ellipse: add ray distance query

geom/ellipse.cpp

@@ -14,10 +14,15 @@
  * Copyright 2015-2017 Danny Robson <danny@nerdcruft.net>
  */
 
-#include "./ellipse.hpp"
+#include "ellipse.hpp"
 
-#include "./ops.hpp"
-#include "./aabb.hpp"
+#include "ops.hpp"
+#include "aabb.hpp"
+#include "ray.hpp"
+#include "sphere.hpp"
+#include "point.hpp"
+
+#include "../matrix.hpp"
 
 using util::geom::ellipse;
 
@@ -46,6 +51,29 @@ template bool util::geom::intersects (ellipse<2,float>, util::point<2,float>);
 template bool util::geom::intersects (ellipse<3,float>, util::point<3,float>);
 
 
+///////////////////////////////////////////////////////////////////////////////
+// query a ray-ellipse distance by transforming spaces such that the ellipse is
+// a sphere
+template <>
+float
+util::geom::distance (ray<3,float> r, ellipse<3,float> e)
+{
+    // find a transform that puts the ellipse at origin and scales it to a
+    // unit sphere.
+    auto const from_scaled = util::scale (e.radius) *
+                             util::look_at (e.origin, {0,0,-1}, e.up);
+    auto const to_scaled = inverse (from_scaled);
+
+    // transform the ray into this new space and query against a unit sphere
+    auto const scaled_r = to_scaled * r;
+    auto const scaled_d = distance (scaled_r, sphere3f {0, 1.f});
+    auto const scaled_p = scaled_r.at (scaled_d);
+
+    // transform the result back into the original space
+    return distance (r.origin, (from_scaled * scaled_p.homog<4> ()).redim<3> ());
+}
+
+
 ///////////////////////////////////////////////////////////////////////////////
 template <size_t S, typename T>
 static util::geom::aabb<S,T>

geom/ellipse.hpp

@@ -19,6 +19,8 @@
 
 #include <cstdlib>
 
+#include "fwd.hpp"
+
 #include "../point.hpp"
 #include "../vector.hpp"
 
@@ -26,9 +28,28 @@ namespace util::geom {
     ///////////////////////////////////////////////////////////////////////////
     template <size_t S, typename ValueT>
     struct ellipse {
+        // the centre point of the ellipsoid
         util::point<S,ValueT> origin;
+
+        // the distance from the centre along each axis to the shape's edge
         util::vector<S,ValueT> radius;
+
+        // the orientation of up for the shape
+        util::vector<S,ValueT> up;
     };
+
+
+    /// returns the distance along a ray to the surface of an ellipse.
+    ///
+    /// returns infinity if there is no intersection
+    template <size_t DimensionV, typename ValueT>
+    ValueT
+    distance (
+        ray<DimensionV,ValueT>,
+        ellipse<DimensionV,ValueT>
+    );
+
+    using ellipse3f = ellipse<3,float>;
 }