diff --git a/crates/fj-kernel/src/algorithms/intersection/line_segment.rs b/crates/fj-kernel/src/algorithms/intersection/line_segment.rs
new file mode 100644
index 000000000..2b1b3b0ba
--- /dev/null
+++ b/crates/fj-kernel/src/algorithms/intersection/line_segment.rs
@@ -0,0 +1,115 @@
+use fj_math::{Aabb, Line, Point, Scalar, Segment, Vector};
+
+/// Determine the intersection between a [`Line`] and a [`Segment`]
+pub fn line_segment(
+    line: &Line<2>,
+    segment: &Segment<2>,
+) -> Option<LineSegmentIntersection> {
+    // Algorithm adapted from Real-Time Collision Detection by Christer Ericson.
+    // See section 5.1.9.1, 2D Segment Intersection.
+
+    let [a, b] = segment.points();
+
+    // Find vector that is orthogonal to `segment`.
+    let n = {
+        let ab = b - a;
+        Vector::from([ab.v, ab.u])
+    };
+
+    let n_dot_origin = n.dot(&(b - line.origin));
+    let n_dot_direction = n.dot(&line.direction);
+
+    if n_dot_origin == Scalar::ZERO && n_dot_direction == Scalar::ZERO {
+        // `line` and `segment` are not just parallel, but coincident!
+        return Some(LineSegmentIntersection::Coincident);
+    }
+
+    if n_dot_direction == Scalar::ZERO {
+        // `line` and `segment` are parallel, but not coincident
+        return None;
+    }
+
+    // Now we ruled out the special cases. Compute where `line` hits the line
+    // defined by `segment`'s points.
+    let t = n_dot_origin / n_dot_direction;
+
+    let point_is_on_segment = Aabb::<2>::from_points(segment.points())
+        .contains(line.convert_point_from_line_coords(&Point::from([t])));
+    if !point_is_on_segment {
+        return None;
+    }
+
+    Some(LineSegmentIntersection::PointOnLine(t))
+}
+
+/// An intersection between a [`Line`] and a [`Segment`]
+#[derive(Debug, Eq, PartialEq)]
+pub enum LineSegmentIntersection {
+    /// Line and segment intersect on a point
+    ///
+    /// Point is given as a coordinate on the line.
+    PointOnLine(Scalar),
+
+    /// Line and segment are coincident
+    Coincident,
+}
+
+#[cfg(test)]
+mod tests {
+    use fj_math::{Line, Point, Scalar, Segment, Vector};
+
+    use crate::algorithms::intersection::LineSegmentIntersection;
+
+    #[test]
+    fn line_segment() {
+        let line = Line {
+            origin: Point::origin(),
+            direction: Vector::unit_u(),
+        };
+
+        // regular hit
+        assert_eq!(
+            super::line_segment(
+                &line,
+                &Segment::from_points([[1., -1.], [1., 1.]]),
+            ),
+            Some(LineSegmentIntersection::PointOnLine(Scalar::ONE)),
+        );
+
+        // hit, where line and segment are parallel
+        assert_eq!(
+            super::line_segment(
+                &line,
+                &Segment::from_points([[1., 0.], [2., 0.]]),
+            ),
+            Some(LineSegmentIntersection::Coincident),
+        );
+
+        // segment above line
+        assert_eq!(
+            super::line_segment(
+                &line,
+                &Segment::from_points([[1., 1.], [1., 2.]]),
+            ),
+            None,
+        );
+
+        // segment below line
+        assert_eq!(
+            super::line_segment(
+                &line,
+                &Segment::from_points([[1., -2.], [1., -1.]]),
+            ),
+            None,
+        );
+
+        // segment parallel to line
+        assert_eq!(
+            super::line_segment(
+                &line,
+                &Segment::from_points([[-1., 1.], [1., 1.]]),
+            ),
+            None,
+        );
+    }
+}
diff --git a/crates/fj-kernel/src/algorithms/intersection/mod.rs b/crates/fj-kernel/src/algorithms/intersection/mod.rs
new file mode 100644
index 000000000..ff6220a6e
--- /dev/null
+++ b/crates/fj-kernel/src/algorithms/intersection/mod.rs
@@ -0,0 +1,9 @@
+//! Intersection algorithms
+
+mod line_segment;
+mod surface;
+
+pub use self::{
+    line_segment::{line_segment, LineSegmentIntersection},
+    surface::surface,
+};
diff --git a/crates/fj-kernel/src/algorithms/intersection.rs b/crates/fj-kernel/src/algorithms/intersection/surface.rs
similarity index 98%
rename from crates/fj-kernel/src/algorithms/intersection.rs
rename to crates/fj-kernel/src/algorithms/intersection/surface.rs
index 4d1b64a31..fc008a0c5 100644
--- a/crates/fj-kernel/src/algorithms/intersection.rs
+++ b/crates/fj-kernel/src/algorithms/intersection/surface.rs
@@ -1,5 +1,3 @@
-//! Intersection algorithms
-
 use fj_math::{Line, Point, Scalar, Vector};
 
 use crate::geometry::{Curve, Surface};
diff --git a/crates/fj-kernel/src/geometry/points.rs b/crates/fj-kernel/src/geometry/points.rs
index 9e260fb40..567b99966 100644
--- a/crates/fj-kernel/src/geometry/points.rs
+++ b/crates/fj-kernel/src/geometry/points.rs
@@ -54,7 +54,7 @@ impl From<fj_math::Point<3>> for Point<3> {
 }
 
 // Some math operations for convenience. Obviously those can never return a new
-// `Point`, or the conversion back to 3D would be broken.
+// `self::Point`, or the conversion back to 3D would be broken.
 
 impl<const D: usize> Add<Vector<D>> for Point<D> {
     type Output = fj_math::Point<D>;
diff --git a/crates/fj-kernel/src/topology/faces.rs b/crates/fj-kernel/src/topology/faces.rs
index e3535d00e..bacbdcb7d 100644
--- a/crates/fj-kernel/src/topology/faces.rs
+++ b/crates/fj-kernel/src/topology/faces.rs
@@ -39,7 +39,7 @@ pub enum Face {
         /// lie in the surface. The data we're using here is 3-dimensional
         /// though, so no such limitation is enforced.
         ///
-        /// It might be less error-prone to specify the edges in surface
+        /// It might be less error-prone to specify the cycles in surface
         /// coordinates.
         exteriors: Vec<Handle<Cycle>>,