diff --git a/experiments/2025-03-18/src/extra/triangulate.rs b/experiments/2025-03-18/src/extra/triangulate.rs
index fe597e60d..9183afb1b 100644
--- a/experiments/2025-03-18/src/extra/triangulate.rs
+++ b/experiments/2025-03-18/src/extra/triangulate.rs
@@ -91,8 +91,18 @@ fn approximate_half_edge(
         end_vertex: end,
     }: HalfEdgeWithEndVertex,
 ) -> Vec<Point<3>> {
-    let [start, _] = [&half_edge.start, end].map(|vertex| vertex.point);
-    vec![start]
+    let [start, end] = [&half_edge.start, end].map(|vertex| vertex.point);
+
+    let points_local = half_edge.curve.geometry.approximate([start, end].map(
+        |point_global| half_edge.curve.geometry.project_point(point_global),
+    ));
+
+    let mut points_global = vec![start];
+    points_global.extend(points_local.into_iter().map(|point_local| {
+        half_edge.curve.geometry.point_from_local(point_local)
+    }));
+
+    points_global
 }
 
 fn polygon_from_half_edges(
diff --git a/experiments/2025-03-18/src/geometry/curve.rs b/experiments/2025-03-18/src/geometry/curve.rs
index 462efd756..b984a2df8 100644
--- a/experiments/2025-03-18/src/geometry/curve.rs
+++ b/experiments/2025-03-18/src/geometry/curve.rs
@@ -5,6 +5,7 @@ pub trait CurveGeometry {
     fn point_from_local(&self, point: Point<1>) -> Point<3>;
     fn project_point(&self, point: Point<3>) -> Point<1>;
     fn translate(&self, offset: Vector<3>) -> Box<dyn CurveGeometry>;
+    fn approximate(&self, boundary: [Point<1>; 2]) -> Vec<Point<1>>;
 }
 
 impl CurveGeometry for Line<3> {
@@ -24,4 +25,8 @@ impl CurveGeometry for Line<3> {
         let translated = self.transform(&Transform::translation(offset));
         Box::new(translated)
     }
+
+    fn approximate(&self, _: [Point<1>; 2]) -> Vec<Point<1>> {
+        vec![]
+    }
 }