Transform normals as pseudovectors, not vectors.

Also clarify the vector transformation API.  Instead of
dmnsn_transform_vector(), we have:
  - dmnsn_transform_point()
  - dmnsn_transform_direction()
  - dmnsn_transform_normal()

2 files changed, 39 insertions, 29 deletions

diff --git a/libdimension/dimension/geometry.h b/libdimension/dimension/geometry.h
index 45aa6c6..d2ad362 100644
--- a/libdimension/dimension/geometry.h
+++ b/libdimension/dimension/geometry.h
@@ -375,9 +375,9 @@ dmnsn_matrix dmnsn_matrix_inverse(dmnsn_matrix A);
 /** Multiply two matricies. */
 dmnsn_matrix dmnsn_matrix_mul(dmnsn_matrix lhs, dmnsn_matrix rhs);
 
-/** Transform a vector by a matrix. */
+/** Transform a point by a matrix. */
 DMNSN_INLINE dmnsn_vector
-dmnsn_transform_vector(dmnsn_matrix T, dmnsn_vector v)
+dmnsn_transform_point(dmnsn_matrix T, dmnsn_vector v)
 {
   /* 9 multiplications, 9 additions */
   dmnsn_vector r;
@@ -387,6 +387,36 @@ dmnsn_transform_vector(dmnsn_matrix T, dmnsn_vector v)
   return r;
 }
 
+/** Transform a direction by a matrix. */
+DMNSN_INLINE dmnsn_vector
+dmnsn_transform_direction(dmnsn_matrix T, dmnsn_vector v)
+{
+  /* 9 multiplications, 9 additions */
+  dmnsn_vector r;
+  r.x = T.n[0][0]*v.x + T.n[0][1]*v.y + T.n[0][2]*v.z;
+  r.y = T.n[1][0]*v.x + T.n[1][1]*v.y + T.n[1][2]*v.z;
+  r.z = T.n[2][0]*v.x + T.n[2][1]*v.y + T.n[2][2]*v.z;
+  return r;
+}
+
+/**
+ * Transform a pseudovector by a matrix.
+ * @param[in] Tinv  The inverse of the transformation matrix.
+ * @param[in] v     The pseudovector to transform
+ * @return The transformed pseudovector.
+ */
+DMNSN_INLINE dmnsn_vector
+dmnsn_transform_normal(dmnsn_matrix Tinv, dmnsn_vector v)
+{
+  /* Multiply by the transpose of the inverse
+     (9 multiplications, 6 additions) */
+  dmnsn_vector r;
+  r.x = Tinv.n[0][0]*v.x + Tinv.n[1][0]*v.y + Tinv.n[2][0]*v.z;
+  r.y = Tinv.n[0][1]*v.x + Tinv.n[1][1]*v.y + Tinv.n[2][1]*v.z;
+  r.z = Tinv.n[0][2]*v.x + Tinv.n[1][2]*v.y + Tinv.n[2][2]*v.z;
+  return r;
+}
+
 /** Transform a bounding box by a matrix. */
 dmnsn_bounding_box dmnsn_transform_bounding_box(dmnsn_matrix T,
                                                 dmnsn_bounding_box box);
@@ -401,11 +431,8 @@ dmnsn_transform_line(dmnsn_matrix T, dmnsn_line l)
 {
   /* 18 multiplications, 24 additions */
   dmnsn_line ret;
-  ret.x0 = dmnsn_transform_vector(T, l.x0);
-  ret.n  = dmnsn_vector_sub(
-    dmnsn_transform_vector(T, dmnsn_vector_add(l.x0, l.n)),
-    ret.x0
-  );
+  ret.x0 = dmnsn_transform_point(T, l.x0);
+  ret.n  = dmnsn_transform_direction(T, l.n);
   return ret;
 }
 
diff --git a/libdimension/dimension/object.h b/libdimension/dimension/object.h
index 8254782..8b497ce 100644
--- a/libdimension/dimension/object.h
+++ b/libdimension/dimension/object.h
@@ -112,24 +112,6 @@ void dmnsn_delete_object(dmnsn_object *object);
 void dmnsn_initialize_object(dmnsn_object *object);
 
 /**
- * Transform a surface normal vector.
- * @param[in] trans   The transformation matrix.
- * @param[in] normal  The normal vector to transform
- * @return The transformed normal vector.
- */
-DMNSN_INLINE dmnsn_vector
-dmnsn_transform_normal(dmnsn_matrix trans, dmnsn_vector normal)
-{
-  return dmnsn_vector_normalized(
-    dmnsn_vector_sub(
-      dmnsn_transform_vector(trans, normal),
-      /* Optimized form of dmnsn_transform_vector(trans, dmnsn_zero) */
-      dmnsn_new_vector(trans.n[0][3], trans.n[1][3], trans.n[2][3])
-    )
-  );
-}
-
-/**
  * Appropriately transform a ray, then test for an intersection.
  * @param[in]  object        The object to test.
  * @param[in]  line          The ray to test.
@@ -144,9 +126,10 @@ dmnsn_object_intersection(const dmnsn_object *object, dmnsn_line line,
   intersection->object = NULL;
   if (object->intersection_fn(object, line_trans, intersection)) {
     /* Get us back into world coordinates */
-    intersection->ray    = line;
-    intersection->normal = dmnsn_transform_normal(object->trans,
-                                                  intersection->normal);
+    intersection->ray = line;
+    intersection->normal = dmnsn_vector_normalized(
+      dmnsn_transform_normal(object->trans_inv, intersection->normal)
+    );
     if (!intersection->object) {
       intersection->object = object;
     }
@@ -166,6 +149,6 @@ dmnsn_object_intersection(const dmnsn_object *object, dmnsn_line line,
 DMNSN_INLINE bool
 dmnsn_object_inside(const dmnsn_object *object, dmnsn_vector point)
 {
-  point = dmnsn_transform_vector(object->trans_inv, point);
+  point = dmnsn_transform_point(object->trans_inv, point);
   return object->inside_fn(object, point);
 }