Rename kD splay trees to Bounding Volume Splay Trees.

1 files changed, 462 insertions, 0 deletions

diff --git a/libdimension/bvst.c b/libdimension/bvst.c
new file mode 100644
index 0000000..a73b4b2
--- /dev/null
+++ b/libdimension/bvst.c
@@ -0,0 +1,462 @@
+/*************************************************************************
+ * Copyright (C) 2009 Tavian Barnes <tavianator@gmail.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/>.                                       *
+ *************************************************************************/
+
+#include "dimension_impl.h"
+#include <stdlib.h>
+
+static dmnsn_bvst_node *dmnsn_new_bvst_node();
+static void dmnsn_delete_bvst_node(dmnsn_bvst_node *node);
+
+/* Return an empty tree */
+dmnsn_bvst *
+dmnsn_new_bvst()
+{
+  dmnsn_bvst *tree = malloc(sizeof(dmnsn_bvst));
+  if (tree) {
+    tree->root = NULL;
+  } else {
+    dmnsn_error(DMNSN_SEVERITY_HIGH, "kD splay tree allocation failed.");
+  }
+  return tree;
+}
+
+/* Recursively copy the nodes of a kD splay tree */
+static dmnsn_bvst_node *
+dmnsn_bvst_copy_recursive(dmnsn_bvst_node *root)
+{
+  dmnsn_bvst_node *node = dmnsn_new_bvst_node();
+  *node = *root;
+  if (node->contains) {
+    node->contains = dmnsn_bvst_copy_recursive(node->contains);
+    node->contains->parent = node;
+  }
+  if (node->container) {
+    node->container = dmnsn_bvst_copy_recursive(node->container);
+    node->container->parent = node;
+  }
+  return node;
+}
+
+/* Copy a kD splay tree */
+dmnsn_bvst *
+dmnsn_bvst_copy(dmnsn_bvst *tree)
+{
+  dmnsn_bvst *copy = dmnsn_new_bvst();
+  if (tree->root)
+    copy->root = dmnsn_bvst_copy_recursive(tree->root);
+  else
+    copy->root = NULL;
+  return copy;
+}
+
+/* Recursively free a kD splay tree */
+void
+dmnsn_delete_bvst_recursive(dmnsn_bvst_node *node)
+{
+  if (node) {
+    dmnsn_delete_bvst_recursive(node->contains);
+    dmnsn_delete_bvst_recursive(node->container);
+    dmnsn_delete_bvst_node(node);
+  }
+}
+
+/* Free a kD splay tree */
+void
+dmnsn_delete_bvst(dmnsn_bvst *tree)
+{
+  if (tree) {
+    dmnsn_delete_bvst_recursive(tree->root);
+    free(tree);
+  }
+}
+
+/* Return whether node1 contains node2 */
+static int dmnsn_box_contains(dmnsn_vector p,
+                              dmnsn_vector min, dmnsn_vector max);
+/* Expand node to contain the bounding box from min to max */
+static void dmnsn_bvst_node_swallow(dmnsn_bvst_node *node,
+                                    dmnsn_vector min, dmnsn_vector max);
+
+/* Insert an object into the tree */
+void
+dmnsn_bvst_insert(dmnsn_bvst *tree, dmnsn_object *object)
+{
+  dmnsn_bvst_node *node = dmnsn_new_bvst_node(), *parent = tree->root;
+
+  /* Store the inverse of the transformation matrix */
+  object->trans_inv = dmnsn_matrix_inverse(object->trans);
+
+  node->contains = NULL;
+  node->container = NULL;
+  node->parent = NULL;
+  node->object = object;
+
+  /* Calculate the new bounding box by finding the minimum coordinate of the
+     transformed corners of the object's original bounding box */
+
+  node->min = dmnsn_matrix_vector_mul(object->trans, object->min);
+  node->max = node->min;
+
+  dmnsn_vector corner;
+  corner = dmnsn_new_vector(object->min.x, object->min.y, object->max.z);
+  corner = dmnsn_matrix_vector_mul(object->trans, corner);
+  dmnsn_bvst_node_swallow(node, corner, corner);
+
+  corner = dmnsn_new_vector(object->min.x, object->max.y, object->min.z);
+  corner = dmnsn_matrix_vector_mul(object->trans, corner);
+  dmnsn_bvst_node_swallow(node, corner, corner);
+
+  corner = dmnsn_new_vector(object->min.x, object->max.y, object->max.z);
+  corner = dmnsn_matrix_vector_mul(object->trans, corner);
+  dmnsn_bvst_node_swallow(node, corner, corner);
+
+  corner = dmnsn_new_vector(object->max.x, object->min.y, object->min.z);
+  corner = dmnsn_matrix_vector_mul(object->trans, corner);
+  dmnsn_bvst_node_swallow(node, corner, corner);
+
+  corner = dmnsn_new_vector(object->max.x, object->min.y, object->max.z);
+  corner = dmnsn_matrix_vector_mul(object->trans, corner);
+  dmnsn_bvst_node_swallow(node, corner, corner);
+
+  corner = dmnsn_new_vector(object->max.x, object->max.y, object->min.z);
+  corner = dmnsn_matrix_vector_mul(object->trans, corner);
+  dmnsn_bvst_node_swallow(node, corner, corner);
+
+  corner = dmnsn_new_vector(object->max.x, object->max.y, object->max.z);
+  corner = dmnsn_matrix_vector_mul(object->trans, corner);
+  dmnsn_bvst_node_swallow(node, corner, corner);
+
+  /* Now insert the node */
+
+  while (parent) {
+    if (dmnsn_box_contains(node->min, parent->min, parent->max)
+        && dmnsn_box_contains(node->max, parent->min, parent->max)) {
+      /* parent fully contains node */
+      if (parent->contains)
+        parent = parent->contains;
+      else {
+        /* We found our parent; insert node into the tree */
+        parent->contains = node;
+        node->parent = parent;
+        break;
+      }
+    } else {
+      /* Expand node's bounding box to fully contain parent's if it doesn't
+         already */
+      dmnsn_bvst_node_swallow(node, parent->min, parent->max);
+      /* node now fully contains parent */
+      if (parent->container)
+        parent = parent->container;
+      else {
+        /* We found our parent; insert node into the tree */
+        parent->container = node;
+        node->parent = parent;
+        break;
+      }
+    }
+  }
+
+  dmnsn_bvst_splay(tree, node);
+}
+
+/* Return whether p is within the axis-aligned box with corners min and max */
+static int
+dmnsn_box_contains(dmnsn_vector p, dmnsn_vector min, dmnsn_vector max)
+{
+  return (p.x >= min.x && p.y >= min.y && p.z >= min.z)
+    && (p.x <= max.x && p.y <= max.y && p.z <= max.z);
+}
+
+/* Expand node to contain the bounding box from min to max */
+static void
+dmnsn_bvst_node_swallow(dmnsn_bvst_node *node,
+                        dmnsn_vector min, dmnsn_vector max)
+{
+  if (node->min.x > min.x) node->min.x = min.x;
+  if (node->min.y > min.y) node->min.y = min.y;
+  if (node->min.z > min.z) node->min.z = min.z;
+
+  if (node->max.x < max.x) node->max.x = max.x;
+  if (node->max.y < max.y) node->max.y = max.y;
+  if (node->max.z < max.z) node->max.z = max.z;
+}
+
+/* Tree rotations */
+static void dmnsn_bvst_rotate(dmnsn_bvst_node *node);
+
+/* Splay a node: move it to the root via tree rotations */
+void
+dmnsn_bvst_splay(dmnsn_bvst *tree, dmnsn_bvst_node *node)
+{
+  while (node->parent) {
+    if (!node->parent->parent) {
+      /* Zig step - we are a child of the root node */
+      dmnsn_bvst_rotate(node);
+      break;
+    } else if ((node == node->parent->contains
+                && node->parent == node->parent->parent->contains)
+               || (node == node->parent->container
+                   && node->parent == node->parent->parent->container)) {
+      /* Zig-zig step - we are a child on the same side as our parent */
+      dmnsn_bvst_rotate(node->parent);
+      dmnsn_bvst_rotate(node);
+    } else {
+      /* Zig-zag step - we are a child on a different side than our parent is */
+      dmnsn_bvst_rotate(node);
+      dmnsn_bvst_rotate(node);
+    }
+  }
+  tree->root = node;
+}
+
+/* Rotate a tree on the edge connecting node and node->parent */
+static void
+dmnsn_bvst_rotate(dmnsn_bvst_node *node)
+{
+  dmnsn_bvst_node *P, *Q, *B;
+  if (node == node->parent->contains) {
+    /* We are a left child; perform a right rotation:
+     *
+     *     Q            P
+     *    / \          / \
+     *   P   C  --->  A   Q
+     *  / \              / \
+     * A   B            B   C
+     */
+    Q = node->parent;
+    P = node;
+    /* A = node->contains; */
+    B = node->container;
+    /* C = node->parent->container; */
+
+    /* First fix up the parents */
+    if (Q->parent) {
+      if (Q->parent->contains == Q)
+        Q->parent->contains = P;
+      else
+        Q->parent->container = P;
+    }
+    P->parent = Q->parent;
+    Q->parent = P;
+    if (B) B->parent = Q;
+
+    /* Then the children */
+    P->container = Q;
+    Q->contains  = B;
+  } else {
+    /* We are a right child; perform a left rotation:
+     *
+     *    P                Q
+     *   / \              / \
+     *  A   Q    --->    P   C
+     *     / \          / \
+     *    B   C        A   B
+     */
+    P = node->parent;
+    Q = node;
+    /* A = node->parent->contains; */
+    B = node->contains;
+    /* C = node->container; */
+
+    /* First fix up the parents */
+    if (P->parent) {
+      if (P->parent->contains == P)
+        P->parent->contains = Q;
+      else
+        P->parent->container = Q;
+    }
+    Q->parent = P->parent;
+    P->parent = Q;
+    if (B) B->parent = P;
+
+    /* Then the children */
+    Q->contains  = P;
+    P->container = B;
+  }
+}
+
+typedef struct {
+  dmnsn_bvst_node *node;
+  dmnsn_intersection  *intersection;
+} dmnsn_bvst_search_result;
+
+static dmnsn_bvst_search_result
+dmnsn_bvst_search_recursive(dmnsn_bvst_node *node, dmnsn_line ray, double t);
+
+dmnsn_intersection *
+dmnsn_bvst_search(dmnsn_bvst *tree, dmnsn_line ray)
+{
+  dmnsn_bvst_search_result result
+    = dmnsn_bvst_search_recursive(tree->root, ray, -1.0);
+
+  if (result.node)
+    dmnsn_bvst_splay(tree, result.node);
+
+  return result.intersection;
+}
+
+static int dmnsn_ray_box_intersection(dmnsn_line ray, dmnsn_vector min,
+                                      dmnsn_vector max, double t);
+
+static dmnsn_bvst_search_result
+dmnsn_bvst_search_recursive(dmnsn_bvst_node *node, dmnsn_line ray, double t)
+{
+  dmnsn_line ray_trans;
+  dmnsn_bvst_search_result result = { NULL, NULL }, result_temp;
+
+  if (!node)
+    return result;
+
+  /* Go down the right subtree first because the closest object is more likely
+     to lie in the larger bounding boxes */
+  result_temp = dmnsn_bvst_search_recursive(node->container, ray, t);
+  if (result_temp.node && (t < 0.0 || result_temp.intersection->t < t)) {
+    result = result_temp;
+    t = result.intersection->t;
+  } else {
+    dmnsn_delete_intersection(result_temp.intersection);
+  }
+
+  if (dmnsn_box_contains(ray.x0, node->min, node->max)
+      || dmnsn_ray_box_intersection(ray, node->min, node->max, t))
+  {
+    /* Transform the ray according to the object */
+    ray_trans = dmnsn_matrix_line_mul(node->object->trans_inv, ray);
+
+    if (dmnsn_box_contains(ray_trans.x0, node->object->min, node->object->max)
+        || dmnsn_ray_box_intersection(ray_trans, node->object->min,
+                                      node->object->max, t))
+    {
+      result_temp.intersection =
+        (*node->object->intersection_fn)(node->object, ray_trans);
+
+      if (result_temp.intersection
+          && (t < 0.0 || result_temp.intersection->t < t)) {
+        dmnsn_delete_intersection(result.intersection);
+        result.node = node;
+        result.intersection = result_temp.intersection;
+        t = result.intersection->t;
+
+        /* Transform the intersection back to the observer's view */
+        result.intersection->ray = ray;
+        result.intersection->normal = dmnsn_vector_normalize(
+          dmnsn_vector_sub(
+            dmnsn_matrix_vector_mul(
+              node->object->trans,
+              result.intersection->normal
+            ),
+            dmnsn_matrix_vector_mul(
+              node->object->trans,
+              dmnsn_zero
+            )
+          )
+        );
+      } else {
+        dmnsn_delete_intersection(result_temp.intersection);
+      }
+    }
+
+    /* Go down the left subtree */
+    result_temp = dmnsn_bvst_search_recursive(node->contains, ray, t);
+    if (result_temp.node && (t < 0.0 || result_temp.intersection->t < t)) {
+      dmnsn_delete_intersection(result.intersection);
+      result = result_temp;
+      t = result.intersection->t;
+    } else {
+      dmnsn_delete_intersection(result_temp.intersection);
+    }
+  }
+
+  return result;
+}
+
+static int
+dmnsn_ray_box_intersection(dmnsn_line line, dmnsn_vector min, dmnsn_vector max,
+                           double t)
+{
+  double t_temp;
+  dmnsn_vector p;
+
+  if (line.n.x != 0.0) {
+    /* x == min.x */
+    t_temp = (min.x - line.x0.x)/line.n.x;
+    p = dmnsn_line_point(line, t_temp);
+    if (p.y >= min.y && p.y <= max.y && p.z >= min.z && p.z <= max.z
+        && t_temp >= 0.0 && (t < 0.0 || t_temp < t))
+      return 1;
+
+    /* x == max.x */
+    t_temp = (max.x - line.x0.x)/line.n.x;
+    p = dmnsn_line_point(line, t_temp);
+    if (p.y >= min.y && p.y <= max.y && p.z >= min.z && p.z <= max.z
+        && t_temp >= 0.0 && (t < 0.0 || t_temp < t))
+      return 1;
+  }
+
+  if (line.n.y != 0.0) {
+    /* y == -1.0 */
+    t_temp = (min.y - line.x0.y)/line.n.y;
+    p = dmnsn_line_point(line, t_temp);
+    if (p.x >= min.x && p.x <= max.x && p.z >= min.z && p.z <= max.z
+        && t_temp >= 0.0 && (t < 0.0 || t_temp < t))
+      return 1;
+
+    /* y == 1.0 */
+    t_temp = (max.y - line.x0.y)/line.n.y;
+    p = dmnsn_line_point(line, t_temp);
+    if (p.x >= min.x && p.x <= max.x && p.z >= min.z && p.z <= max.z
+        && t_temp >= 0.0 && (t < 0.0 || t_temp < t))
+      return 1;
+  }
+
+  if (line.n.z != 0.0) {
+    /* z == -1.0 */
+    t_temp = (min.z - line.x0.z)/line.n.z;
+    p = dmnsn_line_point(line, t_temp);
+    if (p.x >= min.x && p.x <= max.x && p.y >= min.y && p.y <= max.y
+        && t_temp >= 0.0 && (t < 0.0 || t_temp < t))
+      return 1;
+
+    /* z == 1.0 */
+    t_temp = (max.z - line.x0.z)/line.n.z;
+    p = dmnsn_line_point(line, t_temp);
+    if (p.x >= min.x && p.x <= max.x && p.y >= min.y && p.y <= max.y
+        && t_temp >= 0.0 && (t < 0.0 || t_temp < t))
+      return 1;
+  }
+
+  return 0;
+}
+
+static dmnsn_bvst_node *
+dmnsn_new_bvst_node()
+{
+  dmnsn_bvst_node *node = malloc(sizeof(dmnsn_bvst_node));
+  if (!node) {
+    dmnsn_error(DMNSN_SEVERITY_HIGH, "kD splay tree node allocation failed.");
+  }
+  return node;
+}
+
+static void
+dmnsn_delete_bvst_node(dmnsn_bvst_node *node)
+{
+  free(node);
+}