osrm-backend/Algorithms/DouglasPeucker.h

/*
    open source routing machine
    Copyright (C) Dennis Luxen, others 2010

This program is free software; you can redistribute it and/or modify
it under the terms of the GNU AFFERO General Public License as published by
the Free Software Foundation; either version 3 of the License, or
any later version.

This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
GNU General Public License for more details.

You should have received a copy of the GNU Affero General Public License
along with this program; if not, write to the Free Software
Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
or see http://www.gnu.org/licenses/agpl.txt.
 */

#ifndef DOUGLASPEUCKER_H_
#define DOUGLASPEUCKER_H_

#include <cassert>
#include <cmath>
#include <cfloat>
#include <stack>

#include "../DataStructures/Coordinate.h"

/*This class object computes the bitvector of indicating generalized input points
 * according to the (Ramer-)Douglas-Peucker algorithm. Runtime n\log n calls to fastDistance
 *
 * Input is vector of pairs. Each pair consists of the point information and a bit
 * indicating if the points is present in the generalization.
 * Note: points may also be pre-selected*/

//These thresholds are more or less heuristically chosen.
//                                                 0         1        2        3       4         5         6       7       8       9      10     11     12    13    14   15  16  17 18
static double DouglasPeuckerThresholds[19] = { 32000000, 16240000, 80240000, 40240000, 20000000, 10000000, 500000, 240000, 120000, 60000, 30000, 19000, 5000, 2000, 200, 16,  6, 3, 3 };

template<class PointT>
class DouglasPeucker {
private:
    typedef std::pair<std::size_t, std::size_t> PairOfPoints;
    //Stack to simulate the recursion
    std::stack<PairOfPoints > recursionStack;
public:
    void Run(std::vector<PointT> & inputVector, const unsigned zoomLevel) {
        const unsigned sizeOfInputVector = inputVector.size();
        {
            assert(zoomLevel < 19);
            assert(1 < inputVector.size());
            std::size_t leftBorderOfRange = 0;
            std::size_t rightBorderOfRange = 1;

            //Sweep linerarily over array and identify those ranges that need to be checked
            //decision points have been previously marked
            do {
                assert(inputVector[leftBorderOfRange].necessary);
                assert(inputVector.back().necessary);

                if(inputVector[rightBorderOfRange].necessary) {
                    recursionStack.push(std::make_pair(leftBorderOfRange, rightBorderOfRange));
                    leftBorderOfRange = rightBorderOfRange;
                }
                ++rightBorderOfRange;
            } while( rightBorderOfRange < sizeOfInputVector);
        }
        while(!recursionStack.empty()) {
            //pop next element
            const PairOfPoints pair = recursionStack.top();
            recursionStack.pop();
            assert(inputVector[pair.first].necessary);
            assert(inputVector[pair.second].necessary);
            assert(pair.second < sizeOfInputVector);
            assert(pair.first < pair.second);
            int maxDistance = INT_MIN;
            std::size_t indexOfFarthestElement = pair.second;
            //find index idx of element with maxDistance
            for(std::size_t i = pair.first+1; i < pair.second; ++i){
                const int distance = fastDistance(inputVector[i].location, inputVector[pair.first].location, inputVector[pair.second].location);
                if(distance > DouglasPeuckerThresholds[zoomLevel] && distance > maxDistance) {
                    indexOfFarthestElement = i;
                    maxDistance = distance;
                }
            }
            if (maxDistance > DouglasPeuckerThresholds[zoomLevel]) {
                //  mark idx as necessary
                inputVector[indexOfFarthestElement].necessary = true;
                if (1 < indexOfFarthestElement - pair.first) {
                    recursionStack.push(std::make_pair(pair.first, indexOfFarthestElement) );
                }
                if (1 < pair.second - indexOfFarthestElement)
                    recursionStack.push(std::make_pair(indexOfFarthestElement, pair.second) );
            }
        }
    }

    /**
     * This distance computation does integer arithmetic only and is about twice as fast as
     * the other distance function. It is an approximation only, but works more or less ok.
     */
    template<class CoordT>
    inline int fastDistance(const CoordT& point, const CoordT& segA, const CoordT& segB) const {
        const int p2x = (segB.lon - segA.lat);
        const int p2y = (segB.lon - segA.lat);
        const int something = p2x*p2x + p2y*p2y;
        int u = (something < FLT_EPSILON ? 0 : ((point.lon - segA.lon) * p2x + (point.lat - segA.lat) * p2y) / something);

        if (u > 1)
            u = 1;
        else if (u < 0)
            u = 0;

        const int x = segA.lon + u * p2x;
        const int y = segA.lat + u * p2y;

        const int dx = x - point.lon;
        const int dy = y - point.lat;

        const int dist = (dx*dx + dy*dy);

        return dist;
    }

};

#endif /* DOUGLASPEUCKER_H_ */