diff --git a/crates/fj-kernel/src/builder/curve.rs b/crates/fj-kernel/src/builder/curve.rs
index c094c14a5..acc790cf1 100644
--- a/crates/fj-kernel/src/builder/curve.rs
+++ b/crates/fj-kernel/src/builder/curve.rs
@@ -38,6 +38,14 @@ pub trait CurveBuilder {
         &mut self,
         points: [impl Into<Point<2>>; 2],
     ) -> SurfacePath;
+
+    /// Update partial curve to be a line, from provided points and line coords
+    ///
+    /// Returns the updated path.
+    fn update_as_line_from_points_with_line_coords(
+        &mut self,
+        points: [(impl Into<Point<1>>, impl Into<Point<2>>); 2],
+    ) -> SurfacePath;
 }
 
 impl CurveBuilder for PartialCurve {
@@ -82,4 +90,13 @@ impl CurveBuilder for PartialCurve {
         self.path = Some(path.into());
         path
     }
+
+    fn update_as_line_from_points_with_line_coords(
+        &mut self,
+        points: [(impl Into<Point<1>>, impl Into<Point<2>>); 2],
+    ) -> SurfacePath {
+        let path = SurfacePath::from_points_with_line_coords(points);
+        self.path = Some(path.into());
+        path
+    }
 }
diff --git a/crates/fj-kernel/src/builder/edge.rs b/crates/fj-kernel/src/builder/edge.rs
index 3f608935f..247addb01 100644
--- a/crates/fj-kernel/src/builder/edge.rs
+++ b/crates/fj-kernel/src/builder/edge.rs
@@ -150,6 +150,7 @@ impl HalfEdgeBuilder for PartialHalfEdge {
     }
 
     fn update_as_line_segment(&mut self) {
+        let boundary = self.vertices.each_ref_ext().map(|vertex| vertex.0);
         let points_surface = self.vertices.each_ref_ext().map(|vertex| {
             vertex
                 .1
@@ -158,13 +159,23 @@ impl HalfEdgeBuilder for PartialHalfEdge {
                 .expect("Can't infer line segment without surface position")
         });
 
-        self.curve
-            .write()
-            .update_as_line_from_points(points_surface);
-
-        for (vertex, position) in self.vertices.each_mut_ext().zip_ext([0., 1.])
-        {
-            vertex.0 = Some([position].into());
+        if let [Some(start), Some(end)] = boundary {
+            let boundary = [start, end];
+            self.curve
+                .write()
+                .update_as_line_from_points_with_line_coords(
+                    boundary.zip_ext(points_surface),
+                );
+        } else {
+            self.curve
+                .write()
+                .update_as_line_from_points(points_surface);
+
+            for (vertex, position) in
+                self.vertices.each_mut_ext().zip_ext([0., 1.])
+            {
+                vertex.0 = Some([position].into());
+            }
         }
 
         self.infer_global_form();
diff --git a/crates/fj-kernel/src/geometry/path.rs b/crates/fj-kernel/src/geometry/path.rs
index 01fefdf2a..f84b143b2 100644
--- a/crates/fj-kernel/src/geometry/path.rs
+++ b/crates/fj-kernel/src/geometry/path.rs
@@ -58,6 +58,13 @@ impl SurfacePath {
         (Self::Line(line), coords)
     }
 
+    /// Create a line from two points that include line coordinates
+    pub fn from_points_with_line_coords(
+        points: [(impl Into<Point<1>>, impl Into<Point<2>>); 2],
+    ) -> Self {
+        Self::Line(Line::from_points_with_line_coords(points))
+    }
+
     /// Convert a point on the path into surface coordinates
     pub fn point_from_path_coords(
         &self,
diff --git a/crates/fj-math/src/line.rs b/crates/fj-math/src/line.rs
index 900006f58..c2a6c513f 100644
--- a/crates/fj-math/src/line.rs
+++ b/crates/fj-math/src/line.rs
@@ -181,6 +181,30 @@ mod tests {
 
     use super::Line;
 
+    #[test]
+    fn from_points_with_line_coords() {
+        let line = Line::from_points_with_line_coords([
+            ([0.], [0., 0.]),
+            ([1.], [1., 0.]),
+        ]);
+        assert_eq!(line.origin(), Point::from([0., 0.]));
+        assert_eq!(line.direction(), Vector::from([1., 0.]));
+
+        let line = Line::from_points_with_line_coords([
+            ([1.], [0., 1.]),
+            ([0.], [1., 1.]),
+        ]);
+        assert_eq!(line.origin(), Point::from([1., 1.]));
+        assert_eq!(line.direction(), Vector::from([-1., 0.]));
+
+        let line = Line::from_points_with_line_coords([
+            ([-1.], [0., 2.]),
+            ([0.], [1., 2.]),
+        ]);
+        assert_eq!(line.origin(), Point::from([1., 2.]));
+        assert_eq!(line.direction(), Vector::from([1., 0.]));
+    }
+
     #[test]
     fn is_coincident_with() {
         let (line, _) = Line::from_points([[0., 0.], [1., 0.]]);