Quadrotor

//----------------------------------------------------------------------

// File:                        kd_search.cpp

// Programmer:                Sunil Arya and David Mount

// Description:                Standard kd-tree search

// Last modified:        01/04/05 (Version 1.0)

//----------------------------------------------------------------------

// Copyright (c) 1997-2005 University of Maryland and Sunil Arya and

// David Mount.  All Rights Reserved.

// 

// This software and related documentation is part of the Approximate

// Nearest Neighbor Library (ANN).  This software is provided under

// the provisions of the Lesser GNU Public License (LGPL).  See the

// file ../ReadMe.txt for further information.

// 

// The University of Maryland (U.M.) and the authors make no

// representations about the suitability or fitness of this software for

// any purpose.  It is provided "as is" without express or implied

// warranty.

//----------------------------------------------------------------------

// History:

//        Revision 0.1  03/04/98

//                Initial release

//        Revision 1.0  04/01/05

//                Changed names LO, HI to ANN_LO, ANN_HI

//----------------------------------------------------------------------

#include "kd_search.h"                                        // kd-search declarations

//----------------------------------------------------------------------

//        Approximate nearest neighbor searching by kd-tree search

//                The kd-tree is searched for an approximate nearest neighbor.

//                The point is returned through one of the arguments, and the

//                distance returned is the squared distance to this point.

//

//                The method used for searching the kd-tree is an approximate

//                adaptation of the search algorithm described by Friedman,

//                Bentley, and Finkel, ``An algorithm for finding best matches

//                in logarithmic expected time,'' ACM Transactions on Mathematical

//                Software, 3(3):209-226, 1977).

//

//                The algorithm operates recursively.  When first encountering a

//                node of the kd-tree we first visit the child which is closest to

//                the query point.  On return, we decide whether we want to visit

//                the other child.  If the box containing the other child exceeds

//                1/(1+eps) times the current best distance, then we skip it (since

//                any point found in this child cannot be closer to the query point

//                by more than this factor.)  Otherwise, we visit it recursively.

//                The distance between a box and the query point is computed exactly

//                (not approximated as is often done in kd-tree), using incremental

//                distance updates, as described by Arya and Mount in ``Algorithms

//                for fast vector quantization,'' Proc.  of DCC '93: Data Compression

//                Conference, eds. J. A. Storer and M. Cohn, IEEE Press, 1993,

//                381-390.

//

//                The main entry points is annkSearch() which sets things up and

//                then call the recursive routine ann_search().  This is a recursive

//                routine which performs the processing for one node in the kd-tree.

//                There are two versions of this virtual procedure, one for splitting

//                nodes and one for leaves.  When a splitting node is visited, we

//                determine which child to visit first (the closer one), and visit

//                the other child on return.  When a leaf is visited, we compute

//                the distances to the points in the buckets, and update information

//                on the closest points.

//

//                Some trickery is used to incrementally update the distance from

//                a kd-tree rectangle to the query point.  This comes about from

//                the fact that which each successive split, only one component

//                (along the dimension that is split) of the squared distance to

//                the child rectangle is different from the squared distance to

//                the parent rectangle.

//----------------------------------------------------------------------

//----------------------------------------------------------------------

//                To keep argument lists short, a number of global variables

//                are maintained which are common to all the recursive calls.

//                These are given below.

//----------------------------------------------------------------------

int                                ANNkdDim;                                // dimension of space

ANNpoint                ANNkdQ;                                        // query point

double                        ANNkdMaxErr;                        // max tolerable squared error

ANNpointArray        ANNkdPts;                                // the points

ANNmin_k                *ANNkdPointMK;                        // set of k closest points

//----------------------------------------------------------------------

//        annkSearch - search for the k nearest neighbors

//----------------------------------------------------------------------

void ANNkd_tree::annkSearch(

        ANNpoint                        q,                                // the query point

        int                                        k,                                // number of near neighbors to return

        ANNidxArray                        nn_idx,                        // nearest neighbor indices (returned)

        ANNdistArray                dd,                                // the approximate nearest neighbor

        double                                eps)                        // the error bound

{

        ANNkdDim = dim;                                                // copy arguments to static equivs

        ANNkdQ = q;

        ANNkdPts = pts;

        ANNptsVisited = 0;                                        // initialize count of points visited

        if (k > n_pts) {                                        // too many near neighbors?

                annError("Requesting more near neighbors than data points", ANNabort);

        }

        ANNkdMaxErr = ANN_POW(1.0 + eps);

        ANN_FLOP(2)                                                        // increment floating op count

        ANNkdPointMK = new ANNmin_k(k);                // create set for closest k points

                                                                                // search starting at the root

        root->ann_search(annBoxDistance(q, bnd_box_lo, bnd_box_hi, dim));

        for (int i = 0; i < k; i++) {                // extract the k-th closest points

                dd[i] = ANNkdPointMK->ith_smallest_key(i);

                nn_idx[i] = ANNkdPointMK->ith_smallest_info(i);

        }

        delete ANNkdPointMK;                                // deallocate closest point set

}

//----------------------------------------------------------------------

//        kd_split::ann_search - search a splitting node

//----------------------------------------------------------------------

void ANNkd_split::ann_search(ANNdist box_dist)

{

                                                                                // check dist calc term condition

        if (ANNmaxPtsVisited != 0 && ANNptsVisited > ANNmaxPtsVisited) return;

                                                                                // distance to cutting plane

        ANNcoord cut_diff = ANNkdQ[cut_dim] - cut_val;

        if (cut_diff < 0) {                                        // left of cutting plane

                child[ANN_LO]->ann_search(box_dist);// visit closer child first

                ANNcoord box_diff = cd_bnds[ANN_LO] - ANNkdQ[cut_dim];

                if (box_diff < 0)                                // within bounds - ignore

                        box_diff = 0;

                                                                                // distance to further box

                box_dist = (ANNdist) ANN_SUM(box_dist,

                                ANN_DIFF(ANN_POW(box_diff), ANN_POW(cut_diff)));

                                                                                // visit further child if close enough

                if (box_dist * ANNkdMaxErr < ANNkdPointMK->max_key())

                        child[ANN_HI]->ann_search(box_dist);

        }

        else {                                                                // right of cutting plane

                child[ANN_HI]->ann_search(box_dist);// visit closer child first

                ANNcoord box_diff = ANNkdQ[cut_dim] - cd_bnds[ANN_HI];

                if (box_diff < 0)                                // within bounds - ignore

                        box_diff = 0;

                                                                                // distance to further box

                box_dist = (ANNdist) ANN_SUM(box_dist,

                                ANN_DIFF(ANN_POW(box_diff), ANN_POW(cut_diff)));

                                                                                // visit further child if close enough

                if (box_dist * ANNkdMaxErr < ANNkdPointMK->max_key())

                        child[ANN_LO]->ann_search(box_dist);

        }

        ANN_FLOP(10)                                                // increment floating ops

        ANN_SPL(1)                                                        // one more splitting node visited

}

//----------------------------------------------------------------------

//        kd_leaf::ann_search - search points in a leaf node

//                Note: The unreadability of this code is the result of

//                some fine tuning to replace indexing by pointer operations.

//----------------------------------------------------------------------

void ANNkd_leaf::ann_search(ANNdist box_dist)

{

        register ANNdist dist;                                // distance to data point

        register ANNcoord* pp;                                // data coordinate pointer

        register ANNcoord* qq;                                // query coordinate pointer

        register ANNdist min_dist;                        // distance to k-th closest point

        register ANNcoord t;

        register int d;

        min_dist = ANNkdPointMK->max_key(); // k-th smallest distance so far

        for (int i = 0; i < n_pts; i++) {        // check points in bucket

                pp = ANNkdPts[bkt[i]];                        // first coord of next data point

                qq = ANNkdQ;                                        // first coord of query point

                dist = 0;

                for(d = 0; d < ANNkdDim; d++) {

                        ANN_COORD(1)                                // one more coordinate hit

                        ANN_FLOP(4)                                        // increment floating ops

                        t = *(qq++) - *(pp++);                // compute length and adv coordinate

                                                                                // exceeds dist to k-th smallest?

                        if( (dist = ANN_SUM(dist, ANN_POW(t))) > min_dist) {

                                break;

                        }

                }

                if (d >= ANNkdDim &&                                        // among the k best?

                   (ANN_ALLOW_SELF_MATCH || dist!=0)) { // and no self-match problem

                                                                                                // add it to the list

                        ANNkdPointMK->insert(dist, bkt[i]);

                        min_dist = ANNkdPointMK->max_key();

                }

        }

        ANN_LEAF(1)                                                        // one more leaf node visited

        ANN_PTS(n_pts)                                                // increment points visited

        ANNptsVisited += n_pts;                                // increment number of points visited

}