kD-tree 的C語言實現 帶有史上最全的註釋和解釋

原文轉自CSDN  http://blog.csdn.net/daringpig/article/details/7652891

 

語言cstructtreefloatinsert

kdtree的原理就是基於二叉樹的形式，將高維空間用超矩形進行劃分.其主要用途是用來求解高維空間中最近鄰的值.

kdtree的原理就是基於二叉樹的形式，將高維空間用超矩形進行劃分.其主要用途是用來求解高維空間中最近鄰的值.

 

 

下面是kdtree.h文件，是kdtree數據結構的頭文件

#ifndef _KDTREE_H_
#define _KDTREE_H_

#ifdef __cplusplus
extern "C" {
#endif

struct kdtree;
struct kdres;


/* create a kd-tree for "k"-dimensional data */
struct kdtree *kd_create(int k);

/* free the struct kdtree */
void kd_free(struct kdtree *tree);

/* remove all the elements from the tree */
void kd_clear(struct kdtree *tree);

/* if called with non-null 2nd argument, the function provided
 * will be called on data pointers (see kd_insert) when nodes
 * are to be removed from the tree.
 */
void kd_data_destructor(struct kdtree *tree, void (*destr)(void*));

/* insert a node, specifying its position, and optional data */
int kd_insert(struct kdtree *tree, const double *pos, void *data);
int kd_insertf(struct kdtree *tree, const float *pos, void *data);
int kd_insert3(struct kdtree *tree, double x, double y, double z, void *data);
int kd_insert3f(struct kdtree *tree, float x, float y, float z, void *data);

/* Find the nearest node from a given point.
 *
 * This function returns a pointer to a result set with at most one element.
 */
struct kdres *kd_nearest(struct kdtree *tree, const double *pos);
struct kdres *kd_nearestf(struct kdtree *tree, const float *pos);
struct kdres *kd_nearest3(struct kdtree *tree, double x, double y, double z);
struct kdres *kd_nearest3f(struct kdtree *tree, float x, float y, float z);

/* Find the N nearest nodes from a given point.
 *
 * This function returns a pointer to a result set, with at most N elements,
 * which can be manipulated with the kd_res_* functions.
 * The returned pointer can be null as an indication of an error. Otherwise
 * a valid result set is always returned which may contain 0 or more elements.
 * The result set must be deallocated with kd_res_free after use.
 */
/*
struct kdres *kd_nearest_n(struct kdtree *tree, const double *pos, int num);
struct kdres *kd_nearest_nf(struct kdtree *tree, const float *pos, int num);
struct kdres *kd_nearest_n3(struct kdtree *tree, double x, double y, double z);
struct kdres *kd_nearest_n3f(struct kdtree *tree, float x, float y, float z);
*/

/* Find any nearest nodes from a given point within a range.
 *
 * This function returns a pointer to a result set, which can be manipulated
 * by the kd_res_* functions.
 * The returned pointer can be null as an indication of an error. Otherwise
 * a valid result set is always returned which may contain 0 or more elements.
 * The result set must be deallocated with kd_res_free after use.
 */
struct kdres *kd_nearest_range(struct kdtree *tree, const double *pos, double range);
struct kdres *kd_nearest_rangef(struct kdtree *tree, const float *pos, float range);
struct kdres *kd_nearest_range3(struct kdtree *tree, double x, double y, double z, double range);
struct kdres *kd_nearest_range3f(struct kdtree *tree, float x, float y, float z, float range);

/* frees a result set returned by kd_nearest_range() */
void kd_res_free(struct kdres *set);

/* returns the size of the result set (in elements) */
int kd_res_size(struct kdres *set);

/* rewinds the result set iterator */
void kd_res_rewind(struct kdres *set);

/* returns non-zero if the set iterator reached the end after the last element */
int kd_res_end(struct kdres *set);

/* advances the result set iterator, returns non-zero on success, zero if
 * there are no more elements in the result set.
 */
int kd_res_next(struct kdres *set);

/* returns the data pointer (can be null) of the current result set item
 * and optionally sets its position to the pointers(s) if not null.
 */
void *kd_res_item(struct kdres *set, double *pos);
void *kd_res_itemf(struct kdres *set, float *pos);
void *kd_res_item3(struct kdres *set, double *x, double *y, double *z);
void *kd_res_item3f(struct kdres *set, float *x, float *y, float *z);

/* equivalent to kd_res_item(set, 0) */
void *kd_res_item_data(struct kdres *set);


#ifdef __cplusplus
}
#endif

#endif  /* _KDTREE_H_ */

#ifndef _KDTREE_H_
#define _KDTREE_H_

#ifdef __cplusplus
extern "C" {
#endif

struct kdtree;
struct kdres;


/* create a kd-tree for "k"-dimensional data */
struct kdtree *kd_create(int k);

/* free the struct kdtree */
void kd_free(struct kdtree *tree);

/* remove all the elements from the tree */
void kd_clear(struct kdtree *tree);

/* if called with non-null 2nd argument, the function provided
 * will be called on data pointers (see kd_insert) when nodes
 * are to be removed from the tree.
 */
void kd_data_destructor(struct kdtree *tree, void (*destr)(void*));

/* insert a node, specifying its position, and optional data */
int kd_insert(struct kdtree *tree, const double *pos, void *data);
int kd_insertf(struct kdtree *tree, const float *pos, void *data);
int kd_insert3(struct kdtree *tree, double x, double y, double z, void *data);
int kd_insert3f(struct kdtree *tree, float x, float y, float z, void *data);

/* Find the nearest node from a given point.
 *
 * This function returns a pointer to a result set with at most one element.
 */
struct kdres *kd_nearest(struct kdtree *tree, const double *pos);
struct kdres *kd_nearestf(struct kdtree *tree, const float *pos);
struct kdres *kd_nearest3(struct kdtree *tree, double x, double y, double z);
struct kdres *kd_nearest3f(struct kdtree *tree, float x, float y, float z);

/* Find the N nearest nodes from a given point.
 *
 * This function returns a pointer to a result set, with at most N elements,
 * which can be manipulated with the kd_res_* functions.
 * The returned pointer can be null as an indication of an error. Otherwise
 * a valid result set is always returned which may contain 0 or more elements.
 * The result set must be deallocated with kd_res_free after use.
 */
/*
struct kdres *kd_nearest_n(struct kdtree *tree, const double *pos, int num);
struct kdres *kd_nearest_nf(struct kdtree *tree, const float *pos, int num);
struct kdres *kd_nearest_n3(struct kdtree *tree, double x, double y, double z);
struct kdres *kd_nearest_n3f(struct kdtree *tree, float x, float y, float z);
*/

/* Find any nearest nodes from a given point within a range.
 *
 * This function returns a pointer to a result set, which can be manipulated
 * by the kd_res_* functions.
 * The returned pointer can be null as an indication of an error. Otherwise
 * a valid result set is always returned which may contain 0 or more elements.
 * The result set must be deallocated with kd_res_free after use.
 */
struct kdres *kd_nearest_range(struct kdtree *tree, const double *pos, double range);
struct kdres *kd_nearest_rangef(struct kdtree *tree, const float *pos, float range);
struct kdres *kd_nearest_range3(struct kdtree *tree, double x, double y, double z, double range);
struct kdres *kd_nearest_range3f(struct kdtree *tree, float x, float y, float z, float range);

/* frees a result set returned by kd_nearest_range() */
void kd_res_free(struct kdres *set);

/* returns the size of the result set (in elements) */
int kd_res_size(struct kdres *set);

/* rewinds the result set iterator */
void kd_res_rewind(struct kdres *set);

/* returns non-zero if the set iterator reached the end after the last element */
int kd_res_end(struct kdres *set);

/* advances the result set iterator, returns non-zero on success, zero if
 * there are no more elements in the result set.
 */
int kd_res_next(struct kdres *set);

/* returns the data pointer (can be null) of the current result set item
 * and optionally sets its position to the pointers(s) if not null.
 */
void *kd_res_item(struct kdres *set, double *pos);
void *kd_res_itemf(struct kdres *set, float *pos);
void *kd_res_item3(struct kdres *set, double *x, double *y, double *z);
void *kd_res_item3f(struct kdres *set, float *x, float *y, float *z);

/* equivalent to kd_res_item(set, 0) */
void *kd_res_item_data(struct kdres *set);


#ifdef __cplusplus
}
#endif

#endif	/* _KDTREE_H_ */

下面是kdtree.c 文件，上面有我自己精心整理的詳細的漢語註釋，這個版本的kdtree可直接拿來用

//kd_tree.h  kd_tree的頭文件

#include "stdafx.h"

//頭文件
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <math.h>
#include "kd_tree.h"

#if defined(WIN32) || defined(__WIN32__)
#include <malloc.h>
#endif

#ifdef USE_LIST_NODE_ALLOCATOR

#ifndef NO_PTHREADS
#include <pthread.h>
#else

#ifndef I_WANT_THREAD_BUGS
#error "You are compiling with the fast list node allocator, with pthreads disabled! This WILL break if used from multiple threads."
#endif  /* I want thread bugs */

#endif  /* pthread support */
#endif  /* use list node allocator */


//超平面的結構體
//包括一個屬性的維數和每維座標的最大和最小值構成的數組
struct kdhyperrect {
    int dim;
    double *min, *max;              /* minimum/maximum coords */
};

//節點的結構體，也就是事例的結構體
struct kdnode {
    double *pos;
    int dir;
    void *data;

    struct kdnode *left, *right;    /* negative/positive side */
};

//返回結果節點， 包括樹的節點,距離值, 是一個單鏈表的形式
struct res_node {
    struct kdnode *item;
    double dist_sq;
    struct res_node *next;
};

//樹有幾個屬性，一是維數，一是樹根節點，一是超平面，一是銷燬data的函數
struct kdtree {
    int dim;
    struct kdnode *root;
    struct kdhyperrect *rect;
    void (*destr)(void*);
};

//kdtree的返回結果，包括kdtree，這是一個雙鏈表的形式
struct kdres {
    struct kdtree *tree;
    struct res_node *rlist, *riter;  //雙鏈表?
    int size;
};

//計算平方的宏定義,相當於函數
#define SQ(x)           ((x) * (x))


static void clear_rec(struct kdnode *node, void (*destr)(void*));
static int insert_rec(struct kdnode **node, const double *pos, void *data, int dir, int dim);
static int rlist_insert(struct res_node *list, struct kdnode *item, double dist_sq);
static void clear_results(struct kdres *set);

static struct kdhyperrect* hyperrect_create(int dim, const double *min, const double *max);
static void hyperrect_free(struct kdhyperrect *rect);
static struct kdhyperrect* hyperrect_duplicate(const struct kdhyperrect *rect);
static void hyperrect_extend(struct kdhyperrect *rect, const double *pos);
static double hyperrect_dist_sq(struct kdhyperrect *rect, const double *pos);

#ifdef USE_LIST_NODE_ALLOCATOR
static struct res_node *alloc_resnode(void);
static void free_resnode(struct res_node*);
#else
#define alloc_resnode()     malloc(sizeof(struct res_node))
#define free_resnode(n)     free(n)
#endif


//創建一個kdtree
struct kdtree *kd_create(int k)
{
    struct kdtree *tree;

    if(!(tree = (kdtree*)malloc(sizeof *tree))) {
        return 0;
    }

    tree->dim = k;
    tree->root = 0;
    tree->destr = 0;
    tree->rect = 0;

    return tree;
}

//釋放掉kdtree
void kd_free(struct kdtree *tree)
{
    if(tree) {
        kd_clear(tree);
        free(tree);
    }
}

//清除掉超平面,是按節點遞歸地進行的
static void clear_rec(struct kdnode *node, void (*destr)(void*))
{
    if(!node) return;   //一個節點對應一個超平面

    //遞歸函數，遞歸地清除掉二叉樹左分支的超平面和二叉樹右分支的超平面
    clear_rec(node->left, destr);
    clear_rec(node->right, destr);

    //如果data清楚函數不爲空,就釋放掉data
    if(destr)
    {
        destr(node->data);
    }
    //釋放節點的座標數組
    free(node->pos);
    //釋放節點
    free(node);
}

//kdtree清除
void kd_clear(struct kdtree *tree)
{
    //清除樹中每個節點的超平面,釋放樹中的各個節點
    clear_rec(tree->root, tree->destr);
    tree->root = 0;

    //如果樹的超平面指針不爲空,對其進行釋放
    if (tree->rect)
    {
        hyperrect_free(tree->rect);
        tree->rect = 0;
    }
}

//數據銷燬，用一個外來的函數來進行data的銷燬
void kd_data_destructor(struct kdtree *tree, void (*destr)(void*))
{
    //用外來的函數來執行kdtree的銷燬函數
    tree->destr = destr;
}


//在一個樹節點位置處插入超矩形
static int insert_rec(struct kdnode **nptr, const double *pos, void *data, int dir, int dim)
{
    int new_dir;
    struct kdnode *node;

    //如果這個節點是不存在的
    if(!*nptr)
    {
        //分配一個結點
        if(!(node = (kdnode *)malloc(sizeof *node)))
        {
            return -1;
        }
        if(!(node->pos = (double*)malloc(dim * sizeof *node->pos))) {
            free(node);
            return -1;
        }
        memcpy(node->pos, pos, dim * sizeof *node->pos);
        node->data = data;
        node->dir = dir;
        node->left = node->right = 0;
        *nptr = node;
        return 0;
    }

    node = *nptr;
    new_dir = (node->dir + 1) % dim;
    if(pos[node->dir] < node->pos[node->dir]) {
        return insert_rec(&(*nptr)->left, pos, data, new_dir, dim);
    }
    return insert_rec(&(*nptr)->right, pos, data, new_dir, dim);
}

//節點插入操作
//參數爲:要進行插入操作的kdtree,要插入的節點座標,要插入的節點的數據
int kd_insert(struct kdtree *tree, const double *pos, void *data)
{
    //插入超矩形
    if (insert_rec(&tree->root, pos, data, 0, tree->dim))
    {
        return -1;
    }
    //如果樹還沒有超矩形,就創建一個超矩形
    //如果已經有了超矩形,就擴展原有的超矩形
    if (tree->rect == 0)
    {
        tree->rect = hyperrect_create(tree->dim, pos, pos);
    }
    else
    {
        hyperrect_extend(tree->rect, pos);
    }

    return 0;
}

//插入float型座標的節點
//參數爲:要進行插入操作的kdtree,要插入的節點座標,要插入的節點的數據
//將float型的座標賦值給double型的緩衝區,經過這個類型轉化後進行插入
//本質上是一種類型轉化
int kd_insertf(struct kdtree *tree, const float *pos, void *data)
{
    static double sbuf[16];
    double *bptr, *buf = 0;
    int res, dim = tree->dim;

    //如果kdtree的維數大於16, 分配dim維double類型的數組
    if(dim > 16)
    {
#ifndef NO_ALLOCA
        if(dim <= 256)
            bptr = buf = (double*)alloca(dim * sizeof *bptr);
        else
#endif
            if(!(bptr = buf = (double*)malloc(dim * sizeof *bptr)))
            {
                return -1;
            }
    }
    //如果kdtree的維數小於16, 直接將指針指向已分配的內存
    else
    {
        bptr = buf = sbuf;
    }

    //將要插入點的位置座標賦值給分配的數組
    while(dim-- > 0)
    {
        *bptr++ = *pos++;
    }

    //調用節點插入函數kd_insert
    res = kd_insert(tree, buf, data);
#ifndef NO_ALLOCA
    if(tree->dim > 256)
#else
    if(tree->dim > 16)
#endif
        //釋放緩存
        free(buf);
    return res;
}

//給出三維座標值的三維kdtree插入
int kd_insert3(struct kdtree *tree, double x, double y, double z, void *data)
{
    double buf[3];
    buf[0] = x;
    buf[1] = y;
    buf[2] = z;
    return kd_insert(tree, buf, data);
}

//給出三維float型座標值的三維kdtree插入
int kd_insert3f(struct kdtree *tree, float x, float y, float z, void *data)
{
    double buf[3];
    buf[0] = x;
    buf[1] = y;
    buf[2] = z;
    return kd_insert(tree, buf, data);
}

//找到最近鄰的點
//參數爲:樹節點指針, 位置座標, 閾值, 返回結果的節點, bool型排序,維度
static int find_nearest(struct kdnode *node, const double *pos, double range, struct res_node *list, int ordered, int dim)
{
    double dist_sq, dx;
    int i, ret, added_res = 0;

    if(!node) return 0;  //注意這個地方,當節點爲空的時候,表明已經查找到最終的葉子結點,返回值爲零

    dist_sq = 0;
    //計算兩個節點間的平方和
    for(i=0; i<dim; i++)
    {
        dist_sq += SQ(node->pos[i] - pos[i]);
    }
    //如果距離在閾值範圍內,就將其插入到返回結果鏈表中
    if(dist_sq <= SQ(range))
    {
        if(rlist_insert(list, node, ordered ? dist_sq : -1.0) == -1)
        {
            return -1;
        }
        added_res = 1;
    }

    //在這個節點的劃分方向上,求兩者之間的差值
    dx = pos[node->dir] - node->pos[node->dir];

    //根據這個差值的符號, 選擇進行遞歸查找的分支方向
    ret = find_nearest(dx <= 0.0 ? node->left : node->right, pos, range, list, ordered, dim);
    //如果返回的值大於等於零,表明在這個分支中有滿足條件的節點,則返回結果的個數進行累加,並在節點的另一個方向進行查找最近的節點
    if(ret >= 0 && fabs(dx) < range)
    {
        added_res += ret;
        ret = find_nearest(dx <= 0.0 ? node->right : node->left, pos, range, list, ordered, dim);
    }
    if(ret == -1)
    {
        return -1;
    }
    added_res += ret;

    return added_res;
}


//找到最近鄰的n個節點
#if 0
static int find_nearest_n(struct kdnode *node, const double *pos, double range, int num, struct rheap *heap, int dim)
{
    double dist_sq, dx;
    int i, ret, added_res = 0;

    if(!node) return 0;

    /* if the photon is close enough, add it to the result heap */
    //如果足夠近就將其加入到結果堆中
    dist_sq = 0;
    //計算兩者間的歐式距離
    for(i=0; i<dim; i++)
    {
        dist_sq += SQ(node->pos[i] - pos[i]);
    }
    //如果計算所得距離小於閾值
    if(dist_sq <= range_sq) {
    //如果堆的大小大於num,也就是大於總的要找的節點數
        if(heap->size >= num)
        {
            /* get furthest element */
            //得到最遠的節點
            struct res_node *maxelem = rheap_get_max(heap);

            /* and check if the new one is closer than that */
            //測試這個節點是不是比最遠的節點要近
            if(maxelem->dist_sq > dist_sq)
            {
            //如果是的話,就移除最遠的節點
                rheap_remove_max(heap);
                //並將此節點插入堆中
                if(rheap_insert(heap, node, dist_sq) == -1)
                {
                    return -1;
                }
                added_res = 1;

                range_sq = dist_sq;
            }
        }
        //如果堆的大小小於num,直接將此節點插入堆中
        else
        {
            if(rheap_insert(heap, node, dist_sq) == -1)
            {
                return =1;
            }
            added_res = 1;
        }
    }


    /* find signed distance from the splitting plane */
    dx = pos[node->dir] - node->pos[node->dir];

    ret = find_nearest_n(dx <= 0.0 ? node->left : node->right, pos, range, num, heap, dim);
    if(ret >= 0 && fabs(dx) < range) {
        added_res += ret;
        ret = find_nearest_n(dx <= 0.0 ? node->right : node->left, pos, range, num, heap, dim);
    }
}
#endif


static void kd_nearest_i(struct kdnode *node, const double *pos, struct kdnode **result, double *result_dist_sq, struct kdhyperrect* rect)
{
    int dir = node->dir;
    int i;
    double dummy, dist_sq;
    struct kdnode *nearer_subtree, *farther_subtree;
    double *nearer_hyperrect_coord, *farther_hyperrect_coord;

    /* Decide whether to go left or right in the tree */
    //在二叉樹中,決定向左走還是向右走
    dummy = pos[dir] - node->pos[dir];
    if (dummy <= 0)
    {
        nearer_subtree = node->left;
        farther_subtree = node->right;
        nearer_hyperrect_coord = rect->max + dir;
        farther_hyperrect_coord = rect->min + dir;
    }
    else
    {
        nearer_subtree = node->right;
        farther_subtree = node->left;
        nearer_hyperrect_coord = rect->min + dir;
        farther_hyperrect_coord = rect->max + dir;
    }

    if (nearer_subtree) {
        /* Slice the hyperrect to get the hyperrect of the nearer subtree */
        dummy = *nearer_hyperrect_coord;
        *nearer_hyperrect_coord = node->pos[dir];
        /* Recurse down into nearer subtree */
        kd_nearest_i(nearer_subtree, pos, result, result_dist_sq, rect);
        /* Undo the slice */
        *nearer_hyperrect_coord = dummy;
    }

    /* Check the distance of the point at the current node, compare it
     * with our best so far */
    dist_sq = 0;
    for(i=0; i < rect->dim; i++)
    {
        dist_sq += SQ(node->pos[i] - pos[i]);
    }
    if (dist_sq < *result_dist_sq)
    {
        *result = node;
        *result_dist_sq = dist_sq;
    }

    if (farther_subtree) {
        /* Get the hyperrect of the farther subtree */
        dummy = *farther_hyperrect_coord;
        *farther_hyperrect_coord = node->pos[dir];
        /* Check if we have to recurse down by calculating the closest
         * point of the hyperrect and see if it's closer than our
         * minimum distance in result_dist_sq. */
        if (hyperrect_dist_sq(rect, pos) < *result_dist_sq) {
            /* Recurse down into farther subtree */
            kd_nearest_i(farther_subtree, pos, result, result_dist_sq, rect);
        }
        /* Undo the slice on the hyperrect */
        *farther_hyperrect_coord = dummy;
    }
}

//求kdtree中與點pos最近鄰的值
struct kdres *kd_nearest(struct kdtree *kd, const double *pos)
{
    struct kdhyperrect *rect;
    struct kdnode *result;
    struct kdres *rset;
    double dist_sq;
    int i;

    //如果kd不存在,或者其超平面不存在的話,則就不會有結果
    if (!kd) return 0;
    if (!kd->rect) return 0;

    /* Allocate result set */
    //爲返回結果集合分配空間
    if(!(rset = (kdres*)malloc(sizeof *rset)))
    {
        return 0;
    }
    if(!(rset->rlist = (res_node*)alloc_resnode())) {
        free(rset);
        return 0;
    }
    rset->rlist->next = 0;
    rset->tree = kd;

    /* Duplicate the bounding hyperrectangle, we will work on the copy */
    //複製邊界超平面
    if (!(rect = hyperrect_duplicate(kd->rect)))
    {
        kd_res_free(rset);
        return 0;
    }

    /* Our first guesstimate is the root node */
    result = kd->root;
    dist_sq = 0;
    for (i = 0; i < kd->dim; i++)
        dist_sq += SQ(result->pos[i] - pos[i]);

    /* Search for the nearest neighbour recursively */
    //遞歸地查找最近鄰的鄰居
    kd_nearest_i(kd->root, pos, &result, &dist_sq, rect);

    /* Free the copy of the hyperrect */
    //釋放超矩形
    hyperrect_free(rect);

    /* Store the result */
    //存儲結果
    if (result)
    {
        if (rlist_insert(rset->rlist, result, -1.0) == -1)
        {
            kd_res_free(rset);
            return 0;
        }
        rset->size = 1;
        kd_res_rewind(rset);
        return rset;
    }
    else
    {
        kd_res_free(rset);
        return 0;
    }
}

//kd_nearest的float特例
struct kdres *kd_nearestf(struct kdtree *tree, const float *pos)
{
    static double sbuf[16];
    double *bptr, *buf = 0;
    int dim = tree->dim;
    struct kdres *res;

    if(dim > 16) {
#ifndef NO_ALLOCA
        if(dim <= 256)
            bptr = buf = (double*)alloca(dim * sizeof *bptr);
        else
#endif
            if(!(bptr = buf = (double*)malloc(dim * sizeof *bptr))) {
                return 0;
            }
    } else {
        bptr = buf = sbuf;
    }

    while(dim-- > 0) {
        *bptr++ = *pos++;
    }

    res = kd_nearest(tree, buf);
#ifndef NO_ALLOCA
    if(tree->dim > 256)
#else
    if(tree->dim > 16)
#endif
        free(buf);
    return res;
}

//kd_nearest的三座標特例
struct kdres *kd_nearest3(struct kdtree *tree, double x, double y, double z)
{
    double pos[3];
    pos[0] = x;
    pos[1] = y;
    pos[2] = z;
    return kd_nearest(tree, pos);
}

//kd_nearest的三座標float特例
struct kdres *kd_nearest3f(struct kdtree *tree, float x, float y, float z)
{
    double pos[3];
    pos[0] = x;
    pos[1] = y;
    pos[2] = z;
    return kd_nearest(tree, pos);
}

/* ---- nearest N search ---- */
/*
static kdres *kd_nearest_n(struct kdtree *kd, const double *pos, int num)
{
    int ret;
    struct kdres *rset;

    if(!(rset = malloc(sizeof *rset))) {
        return 0;
    }
    if(!(rset->rlist = alloc_resnode())) {
        free(rset);
        return 0;
    }
    rset->rlist->next = 0;
    rset->tree = kd;

    if((ret = find_nearest_n(kd->root, pos, range, num, rset->rlist, kd->dim)) == -1) {
        kd_res_free(rset);
        return 0;
    }
    rset->size = ret;
    kd_res_rewind(rset);
    return rset;
}*/

//找到滿足距離小於range值的節點
struct kdres *kd_nearest_range(struct kdtree *kd, const double *pos, double range)
{
    int ret;
    struct kdres *rset;

    if(!(rset = (kdres*)malloc(sizeof *rset))) {
        return 0;
    }
    if(!(rset->rlist = (res_node*)alloc_resnode())) {
        free(rset);
        return 0;
    }
    rset->rlist->next = 0;
    rset->tree = kd;

    if((ret = find_nearest(kd->root, pos, range, rset->rlist, 0, kd->dim)) == -1) {
        kd_res_free(rset);
        return 0;
    }
    rset->size = ret;
    kd_res_rewind(rset);
    return rset;
}

//kd_nearest_range的float特例
struct kdres *kd_nearest_rangef(struct kdtree *kd, const float *pos, float range)
{
    static double sbuf[16];
    double *bptr, *buf = 0;
    int dim = kd->dim;
    struct kdres *res;

    if(dim > 16) {
#ifndef NO_ALLOCA
        if(dim <= 256)
            bptr = buf = (double*)alloca(dim * sizeof *bptr);
        else
#endif
            if(!(bptr = buf = (double*)malloc(dim * sizeof *bptr))) {
                return 0;
            }
    } else {
        bptr = buf = sbuf;
    }

    while(dim-- > 0) {
        *bptr++ = *pos++;
    }

    res = kd_nearest_range(kd, buf, range);
#ifndef NO_ALLOCA
    if(kd->dim > 256)
#else
    if(kd->dim > 16)
#endif
        free(buf);
    return res;
}

//kd_nearest_range的三座標特例
struct kdres *kd_nearest_range3(struct kdtree *tree, double x, double y, double z, double range)
{
    double buf[3];
    buf[0] = x;
    buf[1] = y;
    buf[2] = z;
    return kd_nearest_range(tree, buf, range);
}

//kd_nearest_range的三座標float特例
struct kdres *kd_nearest_range3f(struct kdtree *tree, float x, float y, float z, float range)
{
    double buf[3];
    buf[0] = x;
    buf[1] = y;
    buf[2] = z;
    return kd_nearest_range(tree, buf, range);
}

//返回結果的釋放
void kd_res_free(struct kdres *rset)
{
    clear_results(rset);
    free_resnode(rset->rlist);
    free(rset);
}

//獲取返回結果集合的大小
int kd_res_size(struct kdres *set)
{
    return (set->size);
}

//再次回到這個節點本身的位置
void kd_res_rewind(struct kdres *rset)
{
    rset->riter = rset->rlist->next;
}

//找到返回結果中的最終節點
int kd_res_end(struct kdres *rset)
{
    return rset->riter == 0;
}

//返回結果列表中的下一個節點
int kd_res_next(struct kdres *rset)
{
    rset->riter = rset->riter->next;
    return rset->riter != 0;
}

//將返回結果的節點的座標和data抽取出來
void *kd_res_item(struct kdres *rset, double *pos)
{
    if(rset->riter) {
        if(pos) {
            memcpy(pos, rset->riter->item->pos, rset->tree->dim * sizeof *pos);
        }
        return rset->riter->item->data;
    }
    return 0;
}

//將返回結果的節點的座標和data抽取出來,座標爲float型的值
void *kd_res_itemf(struct kdres *rset, float *pos)
{
    if(rset->riter) {
        if(pos) {
            int i;
            for(i=0; i<rset->tree->dim; i++) {
                pos[i] = rset->riter->item->pos[i];
            }
        }
        return rset->riter->item->data;
    }
    return 0;
}

//將返回結果的節點的座標和data抽取出來,座標具體形式給出
void *kd_res_item3(struct kdres *rset, double *x, double *y, double *z)
{
    if(rset->riter) {
        if(*x) *x = rset->riter->item->pos[0];
        if(*y) *y = rset->riter->item->pos[1];
        if(*z) *z = rset->riter->item->pos[2];
    }
    return 0;
}

//將返回結果的節點的座標和data抽取出來,座標爲float型的值,座標具體形式給出
void *kd_res_item3f(struct kdres *rset, float *x, float *y, float *z)
{
    if(rset->riter) {
        if(*x) *x = rset->riter->item->pos[0];
        if(*y) *y = rset->riter->item->pos[1];
        if(*z) *z = rset->riter->item->pos[2];
    }
    return 0;
}

//獲取data數據
void *kd_res_item_data(struct kdres *set)
{
    return kd_res_item(set, 0);
}

/* ---- hyperrectangle helpers ---- */
//創建超平面,包括三個參數:維度,每維的最小值和最大值數組
static struct kdhyperrect* hyperrect_create(int dim, const double *min, const double *max)
{
    size_t size = dim * sizeof(double);
    struct kdhyperrect* rect = 0;

    if (!(rect = (kdhyperrect*)malloc(sizeof(struct kdhyperrect))))
    {
        return 0;
    }

    rect->dim = dim;
    if (!(rect->min = (double*)malloc(size))) {
        free(rect);
        return 0;
    }
    if (!(rect->max = (double*)malloc(size))) {
        free(rect->min);
        free(rect);
        return 0;
    }
    memcpy(rect->min, min, size);
    memcpy(rect->max, max, size);

    return rect;
}

//釋放超平面結構體
static void hyperrect_free(struct kdhyperrect *rect)
{
    free(rect->min);
    free(rect->max);
    free(rect);
}

//賦值超平面結構體
static struct kdhyperrect* hyperrect_duplicate(const struct kdhyperrect *rect)
{
    return hyperrect_create(rect->dim, rect->min, rect->max);
}

//更新超平面結構體最大\最小值數組
static void hyperrect_extend(struct kdhyperrect *rect, const double *pos)
{
    int i;

    for (i=0; i < rect->dim; i++) {
        if (pos[i] < rect->min[i]) {
            rect->min[i] = pos[i];
        }
        if (pos[i] > rect->max[i]) {
            rect->max[i] = pos[i];
        }
    }
}

//計算固定座標點與超平面之間的距離
static double hyperrect_dist_sq(struct kdhyperrect *rect, const double *pos)
{
    int i;
    double result = 0;

    for (i=0; i < rect->dim; i++)
    {
        if (pos[i] < rect->min[i])
        {
            result += SQ(rect->min[i] - pos[i]);
        }
        else if (pos[i] > rect->max[i])
        {
            result += SQ(rect->max[i] - pos[i]);
        }
    }
    return result;
}


/* ---- static helpers ---- */
#ifdef USE_LIST_NODE_ALLOCATOR
/* special list node allocators. */
static struct res_node *free_nodes;

#ifndef NO_PTHREADS
static pthread_mutex_t alloc_mutex = PTHREAD_MUTEX_INITIALIZER;
#endif

//創建返回結果節點
static struct res_node *alloc_resnode(void)
{
    struct res_node *node;

#ifndef NO_PTHREADS
    pthread_mutex_lock(&alloc_mutex);
#endif

    if(!free_nodes) {
        node = malloc(sizeof *node);
    } else {
        node = free_nodes;
        free_nodes = free_nodes->next;
        node->next = 0;
    }

#ifndef NO_PTHREADS
    pthread_mutex_unlock(&alloc_mutex);
#endif

    return node;
}

//釋放返回結果節點
static void free_resnode(struct res_node *node)
{
#ifndef NO_PTHREADS
    pthread_mutex_lock(&alloc_mutex);
#endif

    node->next = free_nodes;
    free_nodes = node;

#ifndef NO_PTHREADS
    pthread_mutex_unlock(&alloc_mutex);
#endif
}
#endif  /* list node allocator or not */


/* inserts the item. if dist_sq is >= 0, then do an ordered insert */
/* TODO make the ordering code use heapsort */
//函數參數: 返回結果節點指針,樹節點指針,距離函數
//將一個結果節點插入到返回結果的列表中
static int rlist_insert(struct res_node *list, struct kdnode *item, double dist_sq)
{
    struct res_node *rnode;

    //創建一個返回結果的節點
    if(!(rnode = (res_node*)alloc_resnode()))
    {
        return -1;
    }
    rnode->item = item;           //對應的樹節點
    rnode->dist_sq = dist_sq;     //對應的距離值

    //當距離大於零的時候
    if(dist_sq >= 0.0)
    {
        while(list->next && list->next->dist_sq < dist_sq)
        {
            list = list->next;
        }
    }
    rnode->next = list->next;
    list->next = rnode;
    return 0;
}

//清除返回結果的集合
//本質上是個雙鏈表中單鏈表的清理
static void clear_results(struct kdres *rset)
{
    struct res_node *tmp, *node = rset->rlist->next;

    while(node)
    {
        tmp = node;
        node = node->next;
        free_resnode(tmp);
    }

    rset->rlist->next = 0;
}