Mesh: the triangle primitive for three-cornered sweep regions

A cross-section region with three corners (a fillet's quarter disk, a
pocket corner cut off by a partition) was left to the free all-quad
mesher. It now gets midpoint subdivision's triangle primitive (Tam and
Armstrong 1991; Li, Armstrong, McKeag 1997): lines from a centre to a
node on each side split it into three mapped blocks, the interior then
smoothed and every quadrilateral checked (a fold falls back to free).
Interval assignment gains dominance constraints (a side shorter than
the other two together) so the split always exists.

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

crates/mesh/src/hex/sweep.rs

@@ -331,13 +331,22 @@ fn build(ctx: &Ctx, topo: &Topology, refine: u32) -> Result<Raw> {
         })
         .collect();
     // The rings may start mid-loop: give the mapped scheme its corners as ring positions.
+    // Corners (curve uses) as ring positions, in order; `None` unless every one is found.
+    let positions = |c: &[usize]| {
+        let s0 = starts.first().cloned().unwrap_or_default();
+        let mut pos: Vec<usize> = c.iter().filter_map(|&k| s0.get(k).copied()).collect();
+        pos.sort_unstable();
+        (pos.len() == c.len()).then_some(pos)
+    };
     let (scheme, starts) = match scheme {
-        region::Scheme::Mapped(c) => {
-            let s0 = starts.first().cloned().unwrap_or_default();
-            let mut pos: Vec<usize> = c.iter().filter_map(|&k| s0.get(k).copied()).collect();
-            pos.sort_unstable();
-            if pos.len() == 4 { (region::Scheme::Mapped([0, 1, 2, 3]), vec![pos]) } else { (region::Scheme::Free, starts) }
-        }
+        region::Scheme::Mapped(c) => match positions(&c) {
+            Some(pos) => (region::Scheme::Mapped([0, 1, 2, 3]), vec![pos]),
+            None => (region::Scheme::Free, starts),
+        },
+        region::Scheme::Triangle(c) => match positions(&c) {
+            Some(pos) => (region::Scheme::Triangle([0, 1, 2]), vec![pos]),
+            None => (region::Scheme::Free, starts),
+        },
         other => (other, starts),
     };
     let (mesh, used_scheme) = region::mesh(&loops2, &starts, scheme, &plane_field, &ctx.opts.quad)?;
@@ -400,6 +409,7 @@ fn build(ctx: &Ctx, topo: &Topology, refine: u32) -> Result<Raw> {
         mesh.quads.len(),
         match used_scheme {
             region::Scheme::Mapped(_) => "mapped",
+            region::Scheme::Triangle(_) => "triangle",
             region::Scheme::Annulus => "annulus",
             region::Scheme::Disk => "disk",
             region::Scheme::Free => "free",