#ifndef KDTREE_H
#define KDTREE_H
#include "../../point3.h"
#include "../../box3.h"
#include "mlsutils.h"
#include "priorityqueue.h"
#include <vector>
#include <limits>
#include <iostream>
template<typename _DataType>
class ConstDataWrapper
{
public:
typedef _DataType DataType;
inline ConstDataWrapper()
: mpData(0), mStride(0), mSize(0)
{}
inline ConstDataWrapper(const DataType* pData, int size, int stride = sizeof(DataType))
: mpData(reinterpret_cast<const unsigned char*>(pData)), mStride(stride), mSize(size)
{}
inline const DataType& operator[] (int i) const
{
return *reinterpret_cast<const DataType*>(mpData + i*mStride);
}
inline size_t size() const { return mSize; }
protected:
const unsigned char* mpData;
int mStride;
size_t mSize;
};
template<class StdVectorType>
class VectorConstDataWrapper :public ConstDataWrapper<typename StdVectorType::value_type>
{
public:
inline VectorConstDataWrapper(StdVectorType &vec):
ConstDataWrapper<typename StdVectorType::value_type> ( &(vec[0]), vec.size(), sizeof(typename StdVectorType::value_type))
{}
};
template<class MeshType>
class VertexConstDataWrapper :public ConstDataWrapper<typename MeshType::CoordType>
{
public:
inline VertexConstDataWrapper(MeshType &m):
ConstDataWrapper<typename MeshType::CoordType> ( &(m.vert[0].P()), m.vert.size(), sizeof(typename MeshType::VertexType))
{}
};
/**
* This class allows to create a Kd-Tree thought to perform the k-nearest neighbour query
*/
template<typename _Scalar>
class KdTree
{
public:
typedef _Scalar Scalar;
typedef vcg::Point3<Scalar> VectorType;
typedef vcg::Box3<Scalar> AxisAlignedBoxType;
struct Node
{
union {
//standard node
struct {
Scalar splitValue;
unsigned int firstChildId:24;
unsigned int dim:2;
unsigned int leaf:1;
};
//leaf
struct {
unsigned int start;
unsigned short size;
};
};
};
typedef std::vector<Node> NodeList;
// return the protected members which store the nodes and the points list
inline const NodeList& _getNodes(void) { return mNodes; }
inline const std::vector<VectorType>& _getPoints(void) { return mPoints; }
void setMaxNofNeighbors(unsigned int k);
inline int getNofFoundNeighbors(void) { return mNeighborQueue.getNofElements(); }
inline const VectorType& getNeighbor(int i) { return mPoints[ mNeighborQueue.getIndex(i) ]; }
inline unsigned int getNeighborId(int i) { return mIndices[mNeighborQueue.getIndex(i)]; }
inline float getNeighborSquaredDistance(int i) { return mNeighborQueue.getWeight(i); }
public:
KdTree(const ConstDataWrapper<VectorType>& points, unsigned int nofPointsPerCell = 16, unsigned int maxDepth = 64);
~KdTree();
void doQueryK(const VectorType& p);
protected:
// element of the stack
struct QueryNode
{
QueryNode() {}
QueryNode(unsigned int id) : nodeId(id) {}
unsigned int nodeId; // id of the next node
Scalar sq; // squared distance to the next node
};
// used to build the tree: split the subset [start..end[ according to dim and splitValue,
// and returns the index of the first element of the second subset
unsigned int split(int start, int end, unsigned int dim, float splitValue);
void createTree(unsigned int nodeId, unsigned int start, unsigned int end, unsigned int level, unsigned int targetCellsize, unsigned int targetMaxDepth);
protected:
AxisAlignedBoxType mAABB; //BoundingBox
NodeList mNodes; //kd-tree nodes
std::vector<VectorType> mPoints; //points read from the input DataWrapper
std::vector<int> mIndices; //points indices
HeapMaxPriorityQueue<int,Scalar> mNeighborQueue; //used to perform the knn-query
QueryNode mNodeStack[64]; //used in the implementation of the knn-query
};
template<typename Scalar>
KdTree<Scalar>::KdTree(const ConstDataWrapper<VectorType>& points, unsigned int nofPointsPerCell, unsigned int maxDepth)
: mPoints(points.size()), mIndices(points.size())
{
// compute the AABB of the input
mPoints[0] = points[0];
mAABB.Set(mPoints[0]);
for (unsigned int i=1 ; i<mPoints.size() ; ++i)
{
mPoints[i] = points[i];
mIndices[i] = i;
mAABB.Add(mPoints[i]);
}
mNodes.reserve(4*mPoints.size()/nofPointsPerCell);
//first node inserted (no leaf). The others are made by the createTree function (recursively)
mNodes.resize(1);
mNodes.back().leaf = 0;
createTree(0, 0, mPoints.size(), 1, nofPointsPerCell, maxDepth);
}
template<typename Scalar>
KdTree<Scalar>::~KdTree()
{
}
template<typename Scalar>
void KdTree<Scalar>::setMaxNofNeighbors(unsigned int k)
{
mNeighborQueue.setMaxSize(k);
}
/** Performs the kNN query.
*
* This algorithm uses the simple distance to the split plane to prune nodes.
* A more elaborated approach consists to track the closest corner of the cell
* relatively to the current query point. This strategy allows to save about 5%
* of the leaves. However, in practice the slight overhead due to this tracking
* reduces the overall performance.
*
* This algorithm also use a simple stack while a priority queue using the squared
* distances to the cells as a priority values allows to save about 10% of the leaves.
* But, again, priority queue insertions and deletions are quite involved, and therefore
* a simple stack is by far much faster.
*
* The result of the query, the k-nearest neighbors, are internally stored into a stack, where the
* topmost element [0] is NOT the nearest but the farthest!! (they are not sorted but arranged into a heap)
*/
template<typename Scalar>
void KdTree<Scalar>::doQueryK(const VectorType& queryPoint)
{
mNeighborQueue.init();
mNeighborQueue.insert(0xffffffff, std::numeric_limits<Scalar>::max());
mNodeStack[0].nodeId = 0;
mNodeStack[0].sq = 0.f;
unsigned int count = 1;
while (count)
{
//we select the last node (AABB) inserted in the stack
QueryNode& qnode = mNodeStack[count-1];
//while going down the tree qnode.nodeId is the nearest sub-tree, otherwise,
//in backtracking, qnode.nodeId is the other sub-tree that will be visited iff
//the actual nearest node is further than the split distance.
Node& node = mNodes[qnode.nodeId];
//if the distance is less than the top of the max-heap, it could be one of the k-nearest neighbours
if (qnode.sq < mNeighborQueue.getTopWeight())
{
//when we arrive to a lef
if (node.leaf)
{
--count; //pop of the leaf
//end is the index of the last element of the leaf in mPoints
unsigned int end = node.start+node.size;
//adding the element of the leaf to the heap
for (unsigned int i=node.start ; i<end ; ++i)
mNeighborQueue.insert(i, vcg::SquaredNorm(queryPoint - mPoints[i]));
}
//otherwise, if we're not on a leaf
else
{
// the new offset is the distance between the searched point and the actual split coordinate
float new_off = queryPoint[node.dim] - node.splitValue;
//left sub-tree
if (new_off < 0.)
{
mNodeStack[count].nodeId = node.firstChildId;
//in the father's nodeId we save the index of the other sub-tree (for backtracking)
qnode.nodeId = node.firstChildId+1;
}
//right sub-tree (same as above)
else
{
mNodeStack[count].nodeId = node.firstChildId+1;
qnode.nodeId = node.firstChildId;
}
//distance is inherited from the father (while descending the tree it's equal to 0)
mNodeStack[count].sq = qnode.sq;
//distance of the father is the squared distance from the split plane
qnode.sq = new_off*new_off;
++count;
}
}
else
{
// pop
--count;
}
}
}
/**
* Split the subarray between start and end in two part, one with the elements less than splitValue,
* the other with the elements greater or equal than splitValue. The elements are compared
* using the "dim" coordinate [0 = x, 1 = y, 2 = z].
*/
template<typename Scalar>
unsigned int KdTree<Scalar>::split(int start, int end, unsigned int dim, float splitValue)
{
int l(start), r(end-1);
for ( ; l<r ; ++l, --r)
{
while (l < end && mPoints[l][dim] < splitValue)
l++;
while (r >= start && mPoints[r][dim] >= splitValue)
r--;
if (l > r)
break;
std::swap(mPoints[l],mPoints[r]);
std::swap(mIndices[l],mIndices[r]);
}
//returns the index of the first element on the second part
return (mPoints[l][dim] < splitValue ? l+1 : l);
}
/** recursively builds the kdtree
*
* The heuristic is the following:
* - if the number of points in the node is lower than targetCellsize then make a leaf
* - else compute the AABB of the points of the node and split it at the middle of
* the largest AABB dimension.
*
* This strategy might look not optimal because it does not explicitly prune empty space,
* unlike more advanced SAH-like techniques used for RT. On the other hand it leads to a shorter tree,
* faster to traverse and our experience shown that in the special case of kNN queries,
* this strategy is indeed more efficient (and much faster to build). Moreover, for volume data
* (e.g., fluid simulation) pruning the empty space is useless.
*
* Actually, storing at each node the exact AABB (we therefore have a binary BVH) allows
* to prune only about 10% of the leaves, but the overhead of this pruning (ball/ABBB intersection)
* is more expensive than the gain it provides and the memory consumption is x4 higher !
*/
template<typename Scalar>
void KdTree<Scalar>::createTree(unsigned int nodeId, unsigned int start, unsigned int end, unsigned int level, unsigned int targetCellSize, unsigned int targetMaxDepth)
{
//select the first node
Node& node = mNodes[nodeId];
AxisAlignedBoxType aabb;
//putting all the points in the bounding box
aabb.Set(mPoints[start]);
for (unsigned int i=start+1 ; i<end ; ++i)
aabb.Add(mPoints[i]);
//bounding box diagonal
VectorType diag = aabb.max - aabb.min;
//the split "dim" is the dimension of the box with the biggest value
unsigned int dim = vcg::MaxCoeffId(diag);
node.dim = dim;
//we divide the bounding box in 2 partitions, considering the average of the "dim" dimension
node.splitValue = Scalar(0.5*(aabb.max[dim] + aabb.min[dim]));
//midId is the index of the first element in the second partition
unsigned int midId = split(start, end, dim, node.splitValue);
node.firstChildId = mNodes.size();
mNodes.resize(mNodes.size()+2);
{
// left child
unsigned int childId = mNodes[nodeId].firstChildId;
Node& child = mNodes[childId];
if (midId - start <= targetCellSize || level>=targetMaxDepth)
{
child.leaf = 1;
child.start = start;
child.size = midId - start;
}
else
{
child.leaf = 0;
createTree(childId, start, midId, level+1, targetCellSize, targetMaxDepth);
}
}
{
// right child
unsigned int childId = mNodes[nodeId].firstChildId+1;
Node& child = mNodes[childId];
if (end - midId <= targetCellSize || level>=targetMaxDepth)
{
child.leaf = 1;
child.start = midId;
child.size = end - midId;
}
else
{
child.leaf = 0;
createTree(childId, midId, end, level+1, targetCellSize, targetMaxDepth);
}
}
}
#endif