objects: Implement triangle fans.

4 files changed, 202 insertions, 3 deletions

diff --git a/libdimension/Makefile.am b/libdimension/Makefile.am
index 00d0549..c488016 100644
--- a/libdimension/Makefile.am
+++ b/libdimension/Makefile.am
@@ -117,7 +117,8 @@ libdimension_la_SOURCES = $(nobase_include_HEADERS)                            \
                           threads.h                                            \
                           timer.c                                              \
                           torus.c                                              \
-                          triangle.c
+                          triangle.c                                           \
+                          triangle_fan.c
 libdimension_la_CFLAGS  = $(AM_CFLAGS)
 libdimension_la_LDFLAGS = -version-info 0:0:0 -no-undefined $(AM_LDFLAGS)
 libdimension_la_LIBADD  =
diff --git a/libdimension/dimension/objects.h b/libdimension/dimension/objects.h
index b5d3bd7..b328025 100644
--- a/libdimension/dimension/objects.h
+++ b/libdimension/dimension/objects.h
@@ -26,9 +26,10 @@
 #include <stdbool.h>
 
 /**
- * A flat triangle, without normal interpolation.
+ * A flat triangle.
  * @param[in] pool  The memory pool to allocate from.
  * @param[in] vertices  The corners of the triangle.
+ * @return A triangle.
  */
 dmnsn_object *dmnsn_new_triangle(dmnsn_pool *pool, dmnsn_vector vertices[3]);
 
@@ -37,10 +38,21 @@ dmnsn_object *dmnsn_new_triangle(dmnsn_pool *pool, dmnsn_vector vertices[3]);
  * @param[in] pool  The memory pool to allocate from.
  * @param[in] vertices  The corners of the triangle.
  * @param[in] normals  The normals at each corner.
+ * @return A smooth triangle.
  */
 dmnsn_object *dmnsn_new_smooth_triangle(dmnsn_pool *pool, dmnsn_vector vertices[3], dmnsn_vector normals[3]);
 
 /**
+ * A triangle fan.
+ * @param[in] pool  The memory pool to allocate from.
+ * @param[in] vertices  The vertices of the fan, starting in the center.
+ * @param[in] nvertices  The number of vertices.
+ * @return A triangle fan.
+ */
+dmnsn_object *
+dmnsn_new_triangle_fan(dmnsn_pool *pool, dmnsn_vector vertices[], size_t nvertices);
+
+/**
  * A plane.
  * @param[in] pool  The memory pool to allocate from.
  * @param[in] normal  The normal vector of the plane.
diff --git a/libdimension/triangle.c b/libdimension/triangle.c
index 30ba6c0..6025caa 100644
--- a/libdimension/triangle.c
+++ b/libdimension/triangle.c
@@ -122,7 +122,7 @@ static inline dmnsn_matrix
 dmnsn_triangle_basis(dmnsn_vector vertices[3])
 {
   /*
-   * The new vector space has corners at <0, 1, 0>, <0, 0, 1>, and 0,
+   * The new vector space has corners at <1, 0, 0>, <0, 1, 0>, and 0,
    * corresponding to the basis (ab, ac, ab X ac).
    */
   dmnsn_vector ab = dmnsn_vector_sub(vertices[1], vertices[0]);
diff --git a/libdimension/triangle_fan.c b/libdimension/triangle_fan.c
new file mode 100644
index 0000000..48a64ff
--- /dev/null
+++ b/libdimension/triangle_fan.c
@@ -0,0 +1,186 @@
+/*************************************************************************
+ * Copyright (C) 2014 Tavian Barnes <tavianator@tavianator.com>     *
+ *                                                                       *
+ * This file is part of The Dimension Library.                           *
+ *                                                                       *
+ * The Dimension Library is free software; you can redistribute it and/  *
+ * or modify it under the terms of the GNU Lesser General Public License *
+ * as published by the Free Software Foundation; either version 3 of the *
+ * License, or (at your option) any later version.                       *
+ *                                                                       *
+ * The Dimension Library is distributed in the hope that it will be      *
+ * useful, but WITHOUT ANY WARRANTY; without even the implied warranty   *
+ * of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU  *
+ * Lesser General Public License for more details.                       *
+ *                                                                       *
+ * You should have received a copy of the GNU Lesser General Public      *
+ * License along with this program.  If not, see                         *
+ * <http://www.gnu.org/licenses/>.                                       *
+ *************************************************************************/
+
+/**
+ * @file
+ * Triangle fans.  See
+ * http://tavianator.com/2014/05/a-beautiful-raymesh-intersection-algorithm/
+ * for a description of the intersection algorithm.
+ */
+
+#include "dimension.h"
+
+/** Triangle fan type. */
+typedef struct {
+  dmnsn_object object;
+  size_t ncoeffs;
+  double coeffs[][6];
+} dmnsn_triangle_fan;
+
+/** Change basis from one triangle to the next. */
+static inline dmnsn_vector
+dmnsn_change_basis(const double coeffs[6], dmnsn_vector v)
+{
+  return dmnsn_new_vector(
+    coeffs[0]*v.x + coeffs[1]*v.z + v.y,
+    coeffs[2]*v.x + coeffs[3]*v.z,
+    coeffs[4]*v.x + coeffs[5]*v.z
+  );
+}
+
+/** Change basis from one triangle to the next for a normal vector. */
+static inline dmnsn_vector
+dmnsn_change_normal_basis(const double coeffs[6], dmnsn_vector n)
+{
+  return dmnsn_new_vector(
+    coeffs[0]*n.x + coeffs[2]*n.y + coeffs[4]*n.z,
+    n.x,
+    coeffs[1]*n.x + coeffs[3]*n.y + coeffs[5]*n.z
+  );
+}
+
+/** Triangle intersection callback. */
+static bool
+dmnsn_triangle_fan_intersection_fn(const dmnsn_object *object, dmnsn_line l, dmnsn_intersection *intersection)
+{
+  const dmnsn_triangle_fan *fan = (const dmnsn_triangle_fan *)object;
+
+  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;
+
+  double best_t = INFINITY;
+  if (t >= 0.0 && u >= 0.0 && v >= 0.0 && u + v <= 1.0) {
+    best_t = t;
+  }
+
+  dmnsn_vector normal = dmnsn_z;
+  dmnsn_vector best_normal = normal;
+
+  for (size_t i = 0; i < fan->ncoeffs; ++i) {
+    const double *coeffs = fan->coeffs[i];
+    l = dmnsn_new_line(dmnsn_change_basis(coeffs, l.x0), dmnsn_change_basis(coeffs, l.n));
+    normal = dmnsn_change_normal_basis(coeffs, normal);
+
+    t = -l.x0.z/l.n.z;
+    u = l.x0.x + t*l.n.x;
+    v = l.x0.y + t*l.n.y;
+
+    if (t >= 0.0 && t < best_t && u >= 0.0 && v >= 0.0 && u + v <= 1.0) {
+      best_t = t;
+      best_normal = normal;
+    }
+  }
+
+  if (!isinf(best_t)) {
+    intersection->t = t;
+    intersection->normal = best_normal;
+    return true;
+  }
+
+  return false;
+}
+
+/** Triangle fan inside callback. */
+static bool
+dmnsn_triangle_fan_inside_fn(const dmnsn_object *object, dmnsn_vector point)
+{
+  return false;
+}
+
+/** Triangle fan bounding callback. */
+static dmnsn_bounding_box
+dmnsn_triangle_fan_bounding_fn(const dmnsn_object *object, dmnsn_matrix trans)
+{
+  const dmnsn_triangle_fan *fan = (const dmnsn_triangle_fan *)object;
+
+  dmnsn_vector a = dmnsn_transform_point(trans, dmnsn_zero);
+  dmnsn_vector b = dmnsn_transform_point(trans, dmnsn_x);
+  dmnsn_vector c = dmnsn_transform_point(trans, dmnsn_y);
+
+  dmnsn_bounding_box box = dmnsn_new_bounding_box(a, a);
+  box = dmnsn_bounding_box_swallow(box, b);
+  box = dmnsn_bounding_box_swallow(box, c);
+
+  dmnsn_matrix P = trans;
+
+  for (size_t i = 0; i < fan->ncoeffs; ++i) {
+    const double *coeffs = fan->coeffs[i];
+    dmnsn_matrix incremental = dmnsn_new_matrix(coeffs[0], 1.0, coeffs[1], 0.0,
+                                                coeffs[2], 0.0, coeffs[3], 0.0,
+                                                coeffs[4], 0.0, coeffs[5], 0.0);
+    P = dmnsn_matrix_mul(P, dmnsn_matrix_inverse(incremental));
+    dmnsn_vector d = dmnsn_transform_point(P, dmnsn_y);
+    box = dmnsn_bounding_box_swallow(box, d);
+  }
+
+  return box;
+}
+
+/** Triangle fan vtable. */
+static dmnsn_object_vtable dmnsn_triangle_fan_vtable = {
+  .intersection_fn = dmnsn_triangle_fan_intersection_fn,
+  .inside_fn = dmnsn_triangle_fan_inside_fn,
+  .bounding_fn = dmnsn_triangle_fan_bounding_fn,
+};
+
+dmnsn_object *
+dmnsn_new_triangle_fan(dmnsn_pool *pool, dmnsn_vector vertices[], size_t nvertices)
+{
+  dmnsn_assert(nvertices >= 3, "Not enough vertices for one triangle");
+
+  size_t ncoeffs = nvertices - 3;
+  dmnsn_triangle_fan *fan = dmnsn_palloc(pool, sizeof(dmnsn_triangle_fan) + ncoeffs*sizeof(double[6]));
+  fan->ncoeffs = ncoeffs;
+
+  dmnsn_object *object = &fan->object;
+  dmnsn_init_object(object);
+  object->vtable = &dmnsn_triangle_fan_vtable;
+  object->bounding_box.min = dmnsn_zero;
+  object->bounding_box.max = dmnsn_new_vector(1.0, 1.0, 0.0);
+
+  /* Compute the initial matrix and the coefficients */
+  dmnsn_vector a = vertices[0];
+  dmnsn_vector ab = dmnsn_vector_sub(vertices[1], a);
+  dmnsn_vector ac = dmnsn_vector_sub(vertices[2], a);
+  dmnsn_vector normal = dmnsn_vector_cross(ab, ac);
+  dmnsn_matrix P = dmnsn_new_matrix4(ab, ac, normal, a);
+  object->intrinsic_trans = P;
+
+  for (size_t i = 0; i < ncoeffs; ++i) {
+    ab = ac;
+    ac = dmnsn_vector_sub(vertices[i + 3], a);
+    normal = dmnsn_vector_cross(ab, ac);
+
+    dmnsn_matrix newP = dmnsn_new_matrix4(ab, ac, normal, a);
+    dmnsn_matrix incremental = dmnsn_matrix_mul(dmnsn_matrix_inverse(newP), P);
+    double *coeffs = fan->coeffs[i];
+    coeffs[0] = incremental.n[0][0];
+    coeffs[1] = incremental.n[0][2];
+    coeffs[2] = incremental.n[1][0];
+    coeffs[3] = incremental.n[1][2];
+    coeffs[4] = incremental.n[2][0];
+    coeffs[5] = incremental.n[2][2];
+
+    P = newP;
+  }
+
+  return object;
+}