geom/plane: use a vector for coefficients

this simplifies usage of the coefficients in other routines

geom/plane.cpp

@@ -24,11 +24,12 @@ using util::geom::plane;
 
 ///////////////////////////////////////////////////////////////////////////////
 template <size_t S, typename T>
-plane<S,T>::plane (point<S,T>  _p, vector<S,T> _n):
-    p (_p),
-    n (_n)
+plane<S,T>::plane (point<S,T> base, vector<S,T> normal)
 {
-    CHECK (is_normalised (n));
+    CHECK (is_normalised (normal));
+
+    std::copy (std::begin (normal), std::end (normal), std::begin (coefficients));
+    coefficients[S] = dot (base, normal);
 }
 
 

geom/plane.hpp

@@ -19,17 +19,49 @@
 
 #include "../point.hpp"
 #include "../vector.hpp"
+#include "../matrix.hpp"
 
 namespace util::geom {
+    /// represents an S dimensional plane in parametric form
     template <size_t S, typename T>
     struct plane {
-        plane (util::point<S,T>, util::vector<S,T>);
+        plane () = default;
+        plane (util::point<S,T> base, util::vector<S,T> normal);
 
-        ::util::point<S,T> p;
-        ::util::vector<S,T> n;
+        explicit plane (util::vector<S+1,T> _coefficients):
+            coefficients (_coefficients)
+        { ; }
+
+        util::vector<S+1,T> coefficients;
     };
 
 
+    ///////////////////////////////////////////////////////////////////////////
+    /// returns the normal for a plane
+    template <size_t S, typename T>
+    util::vector<S,T>
+    normal (plane<S,T> p)
+    {
+        return p.coefficients.template redim<S> ();
+    }
+
+
+    ///////////////////////////////////////////////////////////////////////////
+    /// normalises a plane's parametric form
+    ///
+    /// useful only after manually modifying the coefficients (as in default
+    /// construction and piecewise initialisation). a plane will otherwise be
+    /// assumed to be in normal form.
+    template <size_t S, typename T>
+    plane<S,T>
+    normalised (plane<S,T> p)
+    {
+        const auto mag = norm (normal (p));
+        CHECK_NEZ (mag);
+        return plane<S,T> (p.coefficients / mag);
+    }
+
+
     typedef plane<2,float> plane2f;
     typedef plane<3,float> plane3f;
 }

geom/ray.cpp

@@ -33,7 +33,8 @@ template <size_t S, typename T>
 T
 ray<S,T>::intersect (plane<S,T> q) const
 {
-    return dot (q.p - origin, q.n) / dot (direction, q.n);
+    return dot (q.coefficients, origin.   template redim<S+1> (1)) /
+           dot (q.coefficients, direction.template redim<S+1> (0));
 }