Mesh: the tet mesher divides a seeded edge at the seed's nodes

The seed's spacing becomes size-field samples the field grades from, and
after coarsening its nodes are put on the feature curve and pinned, so the
edge has exactly the seeded divisions at the seeded spacing. The quality
report gives, per seed, the boundary edges along it.

Part of #230.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01UhhZMBTviDQxZvwnyP89fo

crates/mesh/src/tet/tests.rs

@@ -195,6 +195,35 @@ mod pipeline {
         assert_eq!(a, b);
     }
 
+    #[test]
+    fn a_seeded_edge_gets_the_seeded_spacing_and_the_size_grows_from_it() {
+        use crate::seeds::EdgeSeed;
+        use fieldcraft_model::SeedConstraint;
+        let s = box_surface();
+        let cdt = tetrahedralize(&s, &CdtOptions::default()).unwrap();
+        let edge = vec![[0.0, 0.0, 0.0], [10.0, 0.0, 0.0]];
+        let seed = EdgeSeed { name: "front".into(), points: edge, tolerance: 0.0, count: 16, bias: None, constraint: SeedConstraint::Exact };
+        let plain = QualityOptions { size: Some(5.0), seeds: vec![EdgeSeed { count: 1, ..seed.clone() }], ..QualityOptions::default() };
+        let seeded = QualityOptions { seeds: vec![seed], ..plain.clone() };
+        let a = quality_mesh(&s, &cdt, Vec::new(), &plain).unwrap();
+        let b = quality_mesh(&s, &cdt, Vec::new(), &seeded).unwrap();
+        let (na, nb) = (a.report.seeds[0].2, b.report.seeds[0].2);
+        // Unseeded, the 10 mm edge gets about two 5 mm elements; seeded, about sixteen.
+        assert!(na <= 4, "{na}");
+        assert_eq!(nb, 16);
+        assert_eq!(b.report.seeds[0].1, 16);
+        assert!(b.report.output.tets > a.report.output.tets && b.report.output.inadmissible == 0);
+        // Biased: the mesh's nodes on the edge are the seed's.
+        let bias = Some(fieldcraft_model::Bias { ratio: 4.0, toward: fieldcraft_model::BiasToward::Start });
+        let biased = QualityOptions { seeds: vec![EdgeSeed { count: 8, bias, ..seeded.seeds[0].clone() }], ..plain.clone() };
+        let c = quality_mesh(&s, &cdt, Vec::new(), &biased).unwrap();
+        let mut x: Vec<f64> = c.points.iter().filter(|p| p[1].abs() < 1e-9 && p[2].abs() < 1e-9).map(|p| p[0]).collect();
+        x.sort_by(f64::total_cmp);
+        let want: Vec<f64> = biased.seeds[0].fractions(8, false).iter().map(|f| 10.0 * f).collect();
+        assert_eq!(x.len(), want.len(), "{x:?}");
+        assert!(x.iter().zip(&want).all(|(a, b)| (a - b).abs() < 1e-9), "{x:?} {want:?}");
+    }
+
     #[test]
     fn a_sphere_keeps_its_boundary_on_the_sphere_to_second_order() {
         let (p, t) = uv_sphere(10, 20);