diff --git a/geom/plane.cpp b/geom/plane.cpp
index d4bea1c2..87d2aa97 100644
--- a/geom/plane.cpp
+++ b/geom/plane.cpp
@@ -29,7 +29,7 @@ plane<S,T>::plane (point<S,T> base, vector<S,T> normal)
     CHECK (is_normalised (normal));
 
     std::copy (std::begin (normal), std::end (normal), std::begin (coefficients));
-    coefficients[S] = dot (base, normal);
+    coefficients[S] = -dot (base, normal);
 }
 
 
diff --git a/geom/plane.hpp b/geom/plane.hpp
index f20a1ee6..b87d99b6 100644
--- a/geom/plane.hpp
+++ b/geom/plane.hpp
@@ -81,7 +81,7 @@ namespace util::geom {
     {
         auto d = dot (
             p.coefficients,
-            q.template redim<S+1> (-1)
+            q.template redim<S+1> (1)
         );
 
         return d / norm (normal (p));