Exact free-form profiles: geom Seg2 gains cubic Béziers and conics (rational quadratics: exact length, area, split, tangents); sketch ellipses, conics, text, fit splines and control splines up to degree 3 enter profiles as exact segments wherever a loop uses a whole segment, and the kernel builds them as B-spline / NURBS edges (an extruded ellipse is three faces with the exact volume)

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01AS5Tn3xieewUSg3uxrMVdL

crates/kernel/src/freeform.rs

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+//! Free-form profile edges: cubic Béziers as B-spline curves and conics as rational quadratic
+//! NURBS curves (exact ellipses, parabolas and hyperbolas from sketches).
+
+use solvecraft_geom::{Plane, Seg2};
+use truck_modeling as mt;
+
+use crate::body::p3;
+
+/// The edge for a free-form segment between two existing vertices (None for lines and arcs).
+pub(crate) fn edge(plane: &Plane, s: &Seg2, a: &mt::Vertex, b: &mt::Vertex) -> Option<mt::Edge> {
+    match *s {
+        Seg2::Cubic { p1, p2, .. } => Some(mt::builder::bezier(a, b, vec![p3(plane.to_world(p1)), p3(plane.to_world(p2))])),
+        Seg2::Conic { apex, w, .. } => {
+            let (pa, pb, px) = (a.point(), b.point(), p3(plane.to_world(apex)));
+            let ctrl = vec![
+                mt::Vector4::new(pa.x, pa.y, pa.z, 1.0),
+                mt::Vector4::new(px.x * w, px.y * w, px.z * w, w),
+                mt::Vector4::new(pb.x, pb.y, pb.z, 1.0),
+            ];
+            let curve = mt::NurbsCurve::new(mt::BSplineCurve::new(mt::KnotVec::bezier_knot(2), ctrl));
+            Some(mt::Edge::new(a, b, mt::Curve::NurbsCurve(curve)))
+        }
+        Seg2::Line { .. } | Seg2::Arc { .. } => None,
+    }
+}