// 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()); } }; 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 specificall, 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