triangles: Use a different implementation for flat and smooth triangles.

1 files changed, 67 insertions, 37 deletions

diff --git a/libdimension/triangle.c b/libdimension/triangle.c
index f7081b4..87efacc 100644
--- a/libdimension/triangle.c
+++ b/libdimension/triangle.c
@@ -20,37 +20,33 @@
 
 /**
  * @file
- * Triangles.
+ * Triangles.  See
+ * http://tavianator.com/2014/05/a-beautiful-raytriangle-intersection-method/
+ * for a description of the intersection algorithm.
  */
 
 #include "dimension.h"
 
-/** Triangle type. */
-typedef struct {
-  dmnsn_object object;
-  dmnsn_vector na, nab, nac;
-} dmnsn_triangle;
+/** Optimized ray/triangle intersection test. */
+static inline bool
+dmnsn_ray_triangle_intersection(dmnsn_line l, double *t, double *u, double *v)
+{
+  /* See the change of basis in dmnsn_triangle_basis() */
+  *t = -l.x0.z/l.n.z;
+  *u = l.x0.x + (*t)*l.n.x;
+  *v = l.x0.y + (*t)*l.n.y;
+  return *t >= 0.0 && *u >= 0.0 && *v >= 0.0 && *u + *v <= 1.0;
+}
 
 /** Triangle intersection callback. */
 static bool
 dmnsn_triangle_intersection_fn(const dmnsn_object *object, dmnsn_line l,
                                dmnsn_intersection *intersection)
 {
-  const dmnsn_triangle *triangle = (const dmnsn_triangle *)object;
-
-  /* See the change of basis in dmnsn_new_triangle() */
-  double t = -l.x0.z/l.n.z;
-  double u = l.x0.x + t*l.n.x;
-  double v = l.x0.y + t*l.n.y;
-  if (t >= 0.0 && u >= 0.0 && v >= 0.0 && u + v <= 1.0) {
-    intersection->t      = t;
-    intersection->normal = dmnsn_vector_add(
-      triangle->na,
-      dmnsn_vector_add(
-        dmnsn_vector_mul(u, triangle->nab),
-        dmnsn_vector_mul(v, triangle->nac)
-      )
-    );
+  double t, u, v;
+  if (dmnsn_ray_triangle_intersection(l, &t, &u, &v)) {
+    intersection->t = t;
+    intersection->normal = dmnsn_z;
     return true;
   }
 
@@ -64,45 +60,79 @@ dmnsn_triangle_inside_fn(const dmnsn_object *triangle, dmnsn_vector point)
   return false;
 }
 
-dmnsn_object *
-dmnsn_new_triangle(dmnsn_pool *pool, dmnsn_vector vertices[3])
+/** Smooth triangle type. */
+typedef struct {
+  dmnsn_object object;
+  dmnsn_vector na, nab, nac;
+} dmnsn_smooth_triangle;
+
+/** Smooth triangle intersection callback. */
+static bool
+dmnsn_smooth_triangle_intersection_fn(const dmnsn_object *object, dmnsn_line l,
+                                      dmnsn_intersection *intersection)
 {
-  dmnsn_vector normal = dmnsn_vector_cross(
-    dmnsn_vector_sub(vertices[1], vertices[0]),
-    dmnsn_vector_sub(vertices[2], vertices[0])
-  );
-  dmnsn_vector normals[] = { normal, normal, normal };
-  return dmnsn_new_smooth_triangle(pool, vertices, normals);
+  const dmnsn_smooth_triangle *triangle = (const dmnsn_smooth_triangle *)object;
+
+  double t, u, v;
+  if (dmnsn_ray_triangle_intersection(l, &t, &u, &v)) {
+    intersection->t = t;
+    intersection->normal = dmnsn_vector_add(
+      triangle->na,
+      dmnsn_vector_add(
+        dmnsn_vector_mul(u, triangle->nab),
+        dmnsn_vector_mul(v, triangle->nac)
+      )
+    );
+    return true;
+  }
+
+  return false;
 }
 
-/* Allocate a new triangle */
-dmnsn_object *
-dmnsn_new_smooth_triangle(dmnsn_pool *pool, dmnsn_vector vertices[3], dmnsn_vector normals[3])
+/** Make a change-of-basis matrix. */
+static inline dmnsn_matrix
+dmnsn_triangle_basis(dmnsn_vector vertices[3])
 {
   /*
-   * Make a change-of-basis matrix
-   *
    * The new vector space has corners at <0, 1, 0>, <0, 0, 1>, and 0,
    * corresponding to the basis (ab, ac, ab X ac).
    */
   dmnsn_vector ab = dmnsn_vector_sub(vertices[1], vertices[0]);
   dmnsn_vector ac = dmnsn_vector_sub(vertices[2], vertices[0]);
   dmnsn_vector normal = dmnsn_vector_cross(ab, ac);
-  dmnsn_matrix P = dmnsn_new_matrix4(ab, ac, normal, vertices[0]);
+  return dmnsn_new_matrix4(ab, ac, normal, vertices[0]);
+}
+
+dmnsn_object *
+dmnsn_new_triangle(dmnsn_pool *pool, dmnsn_vector vertices[3])
+{
+  dmnsn_object *object = dmnsn_new_object(pool);
+  object->intersection_fn = dmnsn_triangle_intersection_fn;
+  object->inside_fn = dmnsn_triangle_inside_fn;
+  object->bounding_box.min = dmnsn_zero;
+  object->bounding_box.max = dmnsn_new_vector(1.0, 1.0, 0.0);
+  object->intrinsic_trans = dmnsn_triangle_basis(vertices);
+  return object;
+}
+
+dmnsn_object *
+dmnsn_new_smooth_triangle(dmnsn_pool *pool, dmnsn_vector vertices[3], dmnsn_vector normals[3])
+{
+  dmnsn_matrix P = dmnsn_triangle_basis(vertices);
 
   /* Transform the given normals. */
   dmnsn_vector na = dmnsn_vector_normalized(dmnsn_transform_normal(P, normals[0]));
   dmnsn_vector nb = dmnsn_vector_normalized(dmnsn_transform_normal(P, normals[1]));
   dmnsn_vector nc = dmnsn_vector_normalized(dmnsn_transform_normal(P, normals[2]));
 
-  dmnsn_triangle *triangle = DMNSN_PALLOC(pool, dmnsn_triangle);
+  dmnsn_smooth_triangle *triangle = DMNSN_PALLOC(pool, dmnsn_smooth_triangle);
   triangle->na  = na;
   triangle->nab = dmnsn_vector_sub(nb, na);
   triangle->nac = dmnsn_vector_sub(nc, na);
 
   dmnsn_object *object = &triangle->object;
   dmnsn_init_object(pool, object);
-  object->intersection_fn = dmnsn_triangle_intersection_fn;
+  object->intersection_fn = dmnsn_smooth_triangle_intersection_fn;
   object->inside_fn = dmnsn_triangle_inside_fn;
   object->bounding_box.min = dmnsn_zero;
   object->bounding_box.max = dmnsn_new_vector(1.0, 1.0, 0.0);