diff --git a/crates/fj-kernel/src/algorithms/intersection/mod.rs b/crates/fj-kernel/src/algorithms/intersection/mod.rs
index c79e801bb..df03b6abd 100644
--- a/crates/fj-kernel/src/algorithms/intersection/mod.rs
+++ b/crates/fj-kernel/src/algorithms/intersection/mod.rs
@@ -9,5 +9,5 @@ pub use self::{
     curve_edge::CurveEdgeIntersection,
     curve_face::{CurveFaceIntersection, CurveFaceIntersectionList},
     line_segment::LineSegmentIntersection,
-    surface_surface::surface_surface,
+    surface_surface::SurfaceSurfaceIntersection,
 };
diff --git a/crates/fj-kernel/src/algorithms/intersection/surface_surface.rs b/crates/fj-kernel/src/algorithms/intersection/surface_surface.rs
index 5b771d384..820cca925 100644
--- a/crates/fj-kernel/src/algorithms/intersection/surface_surface.rs
+++ b/crates/fj-kernel/src/algorithms/intersection/surface_surface.rs
@@ -2,49 +2,61 @@ use fj_math::{Line, Point, Scalar, Vector};
 
 use crate::objects::{Curve, Surface};
 
-/// Test intersection between two surfaces
-pub fn surface_surface(
-    a: &Surface,
-    b: &Surface,
-) -> Option<(Curve<2>, Curve<2>, Curve<3>)> {
-    // Algorithm from Real-Time Collision Detection by Christer Ericson. See
-    // section 5.4.4, Intersection of Two Planes.
-    //
-    // Adaptations were made to get the intersection curves in local coordinates
-    // for each surface.
-
-    let a_parametric = PlaneParametric::extract_from_surface(a);
-    let b_parametric = PlaneParametric::extract_from_surface(b);
-
-    let a = PlaneConstantNormal::from_parametric_plane(&a_parametric);
-    let b = PlaneConstantNormal::from_parametric_plane(&b_parametric);
-
-    let direction = a.normal.cross(&b.normal);
-
-    let denom = direction.dot(&direction);
-    if denom == Scalar::ZERO {
-        // Comparing `denom` against zero looks fishy. It's probably better to
-        // compare it against an epsilon value, but I don't know how large that
-        // epsilon should be.
+/// The intersection between two surfaces
+#[derive(Clone, Debug, Eq, PartialEq, Hash, Ord, PartialOrd)]
+pub struct SurfaceSurfaceIntersection {
+    /// The intersection curves, in the coordinates of the input surfaces
+    pub local_intersection_curves: [Curve<2>; 2],
+
+    /// The intersection curve, in global coordinates
+    pub global_intersection_curve: Curve<3>,
+}
+
+impl SurfaceSurfaceIntersection {
+    /// Compute the intersection between two surfaces
+    pub fn compute(a: &Surface, b: &Surface) -> Option<Self> {
+        // Algorithm from Real-Time Collision Detection by Christer Ericson. See
+        // section 5.4.4, Intersection of Two Planes.
         //
-        // I'll just leave it like that, until we had the opportunity to collect
-        // some experience with this code.
-        // - @hannobraun
-        return None;
-    }
+        // Adaptations were made to get the intersection curves in local
+        // coordinates for each surface.
+
+        let a_parametric = PlaneParametric::extract_from_surface(a);
+        let b_parametric = PlaneParametric::extract_from_surface(b);
+
+        let a = PlaneConstantNormal::from_parametric_plane(&a_parametric);
+        let b = PlaneConstantNormal::from_parametric_plane(&b_parametric);
+
+        let direction = a.normal.cross(&b.normal);
+
+        let denom = direction.dot(&direction);
+        if denom == Scalar::ZERO {
+            // Comparing `denom` against zero looks fishy. It's probably better
+            // to compare it against an epsilon value, but I don't know how
+            // large that epsilon should be.
+            //
+            // I'll just leave it like that, until we had the opportunity to
+            // collect some experience with this code.
+            // - @hannobraun
+            return None;
+        }
 
-    let origin = (b.normal * a.distance - a.normal * b.distance)
-        .cross(&direction)
-        / denom;
-    let origin = Point { coords: origin };
+        let origin = (b.normal * a.distance - a.normal * b.distance)
+            .cross(&direction)
+            / denom;
+        let origin = Point { coords: origin };
 
-    let line = Line { origin, direction };
+        let line = Line { origin, direction };
 
-    let curve_a = project_line_into_plane(&line, &a_parametric);
-    let curve_b = project_line_into_plane(&line, &b_parametric);
-    let curve_global = Curve::Line(Line { origin, direction });
+        let curve_a = project_line_into_plane(&line, &a_parametric);
+        let curve_b = project_line_into_plane(&line, &b_parametric);
+        let curve_global = Curve::Line(Line { origin, direction });
 
-    Some((curve_a, curve_b, curve_global))
+        Some(Self {
+            local_intersection_curves: [curve_a, curve_b],
+            global_intersection_curve: curve_global,
+        })
+    }
 }
 
 /// A plane in parametric form
@@ -134,7 +146,7 @@ mod tests {
         objects::{Curve, Surface},
     };
 
-    use super::surface_surface;
+    use super::SurfaceSurfaceIntersection;
 
     #[test]
     fn plane_plane() {
@@ -142,9 +154,9 @@ mod tests {
         let xz = Surface::xz_plane();
 
         // Coincident and parallel planes don't have an intersection curve.
-        assert_eq!(surface_surface(&xy, &xy), None);
+        assert_eq!(SurfaceSurfaceIntersection::compute(&xy, &xy), None);
         assert_eq!(
-            surface_surface(
+            SurfaceSurfaceIntersection::compute(
                 &xy,
                 &xy.transform(&Transform::translation([0., 0., 1.]))
             ),
@@ -156,8 +168,11 @@ mod tests {
         let expected_global = Curve::x_axis();
 
         assert_eq!(
-            surface_surface(&xy, &xz),
-            Some((expected_xy, expected_xz, expected_global))
+            SurfaceSurfaceIntersection::compute(&xy, &xz),
+            Some(SurfaceSurfaceIntersection {
+                local_intersection_curves: [expected_xy, expected_xz],
+                global_intersection_curve: expected_global,
+            })
         );
     }
 }