diff --git a/geom/plane.hpp b/geom/plane.hpp
index b87d99b6..689470de 100644
--- a/geom/plane.hpp
+++ b/geom/plane.hpp
@@ -75,16 +75,31 @@ namespace util::geom {
     /// calculates the distance from a plane to a point.
     ///
     /// positive distances are in front of the plane, negative is behind;
+    ///
+    /// NOTE: `distance2` is _not_ the squared distance. It is the
+    /// unnormalised distance. It needs to be divided by the norm of the
+    /// plane normal.
+    template <size_t S, typename T>
+    T
+    distance2 (plane<S,T> p, point<S,T> q)
+    {
+        return dot (p.coefficients, q.template redim<S+1> (1));
+    }
+
+
+    template <size_t S, typename T>
+    T
+    distance2 (point<S,T> p, plane<S,T> q)
+    {
+        return -distance2 (q, p);
+    }
+
+
     template <size_t S, typename T>
     T
     distance (plane<S,T> p, point<S,T> q)
     {
-        auto d = dot (
-            p.coefficients,
-            q.template redim<S+1> (1)
-        );
-
-        return d / norm (normal (p));
+        return distance2 (p, q) / norm (normal (p));
     }