1// This file is part of Eigen, a lightweight C++ template library
2// for linear algebra.
3//
4// Copyright (C) 2009 Ilya Baran <ibaran@mit.edu>
5//
6// This Source Code Form is subject to the terms of the Mozilla
7// Public License v. 2.0. If a copy of the MPL was not distributed
8// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
9
10#ifndef KDBVH_H_INCLUDED
11#define KDBVH_H_INCLUDED
12
13namespace Eigen {
14
15namespace internal {
16
17//internal pair class for the BVH--used instead of std::pair because of alignment
18template<typename Scalar, int Dim>
19struct vector_int_pair
20{
21EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(Scalar, Dim)
22  typedef Matrix<Scalar, Dim, 1> VectorType;
23
24  vector_int_pair(const VectorType &v, int i) : first(v), second(i) {}
25
26  VectorType first;
27  int second;
28};
29
30//these templates help the tree initializer get the bounding boxes either from a provided
31//iterator range or using bounding_box in a unified way
32template<typename ObjectList, typename VolumeList, typename BoxIter>
33struct get_boxes_helper {
34  void operator()(const ObjectList &objects, BoxIter boxBegin, BoxIter boxEnd, VolumeList &outBoxes)
35  {
36    outBoxes.insert(outBoxes.end(), boxBegin, boxEnd);
37    eigen_assert(outBoxes.size() == objects.size());
38  }
39};
40
41template<typename ObjectList, typename VolumeList>
42struct get_boxes_helper<ObjectList, VolumeList, int> {
43  void operator()(const ObjectList &objects, int, int, VolumeList &outBoxes)
44  {
45    outBoxes.reserve(objects.size());
46    for(int i = 0; i < (int)objects.size(); ++i)
47      outBoxes.push_back(bounding_box(objects[i]));
48  }
49};
50
51} // end namespace internal
52
53
54/** \class KdBVH
55 *  \brief A simple bounding volume hierarchy based on AlignedBox
56 *
57 *  \param _Scalar The underlying scalar type of the bounding boxes
58 *  \param _Dim The dimension of the space in which the hierarchy lives
59 *  \param _Object The object type that lives in the hierarchy.  It must have value semantics.  Either bounding_box(_Object) must
60 *                 be defined and return an AlignedBox<_Scalar, _Dim> or bounding boxes must be provided to the tree initializer.
61 *
62 *  This class provides a simple (as opposed to optimized) implementation of a bounding volume hierarchy analogous to a Kd-tree.
63 *  Given a sequence of objects, it computes their bounding boxes, constructs a Kd-tree of their centers
64 *  and builds a BVH with the structure of that Kd-tree.  When the elements of the tree are too expensive to be copied around,
65 *  it is useful for _Object to be a pointer.
66 */
67template<typename _Scalar, int _Dim, typename _Object> class KdBVH
68{
69public:
70  enum { Dim = _Dim };
71  typedef _Object Object;
72  typedef std::vector<Object, aligned_allocator<Object> > ObjectList;
73  typedef _Scalar Scalar;
74  typedef AlignedBox<Scalar, Dim> Volume;
75  typedef std::vector<Volume, aligned_allocator<Volume> > VolumeList;
76  typedef int Index;
77  typedef const int *VolumeIterator; //the iterators are just pointers into the tree's vectors
78  typedef const Object *ObjectIterator;
79
80  KdBVH() {}
81
82  /** Given an iterator range over \a Object references, constructs the BVH.  Requires that bounding_box(Object) return a Volume. */
83  template<typename Iter> KdBVH(Iter begin, Iter end) { init(begin, end, 0, 0); } //int is recognized by init as not being an iterator type
84
85  /** Given an iterator range over \a Object references and an iterator range over their bounding boxes, constructs the BVH */
86  template<typename OIter, typename BIter> KdBVH(OIter begin, OIter end, BIter boxBegin, BIter boxEnd) { init(begin, end, boxBegin, boxEnd); }
87
88  /** Given an iterator range over \a Object references, constructs the BVH, overwriting whatever is in there currently.
89    * Requires that bounding_box(Object) return a Volume. */
90  template<typename Iter> void init(Iter begin, Iter end) { init(begin, end, 0, 0); }
91
92  /** Given an iterator range over \a Object references and an iterator range over their bounding boxes,
93    * constructs the BVH, overwriting whatever is in there currently. */
94  template<typename OIter, typename BIter> void init(OIter begin, OIter end, BIter boxBegin, BIter boxEnd)
95  {
96    objects.clear();
97    boxes.clear();
98    children.clear();
99
100    objects.insert(objects.end(), begin, end);
101    int n = static_cast<int>(objects.size());
102
103    if(n < 2)
104      return; //if we have at most one object, we don't need any internal nodes
105
106    VolumeList objBoxes;
107    VIPairList objCenters;
108
109    //compute the bounding boxes depending on BIter type
110    internal::get_boxes_helper<ObjectList, VolumeList, BIter>()(objects, boxBegin, boxEnd, objBoxes);
111
112    objCenters.reserve(n);
113    boxes.reserve(n - 1);
114    children.reserve(2 * n - 2);
115
116    for(int i = 0; i < n; ++i)
117      objCenters.push_back(VIPair(objBoxes[i].center(), i));
118
119    build(objCenters, 0, n, objBoxes, 0); //the recursive part of the algorithm
120
121    ObjectList tmp(n);
122    tmp.swap(objects);
123    for(int i = 0; i < n; ++i)
124      objects[i] = tmp[objCenters[i].second];
125  }
126
127  /** \returns the index of the root of the hierarchy */
128  inline Index getRootIndex() const { return (int)boxes.size() - 1; }
129
130  /** Given an \a index of a node, on exit, \a outVBegin and \a outVEnd range over the indices of the volume children of the node
131    * and \a outOBegin and \a outOEnd range over the object children of the node */
132  EIGEN_STRONG_INLINE void getChildren(Index index, VolumeIterator &outVBegin, VolumeIterator &outVEnd,
133                                       ObjectIterator &outOBegin, ObjectIterator &outOEnd) const
134  { //inlining this function should open lots of optimization opportunities to the compiler
135    if(index < 0) {
136      outVBegin = outVEnd;
137      if(!objects.empty())
138        outOBegin = &(objects[0]);
139      outOEnd = outOBegin + objects.size(); //output all objects--necessary when the tree has only one object
140      return;
141    }
142
143    int numBoxes = static_cast<int>(boxes.size());
144
145    int idx = index * 2;
146    if(children[idx + 1] < numBoxes) { //second index is always bigger
147      outVBegin = &(children[idx]);
148      outVEnd = outVBegin + 2;
149      outOBegin = outOEnd;
150    }
151    else if(children[idx] >= numBoxes) { //if both children are objects
152      outVBegin = outVEnd;
153      outOBegin = &(objects[children[idx] - numBoxes]);
154      outOEnd = outOBegin + 2;
155    } else { //if the first child is a volume and the second is an object
156      outVBegin = &(children[idx]);
157      outVEnd = outVBegin + 1;
158      outOBegin = &(objects[children[idx + 1] - numBoxes]);
159      outOEnd = outOBegin + 1;
160    }
161  }
162
163  /** \returns the bounding box of the node at \a index */
164  inline const Volume &getVolume(Index index) const
165  {
166    return boxes[index];
167  }
168
169private:
170  typedef internal::vector_int_pair<Scalar, Dim> VIPair;
171  typedef std::vector<VIPair, aligned_allocator<VIPair> > VIPairList;
172  typedef Matrix<Scalar, Dim, 1> VectorType;
173  struct VectorComparator //compares vectors, or, more specificall, VIPairs along a particular dimension
174  {
175    VectorComparator(int inDim) : dim(inDim) {}
176    inline bool operator()(const VIPair &v1, const VIPair &v2) const { return v1.first[dim] < v2.first[dim]; }
177    int dim;
178  };
179
180  //Build the part of the tree between objects[from] and objects[to] (not including objects[to]).
181  //This routine partitions the objCenters in [from, to) along the dimension dim, recursively constructs
182  //the two halves, and adds their parent node.  TODO: a cache-friendlier layout
183  void build(VIPairList &objCenters, int from, int to, const VolumeList &objBoxes, int dim)
184  {
185    eigen_assert(to - from > 1);
186    if(to - from == 2) {
187      boxes.push_back(objBoxes[objCenters[from].second].merged(objBoxes[objCenters[from + 1].second]));
188      children.push_back(from + (int)objects.size() - 1); //there are objects.size() - 1 tree nodes
189      children.push_back(from + (int)objects.size());
190    }
191    else if(to - from == 3) {
192      int mid = from + 2;
193      std::nth_element(objCenters.begin() + from, objCenters.begin() + mid,
194                        objCenters.begin() + to, VectorComparator(dim)); //partition
195      build(objCenters, from, mid, objBoxes, (dim + 1) % Dim);
196      int idx1 = (int)boxes.size() - 1;
197      boxes.push_back(boxes[idx1].merged(objBoxes[objCenters[mid].second]));
198      children.push_back(idx1);
199      children.push_back(mid + (int)objects.size() - 1);
200    }
201    else {
202      int mid = from + (to - from) / 2;
203      nth_element(objCenters.begin() + from, objCenters.begin() + mid,
204                  objCenters.begin() + to, VectorComparator(dim)); //partition
205      build(objCenters, from, mid, objBoxes, (dim + 1) % Dim);
206      int idx1 = (int)boxes.size() - 1;
207      build(objCenters, mid, to, objBoxes, (dim + 1) % Dim);
208      int idx2 = (int)boxes.size() - 1;
209      boxes.push_back(boxes[idx1].merged(boxes[idx2]));
210      children.push_back(idx1);
211      children.push_back(idx2);
212    }
213  }
214
215  std::vector<int> children; //children of x are children[2x] and children[2x+1], indices bigger than boxes.size() index into objects.
216  VolumeList boxes;
217  ObjectList objects;
218};
219
220} // end namespace Eigen
221
222#endif //KDBVH_H_INCLUDED
223