kdtree.cpp

/*
This file is part of ``kdtree'', a library for working with kd-trees.
Copyright (C) 2007-2009 John Tsiombikas <nuclear@siggraph.org>

Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are met:

1. Redistributions of source code must retain the above copyright notice, this
   list of conditions and the following disclaimer.
2. Redistributions in binary form must reproduce the above copyright notice,
   this list of conditions and the following disclaimer in the documentation
   and/or other materials provided with the distribution.
3. The name of the author may not be used to endorse or promote products
   derived from this software without specific prior written permission.

THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR IMPLIED
WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO
EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT
OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING
IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY
OF SUCH DAMAGE.
*/
/* single nearest neighbor search written by Tamas Nepusz <tamas@cs.rhul.ac.uk> */

#include <string.h>
#include <math.h>
#include "kdtree.h"

#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);

struct kdtree *kd_create(int k)
{
    struct kdtree *tree;

    if(!(tree = new kdtree)) {
        return 0;
    }

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

    return tree;
}

void kd_free(struct kdtree *tree)
{
    if(tree) {
        kd_clear(tree);
        delete tree;
    }
}

static void clear_rec(struct kdnode *node, void (*destr)(void*))
{
    if(!node) return;

    clear_rec(node->left, destr);
    clear_rec(node->right, destr);

    if(destr) {
        destr(node->data);
    }
    delete[] node->pos;
    delete node;
}

void kd_clear(struct kdtree *tree)
{
    clear_rec(tree->root, tree->destr);
    tree->root = 0;

    if (tree->rect) {
        hyperrect_free(tree->rect);
        tree->rect = 0;
    }
}

void kd_data_destructor(struct kdtree *tree, void (*destr)(void*))
{
    tree->destr = destr;
}


static int insert_rec(struct kdnode **nptr, const double *pos, void *data, int dir, int dim)
{
    int new_dir;
    struct kdnode *node;

    if(!*nptr) {
        if(!(node = new kdnode)) {
            return -1;
        }
        if(!(node->pos = new double[dim])) {
            delete[] 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);
}

int kd_insert(struct kdtree *tree, const double *pos, void *data)
{
    if (insert_rec(&tree->root, pos, data, 0, tree->dim)) {
        return -1;
    }

    if (tree->rect == 0) {
        tree->rect = hyperrect_create(tree->dim, pos, pos);
    } else {
        hyperrect_extend(tree->rect, pos);
    }

    return 0;
}

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;

    dist_sq = 0;
    for(i=0; i<dim; i++) {
        dist_sq += SQ(node->pos[i] - pos[i]);
    }
    if(dist_sq <= SQ(range)) {
        if(rlist_insert(list, node, ordered ? dist_sq : -1.0) == -1) {
            return -1;
        }
        added_res = 1;
    }

    dx = pos[node->dir] - node->pos[node->dir];

    ret = find_nearest(dx <= 0.0 ? node->left : node->right, pos, range, list, ordered, dim);
    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;
}

#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 */
    dist_sq = 0;
    for(i=0; i<dim; i++) {
        dist_sq += SQ(node->pos[i] - pos[i]);
    }
    if(dist_sq <= range_sq) {
        if(heap->size >= num) {
            /* get furthest element */
            struct res_node *maxelem = rheap_get_max(heap);

            /* and check if the new one is closer than that */
            if(maxelem->dist_sq > dist_sq) {
                rheap_remove_max(heap);

                if(rheap_insert(heap, node, dist_sq) == -1) {
                    return -1;
                }
                added_res = 1;

                range_sq = dist_sq;
            }
        } 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 */
    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;
    }
}

struct kdres *kd_nearest(struct kdtree *kd, const double *pos)
{
    struct kdhyperrect *rect;
    struct kdnode *result;
    struct kdres *rset;
    double dist_sq;
    int i;

    if (!kd) return 0;
    if (!kd->rect) return 0;

    /* Allocate result set */
    if(!(rset = new kdres)) {
        return 0;
    }
    if(!(rset->rlist = new res_node)) {
        delete rset;
        return 0;
    }
    rset->rlist->next = 0;
    rset->tree = kd;

    /* Duplicate the bounding hyperrectangle, we will work on the copy */
    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 */
    kd_nearest_i(kd->root, pos, &result, &dist_sq, rect);

    /* Free the copy of the hyperrect */
    hyperrect_free(rect);

    /* Store the result */
    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;
    }
}

struct kdres *kd_nearest_range(struct kdtree *kd, const double *pos, double range)
{
    int ret;
    struct kdres *rset;

    if(!(rset = new kdres)) {
        return 0;
    }
    if(!(rset->rlist = new res_node)) {
        delete 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;
}

void kd_res_free(struct kdres *rset)
{
    clear_results(rset);
    delete rset->rlist;
    delete rset;
}

int kd_res_size(struct kdres *set)
{
    return (set->size);
}

void kd_res_rewind(struct kdres *rset)
{
    rset->riter = rset->rlist->next;
}

int kd_res_end(struct kdres *rset)
{
    return rset->riter == 0;
}

int kd_res_next(struct kdres *rset)
{
    rset->riter = rset->riter->next;
    return rset->riter != 0;
}

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;
}

void *kd_res_item_data(struct kdres *set)
{
    return kd_res_item(set, 0);
}

/* ---- hyperrectangle helpers ---- */
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 = new kdhyperrect)) {
        return 0;
    }

    rect->dim = dim;
    if (!(rect->min = new double[size])) {
        delete rect;
        return 0;
    }
    if (!(rect->max = new double[size])) {
        delete[] rect->min;
        delete rect;
        return 0;
    }
    memcpy(rect->min, min, size);
    memcpy(rect->max, max, size);

    return rect;
}

static void hyperrect_free(struct kdhyperrect *rect)
{
    delete[] rect->min;
    delete[] rect->max;
    delete rect;
}

static struct kdhyperrect* hyperrect_duplicate(const struct kdhyperrect *rect)
{
    return hyperrect_create(rect->dim, rect->min, rect->max);
}

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];
        }
    }
}

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;
}

/* inserts the item. if dist_sq is >= 0, then do an ordered insert */
/* TODO make the ordering code use heapsort */
static int rlist_insert(struct res_node *list, struct kdnode *item, double dist_sq)
{
    struct res_node *rnode;

    if(!(rnode = new res_node)) {
        return -1;
    }
    rnode->item = item;
    rnode->dist_sq = dist_sq;

    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;
}

static void clear_results(struct kdres *rset)
{
    struct res_node *tmp, *node = rset->rlist->next;

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

    rset->rlist->next = 0;
}