WebSVN – gelsvn – Diff – /branches/restructuring/src/Geometry/KDTree.h


#ifndef __KDTREE_H
#define __KDTREE_H
 
#include <cmath>
#include <iostream>
#include <vector>
#include <algorithm>
#include "CGLA/CGLA.h"
#include "CGLA/ArithVec.h"
 
namespace Geometry
{
	/** \brief A classic K-D tree. 
 
			A K-D tree is a good data structure for storing points in space
			and for nearest neighbour queries. It is basically a generalized 
			binary tree in K dimensions. */
	template<class KeyT, class ValT>
	class KDTree
	{
		typedef typename KeyT::ScalarType ScalarType;
		typedef KeyT KeyType;
		typedef std::vector<KeyT> KeyVectorType;
		typedef std::vector<ValT> ValVectorType;
	
		/// KDNode struct represents node in KD tree
		struct KDNode
		{
			KeyT key;
			ValT val;
			short dsc;
 
			KDNode(): dsc(0) {}
 
			KDNode(const KeyT& _key, const ValT& _val):
				key(_key), val(_val), dsc(-1) {}
 
			ScalarType dist(const KeyType& p) const 
			{
				KeyType dist_vec = p;
				dist_vec  -= key;
				return dot(dist_vec, dist_vec);
			}
		};
 
		typedef std::vector<KDNode> NodeVecType;
		NodeVecType init_nodes;
		NodeVecType nodes;
		bool is_built;
 
		/// The greatest depth of KD tree.
		int max_depth;
 
		/// Total number of elements in tree
		int elements;
 
		/** Comp is a class used for comparing two keys. Comp is constructed
				with the discriminator - i.e. the coordinate of the key that is used
				for comparing keys - Comp objects are passed to the sort algorithm.*/
		class Comp
		{
			const int dsc;
		public:
			Comp(int _dsc): dsc(_dsc) {}
			bool operator()(const KeyType& k0, const KeyType& k1) const
			{
				int dim=KeyType::get_dim();
				for(int i=0;i<dim;i++)
					{
						int j=(dsc+i)%dim;
						if(k0[j]<k1[j])
							return true;
						if(k0[j]>k1[j])
							return false;
					}
				return false;
			}
 
			bool operator()(const KDNode& k0, const KDNode& k1) const
			{
				return (*this)(k0.key,k1.key);
			}
		};
 
		/// The dimension -- K
		const int DIM;
 
		/** Passed a vector of keys, this function will construct an optimal tree.
				It is called recursively - second argument is level in tree. */
		void optimize(int, int, int, int);
 
		/** Finde nearest neighbour. */
		int closest_point_priv(int, const KeyType&, ScalarType&) const;
 
							
		void in_sphere_priv(int n, 
												const KeyType& p, 
												const ScalarType& dist,
												std::vector<KeyT>& keys,
												std::vector<ValT>& vals) const;
	
		/** Finds the optimal discriminator. There are more ways, but this 
				function traverses the vector and finds out what dimension has
				the greatest difference between min and max element. That dimension
				is used for discriminator */
		int opt_disc(int,int) const;
	
	public:
 
		/** Build tree from vector of keys passed as argument. */
		KDTree():
			is_built(false), max_depth(0), DIM(KeyType::get_dim()), elements(0)
		{
		}
 
		/** Insert a key value pair into the tree. Note that the tree needs to 
				be built - by calling the build function - before you can search. */
		void insert(const KeyT& key, const ValT& val)
		{
			assert(!is_built);
			init_nodes.push_back(KDNode(key,val));
		}
 
		/** Build the tree. After this function have been called, it is no longer 
				legal to insert elements, but you can perform searches. */
		void build()
		{
			assert(!is_built);
			nodes.resize(init_nodes.size()+1);
			if(init_nodes.size() > 0)	
				optimize(1,0,init_nodes.size(),0);
			NodeVecType v(0);
			init_nodes.swap(v);
			is_built = true;
		}
 
		/** Find the key value pair closest to the key given as first 
				argument. The second argument is the maximum search distance.
				The final two arguments contain the closest key and its 
				associated value upon return. */
		bool closest_point(const KeyT& p, float& dist, KeyT&k, ValT&v) const
		{
			assert(is_built);
			float max_sq_dist = CGLA::sqr(dist);
			if(int n = closest_point_priv(1, p, max_sq_dist))
				{
					k = nodes[n].key;
					v = nodes[n].val;
					dist = std::sqrt(max_sq_dist);
					return true;
				}
			return false;
		}
 
		/** Find all the elements within a given radius (second argument) of
				the key (first argument). The key value pairs inside the sphere are
				returned in a pair of vectors passed as the two last arguments. */
		int in_sphere(const KeyType& p, 
									float dist,
									std::vector<KeyT>& keys,
									std::vector<ValT>& vals) const
		{
			assert(is_built);
			float max_sq_dist = CGLA::sqr(dist);
			in_sphere_priv(1,p,max_sq_dist,keys,vals);
			return keys.size();
		}
		
 
	};
 
	template<class KeyT, class ValT>
	int KDTree<KeyT,ValT>::opt_disc(int kvec_beg,  
																	int kvec_end) const 
	{
		KeyType vmin = init_nodes[kvec_beg].key;
		KeyType vmax = init_nodes[kvec_beg].key;
		for(int i=kvec_beg;i<kvec_end;i++)
			{
				vmin = CGLA::v_min(vmin,init_nodes[i].key);
				vmax = CGLA::v_max(vmax,init_nodes[i].key);
			}
		int od=0;
		KeyType ave_v = vmax-vmin;
		for(int i=1;i<KeyType::get_dim();i++)
			if(ave_v[i]>ave_v[od]) od = i;
		return od;
	} 
 
	template<class KeyT, class ValT>
	void KDTree<KeyT,ValT>::optimize(int cur,
																	 int kvec_beg,  
																	 int kvec_end,  
																	 int level)
	{
		// Assert that we are not inserting beyond capacity.
		assert(cur < nodes.size());
 
		// If there is just a single element, we simply insert.
		if(kvec_beg+1==kvec_end) 
			{
				max_depth  = std::max(level,max_depth);
				nodes[cur] = init_nodes[kvec_beg];
				nodes[cur].dsc = -1;
				return;
			}
	
		// Find the axis that best separates the data.
		int disc = opt_disc(kvec_beg, kvec_end);
 
		// Compute the median element. See my document on how to do this
		// www.imm.dtu.dk/~jab/publications.html
		int N = kvec_end-kvec_beg;
		int M = 1<< (CGLA::two_to_what_power(N));
		int R = N-(M-1);
		int left_size  = (M-2)/2;
		int right_size = (M-2)/2;
		if(R < M/2)
			{
				left_size += R;
			}
		else
			{
				left_size += M/2;
				right_size += R-M/2;
			}
 
		int median = kvec_beg + left_size;
 
		// Sort elements but use nth_element (which is cheaper) than
		// a sorting algorithm. All elements to the left of the median
		// will be smaller than or equal the median. All elements to the right
		// will be greater than or equal to the median.
		const Comp comp(disc);
		std::nth_element(&init_nodes[kvec_beg], 
										 &init_nodes[median], 
										 &init_nodes[kvec_end], comp);
 
		// Insert the node in the final data structure.
		nodes[cur] = init_nodes[median];
		nodes[cur].dsc = disc;
 
		// Recursively build left and right tree.
		if(left_size>0)	
			optimize(2*cur, kvec_beg, median,level+1);
		
		if(right_size>0) 
			optimize(2*cur+1, median+1, kvec_end,level+1);
	}
 
	template<class KeyT, class ValT>
	int KDTree<KeyT,ValT>::closest_point_priv(int n, const KeyType& p, 
																						ScalarType& dist) const
	{
		int ret_node = 0;
		ScalarType this_dist = nodes[n].dist(p);
 
		if(this_dist<dist)
			{
				dist = this_dist;
				ret_node = n;
			}
		if(nodes[n].dsc != -1)
			{
				int dsc         = nodes[n].dsc;
				float dsc_dist  = CGLA::sqr(nodes[n].key[dsc]-p[dsc]);
				bool left_son   = Comp(dsc)(p,nodes[n].key);
 
				if(left_son||dsc_dist<dist)
					{
						int left_child = 2*n;
						if(left_child < nodes.size())
							if(int nl=closest_point_priv(left_child, p, dist))
								ret_node = nl;
					}
				if(!left_son||dsc_dist<dist)
					{
						int right_child = 2*n+1;
						if(right_child < nodes.size())
							if(int nr=closest_point_priv(right_child, p, dist))
								ret_node = nr;
					}
			}
		return ret_node;
	}
 
	template<class KeyT, class ValT>
	void KDTree<KeyT,ValT>::in_sphere_priv(int n, 
																				 const KeyType& p, 
																				 const ScalarType& dist,
																				 std::vector<KeyT>& keys,
																				 std::vector<ValT>& vals) const
	{
		ScalarType this_dist = nodes[n].dist(p);
		assert(n<nodes.size());
		if(this_dist<dist)
			{
				keys.push_back(nodes[n].key);
				vals.push_back(nodes[n].val);
			}
		if(nodes[n].dsc != -1)
			{
				const int dsc         = nodes[n].dsc;
				const float dsc_dist  = CGLA::sqr(nodes[n].key[dsc]-p[dsc]);
 
				bool left_son = Comp(dsc)(p,nodes[n].key);
 
				if(left_son||dsc_dist<dist)
					{
						int left_child = 2*n;
						if(left_child < nodes.size())
							in_sphere_priv(left_child, p, dist, keys, vals);
					}
				if(!left_son||dsc_dist<dist)
					{
						int right_child = 2*n+1;
						if(right_child < nodes.size())
							in_sphere_priv(right_child, p, dist, keys, vals);
					}
			}
	}
}
namespace GEO = Geometry;
 
#endif
 

Rev 125	Rev 145
1	`#ifndef __KDTREE_H`	1	`#ifndef __KDTREE_H`
2	`#define __KDTREE_H`	2	`#define __KDTREE_H`
3		3
4	`#include <cmath>`	4	`#include <cmath>`
5	`#include <iostream>`	5	`#include <iostream>`
6	`#include <vector>`	6	`#include <vector>`
7	`#include <algorithm>`	7	`#include <algorithm>`
8	`#include "CGLA/CGLA.h"`	8	`#include "CGLA/CGLA.h"`
9	`#include "CGLA/ArithVec.h"`	9	`#include "CGLA/ArithVec.h"`
10		10
11	`namespace Geometry`	11	`namespace Geometry`
12	`{`	12	`{`
13	`/** \brief A classic K-D tree.`	13	`/** \brief A classic K-D tree.`
14		14
15	`A K-D tree is a good data structure for storing points in space`	15	`A K-D tree is a good data structure for storing points in space`
16	`and for nearest neighbour queries. It is basically a generalized`	16	`and for nearest neighbour queries. It is basically a generalized`
17	`binary tree in K dimensions. */`	17	`binary tree in K dimensions. */`
18	`template<class KeyT, class ValT>`	18	`template<class KeyT, class ValT>`
19	`class KDTree`	19	`class KDTree`
20	`{`	20	`{`
21	`typedef typename KeyT::ScalarType ScalarType;`	21	`typedef typename KeyT::ScalarType ScalarType;`
22	`typedef KeyT KeyType;`	22	`typedef KeyT KeyType;`
23	`typedef std::vector<KeyT> KeyVectorType;`	23	`typedef std::vector<KeyT> KeyVectorType;`
24	`typedef std::vector<ValT> ValVectorType;`	24	`typedef std::vector<ValT> ValVectorType;`
25		25
26	`/// KDNode struct represents node in KD tree`	26	`/// KDNode struct represents node in KD tree`
27	`struct KDNode`	27	`struct KDNode`
28	`{`	28	`{`
29	`KeyT key;`	29	`KeyT key;`
30	`ValT val;`	30	`ValT val;`
31	`short dsc;`	31	`short dsc;`
32		32
33	`KDNode(): dsc(0) {}`	33	`KDNode(): dsc(0) {}`
34		34
35	`KDNode(const KeyT& _key, const ValT& _val):`	35	`KDNode(const KeyT& _key, const ValT& _val):`
36	`key(_key), val(_val), dsc(-1) {}`	36	`key(_key), val(_val), dsc(-1) {}`
37		37
38	`ScalarType dist(const KeyType& p) const`	38	`ScalarType dist(const KeyType& p) const`
39	`{`	39	`{`
40	`KeyType dist_vec = p;`	40	`KeyType dist_vec = p;`
41	`dist_vec -= key;`	41	`dist_vec -= key;`
42	`return dot(dist_vec, dist_vec);`	42	`return dot(dist_vec, dist_vec);`
43	`}`	43	`}`
44	`};`	44	`};`
45		45
46	`typedef std::vector<KDNode> NodeVecType;`	46	`typedef std::vector<KDNode> NodeVecType;`
47	`NodeVecType init_nodes;`	47	`NodeVecType init_nodes;`
48	`NodeVecType nodes;`	48	`NodeVecType nodes;`
49	`bool is_built;`	49	`bool is_built;`
50		50
51	`/// The greatest depth of KD tree.`	51	`/// The greatest depth of KD tree.`
52	`int max_depth;`	52	`int max_depth;`
53		53
54	`/// Total number of elements in tree`	54	`/// Total number of elements in tree`
55	`int elements;`	55	`int elements;`
56		56
57	`/** Comp is a class used for comparing two keys. Comp is constructed`	57	`/** Comp is a class used for comparing two keys. Comp is constructed`
58	`with the discriminator - i.e. the coordinate of the key that is used`	58	`with the discriminator - i.e. the coordinate of the key that is used`
59	`for comparing keys - Comp objects are passed to the sort algorithm.*/`	59	`for comparing keys - Comp objects are passed to the sort algorithm.*/`
60	`class Comp`	60	`class Comp`
61	`{`	61	`{`
62	`const int dsc;`	62	`const int dsc;`
63	`public:`	63	`public:`
64	`Comp(int _dsc): dsc(_dsc) {}`	64	`Comp(int _dsc): dsc(_dsc) {}`
65	`bool operator()(const KeyType& k0, const KeyType& k1) const`	65	`bool operator()(const KeyType& k0, const KeyType& k1) const`
66	`{`	66	`{`
67	`int dim=KeyType::get_dim();`	67	`int dim=KeyType::get_dim();`
68	`for(int i=0;i<dim;i++)`	68	`for(int i=0;i<dim;i++)`
69	`{`	69	`{`
70	`int j=(dsc+i)%dim;`	70	`int j=(dsc+i)%dim;`
71	`if(k0[j]<k1[j])`	71	`if(k0[j]<k1[j])`
72	`return true;`	72	`return true;`
73	`if(k0[j]>k1[j])`	73	`if(k0[j]>k1[j])`
74	`return false;`	74	`return false;`
75	`}`	75	`}`
76	`return false;`	76	`return false;`
77	`}`	77	`}`
78		78
79	`bool operator()(const KDNode& k0, const KDNode& k1) const`	79	`bool operator()(const KDNode& k0, const KDNode& k1) const`
80	`{`	80	`{`
81	`return (*this)(k0.key,k1.key);`	81	`return (*this)(k0.key,k1.key);`
82	`}`	82	`}`
83	`};`	83	`};`
84		84
85	`/// The dimension -- K`	85	`/// The dimension -- K`
86	`const int DIM;`	86	`const int DIM;`
87		87
88	`/** Passed a vector of keys, this function will construct an optimal tree.`	88	`/** Passed a vector of keys, this function will construct an optimal tree.`
89	`It is called recursively - second argument is level in tree. */`	89	`It is called recursively - second argument is level in tree. */`
90	`void optimize(int, int, int, int);`	90	`void optimize(int, int, int, int);`
91		91
92	`/** Finde nearest neighbour. */`	92	`/** Finde nearest neighbour. */`
93	`int closest_point_priv(int, const KeyType&, ScalarType&) const;`	93	`int closest_point_priv(int, const KeyType&, ScalarType&) const;`
94		94
95		95
96	`void in_sphere_priv(int n,`	96	`void in_sphere_priv(int n,`
97	`const KeyType& p,`	97	`const KeyType& p,`
98	`const ScalarType& dist,`	98	`const ScalarType& dist,`
99	`std::vector<KeyT>& keys,`	99	`std::vector<KeyT>& keys,`
100	`std::vector<ValT>& vals) const;`	100	`std::vector<ValT>& vals) const;`
101		101
102	`/** Finds the optimal discriminator. There are more ways, but this`	102	`/** Finds the optimal discriminator. There are more ways, but this`
103	`function traverses the vector and finds out what dimension has`	103	`function traverses the vector and finds out what dimension has`
104	`the greatest difference between min and max element. That dimension`	104	`the greatest difference between min and max element. That dimension`
105	`is used for discriminator */`	105	`is used for discriminator */`
106	`int opt_disc(int,int) const;`	106	`int opt_disc(int,int) const;`
107		107
108	`public:`	108	`public:`
109		109
110	`/** Build tree from vector of keys passed as argument. */`	110	`/** Build tree from vector of keys passed as argument. */`
111	`KDTree():`	111	`KDTree():`
112	`is_built(false), max_depth(0), DIM(KeyType::get_dim()), elements(0)`	112	`is_built(false), max_depth(0), DIM(KeyType::get_dim()), elements(0)`
113	`{`	113	`{`
114	`}`	114	`}`
115		115
116	`/** Insert a key value pair into the tree. Note that the tree needs to`	116	`/** Insert a key value pair into the tree. Note that the tree needs to`
117	`be built - by calling the build function - before you can search. */`	117	`be built - by calling the build function - before you can search. */`
118	`void insert(const KeyT& key, const ValT& val)`	118	`void insert(const KeyT& key, const ValT& val)`
119	`{`	119	`{`
120	`assert(!is_built);`	120	`assert(!is_built);`
121	`init_nodes.push_back(KDNode(key,val));`	121	`init_nodes.push_back(KDNode(key,val));`
122	`}`	122	`}`
123		123
124	`/** Build the tree. After this function have been called, it is no longer`	124	`/** Build the tree. After this function have been called, it is no longer`
125	`legal to insert elements, but you can perform searches. */`	125	`legal to insert elements, but you can perform searches. */`
126	`void build()`	126	`void build()`
127	`{`	127	`{`
128	`assert(!is_built);`	128	`assert(!is_built);`
129	`nodes.resize(init_nodes.size()+1);`	129	`nodes.resize(init_nodes.size()+1);`
130	`if(init_nodes.size() > 0)`	130	`if(init_nodes.size() > 0)`
131	`optimize(1,0,init_nodes.size(),0);`	131	`optimize(1,0,init_nodes.size(),0);`
132	`NodeVecType v(0);`	132	`NodeVecType v(0);`
133	`init_nodes.swap(v);`	133	`init_nodes.swap(v);`
134	`is_built = true;`	134	`is_built = true;`
135	`}`	135	`}`
136		136
137	`/** Find the key value pair closest to the key given as first`	137	`/** Find the key value pair closest to the key given as first`
138	`argument. The second argument is the maximum search distance.`	138	`argument. The second argument is the maximum search distance.`
139	`The final two arguments contain the closest key and its`	139	`The final two arguments contain the closest key and its`
140	`associated value upon return. */`	140	`associated value upon return. */`
141	`bool closest_point(const KeyT& p, float& dist, KeyT&k, ValT&v) const`	141	`bool closest_point(const KeyT& p, float& dist, KeyT&k, ValT&v) const`
142	`{`	142	`{`
143	`assert(is_built);`	143	`assert(is_built);`
144	`float max_sq_dist = CGLA::sqr(dist);`	144	`float max_sq_dist = CGLA::sqr(dist);`
145	`if(int n = closest_point_priv(1, p, max_sq_dist))`	145	`if(int n = closest_point_priv(1, p, max_sq_dist))`
146	`{`	146	`{`
147	`k = nodes[n].key;`	147	`k = nodes[n].key;`
148	`v = nodes[n].val;`	148	`v = nodes[n].val;`
149	`dist = std::sqrt(max_sq_dist);`	149	`dist = std::sqrt(max_sq_dist);`
150	`return true;`	150	`return true;`
151	`}`	151	`}`
152	`return false;`	152	`return false;`
153	`}`	153	`}`
154		154
155	`/** Find all the elements within a given radius (second argument) of`	155	`/** Find all the elements within a given radius (second argument) of`
156	`the key (first argument). The key value pairs inside the sphere are`	156	`the key (first argument). The key value pairs inside the sphere are`
157	`returned in a pair of vectors passed as the two last arguments. */`	157	`returned in a pair of vectors passed as the two last arguments. */`
158	`int in_sphere(const KeyType& p,`	158	`int in_sphere(const KeyType& p,`
159	`float dist,`	159	`float dist,`
160	`std::vector<KeyT>& keys,`	160	`std::vector<KeyT>& keys,`
161	`std::vector<ValT>& vals) const`	161	`std::vector<ValT>& vals) const`
162	`{`	162	`{`
163	`assert(is_built);`	163	`assert(is_built);`
164	`float max_sq_dist = CGLA::sqr(dist);`	164	`float max_sq_dist = CGLA::sqr(dist);`
165	`in_sphere_priv(1,p,max_sq_dist,keys,vals);`	165	`in_sphere_priv(1,p,max_sq_dist,keys,vals);`
166	`return keys.size();`	166	`return keys.size();`
167	`}`	167	`}`
168		168
169		169
170	`};`	170	`};`
171		171
172	`template<class KeyT, class ValT>`	172	`template<class KeyT, class ValT>`
173	`int KDTree<KeyT,ValT>::opt_disc(int kvec_beg,`	173	`int KDTree<KeyT,ValT>::opt_disc(int kvec_beg,`
174	`int kvec_end) const`	174	`int kvec_end) const`
175	`{`	175	`{`
176	`KeyType vmin = init_nodes[kvec_beg].key;`	176	`KeyType vmin = init_nodes[kvec_beg].key;`
177	`KeyType vmax = init_nodes[kvec_beg].key;`	177	`KeyType vmax = init_nodes[kvec_beg].key;`
178	`for(int i=kvec_beg;i<kvec_end;i++)`	178	`for(int i=kvec_beg;i<kvec_end;i++)`
179	`{`	179	`{`
180	`vmin = CGLA::v_min(vmin,init_nodes[i].key);`	180	`vmin = CGLA::v_min(vmin,init_nodes[i].key);`
181	`vmax = CGLA::v_max(vmax,init_nodes[i].key);`	181	`vmax = CGLA::v_max(vmax,init_nodes[i].key);`
182	`}`	182	`}`
183	`int od=0;`	183	`int od=0;`
184	`KeyType ave_v = vmax-vmin;`	184	`KeyType ave_v = vmax-vmin;`
185	`for(int i=1;i<KeyType::get_dim();i++)`	185	`for(int i=1;i<KeyType::get_dim();i++)`
186	`if(ave_v[i]>ave_v[od]) od = i;`	186	`if(ave_v[i]>ave_v[od]) od = i;`
187	`return od;`	187	`return od;`
188	`}`	188	`}`
189		189
190	`template<class KeyT, class ValT>`	190	`template<class KeyT, class ValT>`
191	`void KDTree<KeyT,ValT>::optimize(int cur,`	191	`void KDTree<KeyT,ValT>::optimize(int cur,`
192	`int kvec_beg,`	192	`int kvec_beg,`
193	`int kvec_end,`	193	`int kvec_end,`
194	`int level)`	194	`int level)`
195	`{`	195	`{`
196	`// Assert that we are not inserting beyond capacity.`	196	`// Assert that we are not inserting beyond capacity.`
197	`assert(cur < nodes.size());`	197	`assert(cur < nodes.size());`
198		198
199	`// If there is just a single element, we simply insert.`	199	`// If there is just a single element, we simply insert.`
200	`if(kvec_beg+1==kvec_end)`	200	`if(kvec_beg+1==kvec_end)`
201	`{`	201	`{`
202	`max_depth = std::max(level,max_depth);`	202	`max_depth = std::max(level,max_depth);`
203	`nodes[cur] = init_nodes[kvec_beg];`	203	`nodes[cur] = init_nodes[kvec_beg];`
204	`nodes[cur].dsc = -1;`	204	`nodes[cur].dsc = -1;`
205	`return;`	205	`return;`
206	`}`	206	`}`
207		207
208	`// Find the axis that best separates the data.`	208	`// Find the axis that best separates the data.`
209	`int disc = opt_disc(kvec_beg, kvec_end);`	209	`int disc = opt_disc(kvec_beg, kvec_end);`
210		210
211	`// Compute the median element. See my document on how to do this`	211	`// Compute the median element. See my document on how to do this`
212	`// www.imm.dtu.dk/~jab/publications.html`	212	`// www.imm.dtu.dk/~jab/publications.html`
213	`int N = kvec_end-kvec_beg;`	213	`int N = kvec_end-kvec_beg;`
214	`int M = 1<< (CGLA::two_to_what_power(N));`	214	`int M = 1<< (CGLA::two_to_what_power(N));`
215	`int R = N-(M-1);`	215	`int R = N-(M-1);`
216	`int left_size = (M-2)/2;`	216	`int left_size = (M-2)/2;`
217	`int right_size = (M-2)/2;`	217	`int right_size = (M-2)/2;`
218	`if(R < M/2)`	218	`if(R < M/2)`
219	`{`	219	`{`
220	`left_size += R;`	220	`left_size += R;`
221	`}`	221	`}`
222	`else`	222	`else`
223	`{`	223	`{`
224	`left_size += M/2;`	224	`left_size += M/2;`
225	`right_size += R-M/2;`	225	`right_size += R-M/2;`
226	`}`	226	`}`
227		227
228	`int median = kvec_beg + left_size;`	228	`int median = kvec_beg + left_size;`
229		229
230	`// Sort elements but use nth_element (which is cheaper) than`	230	`// Sort elements but use nth_element (which is cheaper) than`
231	`// a sorting algorithm. All elements to the left of the median`	231	`// a sorting algorithm. All elements to the left of the median`
232	`// will be smaller than or equal the median. All elements to the right`	232	`// will be smaller than or equal the median. All elements to the right`
233	`// will be greater than or equal to the median.`	233	`// will be greater than or equal to the median.`
234	`const Comp comp(disc);`	234	`const Comp comp(disc);`
235	`std::nth_element(&init_nodes[kvec_beg],`	235	`std::nth_element(&init_nodes[kvec_beg],`
236	`&init_nodes[median],`	236	`&init_nodes[median],`
237	`&init_nodes[kvec_end], comp);`	237	`&init_nodes[kvec_end], comp);`
238		238
239	`// Insert the node in the final data structure.`	239	`// Insert the node in the final data structure.`
240	`nodes[cur] = init_nodes[median];`	240	`nodes[cur] = init_nodes[median];`
241	`nodes[cur].dsc = disc;`	241	`nodes[cur].dsc = disc;`
242		242
243	`// Recursively build left and right tree.`	243	`// Recursively build left and right tree.`
244	`if(left_size>0)`	244	`if(left_size>0)`
245	`optimize(2*cur, kvec_beg, median,level+1);`	245	`optimize(2*cur, kvec_beg, median,level+1);`
246		246
247	`if(right_size>0)`	247	`if(right_size>0)`
248	`optimize(2*cur+1, median+1, kvec_end,level+1);`	248	`optimize(2*cur+1, median+1, kvec_end,level+1);`
249	`}`	249	`}`
250		250
251	`template<class KeyT, class ValT>`	251	`template<class KeyT, class ValT>`
252	`int KDTree<KeyT,ValT>::closest_point_priv(int n, const KeyType& p,`	252	`int KDTree<KeyT,ValT>::closest_point_priv(int n, const KeyType& p,`
253	`ScalarType& dist) const`	253	`ScalarType& dist) const`
254	`{`	254	`{`
255	`int ret_node = 0;`	255	`int ret_node = 0;`
256	`ScalarType this_dist = nodes[n].dist(p);`	256	`ScalarType this_dist = nodes[n].dist(p);`
257		257
258	`if(this_dist<dist)`	258	`if(this_dist<dist)`
259	`{`	259	`{`
260	`dist = this_dist;`	260	`dist = this_dist;`
261	`ret_node = n;`	261	`ret_node = n;`
262	`}`	262	`}`
263	`if(nodes[n].dsc != -1)`	263	`if(nodes[n].dsc != -1)`
264	`{`	264	`{`
265	`int dsc = nodes[n].dsc;`	265	`int dsc = nodes[n].dsc;`
266	`float dsc_dist = CGLA::sqr(nodes[n].key[dsc]-p[dsc]);`	266	`float dsc_dist = CGLA::sqr(nodes[n].key[dsc]-p[dsc]);`
267	`bool left_son = Comp(dsc)(p,nodes[n].key);`	267	`bool left_son = Comp(dsc)(p,nodes[n].key);`
268		268
269	`if(left_son\|\|dsc_dist<dist)`	269	`if(left_son\|\|dsc_dist<dist)`
270	`{`	270	`{`
271	`int left_child = 2*n;`	271	`int left_child = 2*n;`
272	`if(left_child < nodes.size())`	272	`if(left_child < nodes.size())`
273	`if(int nl=closest_point_priv(left_child, p, dist))`	273	`if(int nl=closest_point_priv(left_child, p, dist))`
274	`ret_node = nl;`	274	`ret_node = nl;`
275	`}`	275	`}`
276	`if(!left_son\|\|dsc_dist<dist)`	276	`if(!left_son\|\|dsc_dist<dist)`
277	`{`	277	`{`
278	`int right_child = 2*n+1;`	278	`int right_child = 2*n+1;`
279	`if(right_child < nodes.size())`	279	`if(right_child < nodes.size())`
280	`if(int nr=closest_point_priv(right_child, p, dist))`	280	`if(int nr=closest_point_priv(right_child, p, dist))`
281	`ret_node = nr;`	281	`ret_node = nr;`
282	`}`	282	`}`
283	`}`	283	`}`
284	`return ret_node;`	284	`return ret_node;`
285	`}`	285	`}`
286		286
287	`template<class KeyT, class ValT>`	287	`template<class KeyT, class ValT>`
288	`void KDTree<KeyT,ValT>::in_sphere_priv(int n,`	288	`void KDTree<KeyT,ValT>::in_sphere_priv(int n,`
289	`const KeyType& p,`	289	`const KeyType& p,`
290	`const ScalarType& dist,`	290	`const ScalarType& dist,`
291	`std::vector<KeyT>& keys,`	291	`std::vector<KeyT>& keys,`
292	`std::vector<ValT>& vals) const`	292	`std::vector<ValT>& vals) const`
293	`{`	293	`{`
294	`ScalarType this_dist = nodes[n].dist(p);`	294	`ScalarType this_dist = nodes[n].dist(p);`
295	`assert(n<nodes.size());`	295	`assert(n<nodes.size());`
296	`if(this_dist<dist)`	296	`if(this_dist<dist)`
297	`{`	297	`{`
298	`keys.push_back(nodes[n].key);`	298	`keys.push_back(nodes[n].key);`
299	`vals.push_back(nodes[n].val);`	299	`vals.push_back(nodes[n].val);`
300	`}`	300	`}`
301	`if(nodes[n].dsc != -1)`	301	`if(nodes[n].dsc != -1)`
302	`{`	302	`{`
303	`const int dsc = nodes[n].dsc;`	303	`const int dsc = nodes[n].dsc;`
304	`const float dsc_dist = CGLA::sqr(nodes[n].key[dsc]-p[dsc]);`	304	`const float dsc_dist = CGLA::sqr(nodes[n].key[dsc]-p[dsc]);`
305		305
306	`bool left_son = Comp(dsc)(p,nodes[n].key);`	306	`bool left_son = Comp(dsc)(p,nodes[n].key);`
307		307
308	`if(left_son\|\|dsc_dist<dist)`	308	`if(left_son\|\|dsc_dist<dist)`
309	`{`	309	`{`
310	`int left_child = 2*n;`	310	`int left_child = 2*n;`
311	`if(left_child < nodes.size())`	311	`if(left_child < nodes.size())`
312	`in_sphere_priv(left_child, p, dist, keys, vals);`	312	`in_sphere_priv(left_child, p, dist, keys, vals);`
313	`}`	313	`}`
314	`if(!left_son\|\|dsc_dist<dist)`	314	`if(!left_son\|\|dsc_dist<dist)`
315	`{`	315	`{`
316	`int right_child = 2*n+1;`	316	`int right_child = 2*n+1;`
317	`if(right_child < nodes.size())`	317	`if(right_child < nodes.size())`
318	`in_sphere_priv(right_child, p, dist, keys, vals);`	318	`in_sphere_priv(right_child, p, dist, keys, vals);`
319	`}`	319	`}`
320	`}`	320	`}`
321	`}`	321	`}`
322	`}`	322	`}`
323	`namespace GEO = Geometry;`	323	`namespace GEO = Geometry;`
324		324
325	`#endif`	325	`#endif`
326		326

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