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 // This file is part of Eigen, a lightweight C++ template library
 // for linear algebra.
 //
 // Copyright (C) 2009 Ilya Baran <ibaran@mit.edu>
 //
 // This Source Code Form is subject to the terms of the Mozilla
 // Public License v. 2.0. If a copy of the MPL was not distributed
 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
 
 #ifndef KDBVH_H_INCLUDED
 #define KDBVH_H_INCLUDED
 
 namespace Eigen { 
 
 namespace internal {
 
 //internal pair class for the BVH--used instead of std::pair because of alignment
 template<typename Scalar, int Dim>
 struct vector_int_pair
 {
 EIGEN_MAKE_ALIGNED_OPERATOR_NEW_IF_VECTORIZABLE_FIXED_SIZE(Scalar, Dim)
   typedef Matrix<Scalar, Dim, 1> VectorType;
 
   vector_int_pair(const VectorType &v, int i) : first(v), second(i) {}
 
   VectorType first;
   int second;
 };
 
 //these templates help the tree initializer get the bounding boxes either from a provided
 //iterator range or using bounding_box in a unified way
 template<typename ObjectList, typename VolumeList, typename BoxIter>
 struct get_boxes_helper {
   void operator()(const ObjectList &objects, BoxIter boxBegin, BoxIter boxEnd, VolumeList &outBoxes)
   {
     outBoxes.insert(outBoxes.end(), boxBegin, boxEnd);
     eigen_assert(outBoxes.size() == objects.size());
     EIGEN_ONLY_USED_FOR_DEBUG(objects);
   }
 };
 
 template<typename ObjectList, typename VolumeList>
 struct get_boxes_helper<ObjectList, VolumeList, int> {
   void operator()(const ObjectList &objects, int, int, VolumeList &outBoxes)
   {
     outBoxes.reserve(objects.size());
     for(int i = 0; i < (int)objects.size(); ++i)
       outBoxes.push_back(bounding_box(objects[i]));
   }
 };
 
 } // end namespace internal
 
 
 /** \class KdBVH
  *  \brief A simple bounding volume hierarchy based on AlignedBox
  *
  *  \param _Scalar The underlying scalar type of the bounding boxes
  *  \param _Dim The dimension of the space in which the hierarchy lives
  *  \param _Object The object type that lives in the hierarchy.  It must have value semantics.  Either bounding_box(_Object) must
  *                 be defined and return an AlignedBox<_Scalar, _Dim> or bounding boxes must be provided to the tree initializer.
  *
  *  This class provides a simple (as opposed to optimized) implementation of a bounding volume hierarchy analogous to a Kd-tree.
  *  Given a sequence of objects, it computes their bounding boxes, constructs a Kd-tree of their centers
  *  and builds a BVH with the structure of that Kd-tree.  When the elements of the tree are too expensive to be copied around,
  *  it is useful for _Object to be a pointer.
  */
 template<typename _Scalar, int _Dim, typename _Object> class KdBVH
 {
 public:
   enum { Dim = _Dim };
   typedef _Object Object;
   typedef std::vector<Object, aligned_allocator<Object> > ObjectList;
   typedef _Scalar Scalar;
   typedef AlignedBox<Scalar, Dim> Volume;
   typedef std::vector<Volume, aligned_allocator<Volume> > VolumeList;
   typedef int Index;
   typedef const int *VolumeIterator; //the iterators are just pointers into the tree's vectors
   typedef const Object *ObjectIterator;
 
   KdBVH() {}
 
   /** Given an iterator range over \a Object references, constructs the BVH.  Requires that bounding_box(Object) return a Volume. */
   template<typename Iter> KdBVH(Iter begin, Iter end) { init(begin, end, 0, 0); } //int is recognized by init as not being an iterator type
 
   /** Given an iterator range over \a Object references and an iterator range over their bounding boxes, constructs the BVH */
   template<typename OIter, typename BIter> KdBVH(OIter begin, OIter end, BIter boxBegin, BIter boxEnd) { init(begin, end, boxBegin, boxEnd); }
 
   /** Given an iterator range over \a Object references, constructs the BVH, overwriting whatever is in there currently.
     * Requires that bounding_box(Object) return a Volume. */
   template<typename Iter> void init(Iter begin, Iter end) { init(begin, end, 0, 0); }
 
   /** Given an iterator range over \a Object references and an iterator range over their bounding boxes,
     * constructs the BVH, overwriting whatever is in there currently. */
   template<typename OIter, typename BIter> void init(OIter begin, OIter end, BIter boxBegin, BIter boxEnd)
   {
     objects.clear();
     boxes.clear();
     children.clear();
 
     objects.insert(objects.end(), begin, end);
     int n = static_cast<int>(objects.size());
 
     if(n < 2)
       return; //if we have at most one object, we don't need any internal nodes
 
     VolumeList objBoxes;
     VIPairList objCenters;
 
     //compute the bounding boxes depending on BIter type
     internal::get_boxes_helper<ObjectList, VolumeList, BIter>()(objects, boxBegin, boxEnd, objBoxes);
 
     objCenters.reserve(n);
     boxes.reserve(n - 1);
     children.reserve(2 * n - 2);
 
     for(int i = 0; i < n; ++i)
       objCenters.push_back(VIPair(objBoxes[i].center(), i));
 
     build(objCenters, 0, n, objBoxes, 0); //the recursive part of the algorithm
 
     ObjectList tmp(n);
     tmp.swap(objects);
     for(int i = 0; i < n; ++i)
       objects[i] = tmp[objCenters[i].second];
   }
 
   /** \returns the index of the root of the hierarchy */
   inline Index getRootIndex() const { return (int)boxes.size() - 1; }
 
   /** 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
     * and \a outOBegin and \a outOEnd range over the object children of the node */
   EIGEN_STRONG_INLINE void getChildren(Index index, VolumeIterator &outVBegin, VolumeIterator &outVEnd,
                                        ObjectIterator &outOBegin, ObjectIterator &outOEnd) const
   { //inlining this function should open lots of optimization opportunities to the compiler
     if(index < 0) {
       outVBegin = outVEnd;
       if(!objects.empty())
         outOBegin = &(objects[0]);
       outOEnd = outOBegin + objects.size(); //output all objects--necessary when the tree has only one object
       return;
     }
 
     int numBoxes = static_cast<int>(boxes.size());
 
     int idx = index * 2;
     if(children[idx + 1] < numBoxes) { //second index is always bigger
       outVBegin = &(children[idx]);
       outVEnd = outVBegin + 2;
       outOBegin = outOEnd;
     }
     else if(children[idx] >= numBoxes) { //if both children are objects
       outVBegin = outVEnd;
       outOBegin = &(objects[children[idx] - numBoxes]);
       outOEnd = outOBegin + 2;
     } else { //if the first child is a volume and the second is an object
       outVBegin = &(children[idx]);
       outVEnd = outVBegin + 1;
       outOBegin = &(objects[children[idx + 1] - numBoxes]);
       outOEnd = outOBegin + 1;
     }
   }
 
   /** \returns the bounding box of the node at \a index */
   inline const Volume &getVolume(Index index) const
   {
     return boxes[index];
   }
 
 private:
   typedef internal::vector_int_pair<Scalar, Dim> VIPair;
   typedef std::vector<VIPair, aligned_allocator<VIPair> > VIPairList;
   typedef Matrix<Scalar, Dim, 1> VectorType;
   struct VectorComparator //compares vectors, or more specifically, VIPairs along a particular dimension
   {
     VectorComparator(int inDim) : dim(inDim) {}
     inline bool operator()(const VIPair &v1, const VIPair &v2) const { return v1.first[dim] < v2.first[dim]; }
     int dim;
   };
 
   //Build the part of the tree between objects[from] and objects[to] (not including objects[to]).
   //This routine partitions the objCenters in [from, to) along the dimension dim, recursively constructs
   //the two halves, and adds their parent node.  TODO: a cache-friendlier layout
   void build(VIPairList &objCenters, int from, int to, const VolumeList &objBoxes, int dim)
   {
     eigen_assert(to - from > 1);
     if(to - from == 2) {
       boxes.push_back(objBoxes[objCenters[from].second].merged(objBoxes[objCenters[from + 1].second]));
       children.push_back(from + (int)objects.size() - 1); //there are objects.size() - 1 tree nodes
       children.push_back(from + (int)objects.size());
     }
     else if(to - from == 3) {
       int mid = from + 2;
       std::nth_element(objCenters.begin() + from, objCenters.begin() + mid,
                         objCenters.begin() + to, VectorComparator(dim)); //partition
       build(objCenters, from, mid, objBoxes, (dim + 1) % Dim);
       int idx1 = (int)boxes.size() - 1;
       boxes.push_back(boxes[idx1].merged(objBoxes[objCenters[mid].second]));
       children.push_back(idx1);
       children.push_back(mid + (int)objects.size() - 1);
     }
     else {
       int mid = from + (to - from) / 2;
       nth_element(objCenters.begin() + from, objCenters.begin() + mid,
                   objCenters.begin() + to, VectorComparator(dim)); //partition
       build(objCenters, from, mid, objBoxes, (dim + 1) % Dim);
       int idx1 = (int)boxes.size() - 1;
       build(objCenters, mid, to, objBoxes, (dim + 1) % Dim);
       int idx2 = (int)boxes.size() - 1;
       boxes.push_back(boxes[idx1].merged(boxes[idx2]));
       children.push_back(idx1);
       children.push_back(idx2);
     }
   }
 
   std::vector<int> children; //children of x are children[2x] and children[2x+1], indices bigger than boxes.size() index into objects.
   VolumeList boxes;
   ObjectList objects;
 };
 
 } // end namespace Eigen
 
 #endif //KDBVH_H_INCLUDED

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