a drill tip works again (#567).

crates/doc/src/name_lookup.rs

@@ -104,7 +104,8 @@ fn nearest_on_face(m: &Mesh, face: usize, p: Vec3) -> Option<(f64, Vec3)> {
         let Some([a, b, c]) = m.tri(t) else { continue };
         let q = closest(p, a, b, c);
         let d = q.dist(p);
-        if best.is_none_or(|x| d < x.0) {
+        // A non-finite candidate must never become the best: nothing compares less than NaN.
+        if d.is_finite() && best.is_none_or(|x| d < x.0) {
             best = Some((d, q));
         }
     }
@@ -317,7 +318,7 @@ fn legacy_locate<'a>(bodies: impl Iterator<Item = (usize, &'a ModelBody)>, name:
             let Some([a, bb, c]) = m.tri(t) else { continue };
             let q = closest(p, a, bb, c);
             let d = q.dist(p) - if exact { 1e-9 } else { 0.0 };
-            if best.is_none_or(|x| d < x.0) {
+            if d.is_finite() && best.is_none_or(|x| d < x.0) {
                 best = Some((d, bi, *f as usize, q, !exact, tol));
             }
         }

crates/doc/src/naming.rs

@@ -114,6 +114,8 @@ fn samples(m: &Mesh, nf: usize) -> Vec<Vec<Vec3>> {
         .collect()
 }
 
+/// The point of triangle `abc` nearest `p`. A zero-length edge (a cone's tip repeats its apex
+/// vertex) has no interior to project onto, so its branch is skipped rather than dividing 0 by 0.
 pub(crate) fn closest(p: Vec3, a: Vec3, b: Vec3, c: Vec3) -> Vec3 {
     let (ab, ac, ap) = (b - a, c - a, p - a);
     let (d1, d2) = (ab.dot(ap), ac.dot(ap));
@@ -126,7 +128,7 @@ pub(crate) fn closest(p: Vec3, a: Vec3, b: Vec3, c: Vec3) -> Vec3 {
         return b;
     }
     let vc = d1 * d4 - d3 * d2;
-    if vc <= 0.0 && d1 >= 0.0 && d3 <= 0.0 {
+    if vc <= 0.0 && d1 >= 0.0 && d3 <= 0.0 && d1 - d3 > 0.0 {
         return a + ab * (d1 / (d1 - d3));
     }
     let cp = p - c;
@@ -135,11 +137,11 @@ pub(crate) fn closest(p: Vec3, a: Vec3, b: Vec3, c: Vec3) -> Vec3 {
         return c;
     }
     let vb = d5 * d2 - d1 * d6;
-    if vb <= 0.0 && d2 >= 0.0 && d6 <= 0.0 {
+    if vb <= 0.0 && d2 >= 0.0 && d6 <= 0.0 && d2 - d6 > 0.0 {
         return a + ac * (d2 / (d2 - d6));
     }
     let va = d3 * d6 - d5 * d4;
-    if va <= 0.0 && (d4 - d3) >= 0.0 && (d5 - d6) >= 0.0 {
+    if va <= 0.0 && (d4 - d3) >= 0.0 && (d5 - d6) >= 0.0 && (d4 - d3) + (d5 - d6) > 0.0 {
         return b + (c - b) * ((d4 - d3) / ((d4 - d3) + (d5 - d6)));
     }
     let den = va + vb + vc;
@@ -753,6 +755,20 @@ pub fn face_on_body(body: &ModelBody, name: &str, p: Vec3) -> Option<(usize, Vec
 mod tests {
     use super::*;
 
+    /// A cone's tip repeats its apex vertex, so a triangle can have a zero-length edge. The nearest
+    /// point on it must still be a real point (it used to be NaN, which broke picking the tip).
+    #[test]
+    fn closest_point_on_a_degenerate_triangle_is_finite() {
+        let (a, c) = (Vec3::new(0., 0., 0.), Vec3::new(2., 0., 0.));
+        for (b, c) in [(a, c), (c, c), (a, a)] {
+            for p in [Vec3::new(1., 1., 0.), Vec3::new(-1., 0.5, 0.), Vec3::new(3., -2., 1.), a] {
+                let q = closest(p, a, b, c);
+                assert!(q.x.is_finite() && q.y.is_finite() && q.z.is_finite(), "{a:?} {b:?} {c:?} {p:?} -> {q:?}");
+            }
+        }
+        assert_eq!(closest(Vec3::new(1., 1., 0.), a, a, c), Vec3::new(1., 0., 0.));
+    }
+
     #[test]
     fn merged_face_votes_collectively_for_pieces_of_one_source() {
         let body = ModelBody::new("Input".into(), solidcraft_kernel::box_solid(Vec3::ZERO, Vec3::new(4., 1., 1.)).unwrap(), 1);