osrm-backend/Algorithms/DouglasPeucker.h

/*

Copyright (c) 2013, Project OSRM, Dennis Luxen, others
All rights reserved.

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

Redistributions of source code must retain the above copyright notice, this list
of conditions and the following disclaimer.
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.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "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 COPYRIGHT HOLDER OR CONTRIBUTORS 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
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(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

*/

#ifndef DOUGLASPEUCKER_H_
#define DOUGLASPEUCKER_H_

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

#include <boost/assert.hpp>

#include <cmath>

#include <limits>
#include <stack>
#include <vector>

/*This class object computes the bitvector of indicating generalized input points
 * according to the (Ramer-)Douglas-Peucker algorithm.
 *
 * 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 > recursion_stack;

    /**
     * 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 = ( 0 == something  ? 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;
    }


public:
    void Run(std::vector<PointT> & input_geometry, const unsigned zoom_level) {
        {
            BOOST_ASSERT_MSG(zoom_level < 19, "unsupported zoom level");
            BOOST_ASSERT_MSG(1 < input_geometry.size(), "geometry invalid");
            std::size_t left_border = 0;
            std::size_t right_border = 1;
            //Sweep linerarily over array and identify those ranges that need to be checked
            do {
                BOOST_ASSERT_MSG(
                    input_geometry[left_border].necessary,
                    "left border must be necessary"
                );
                BOOST_ASSERT_MSG(
                    input_geometry.back().necessary,
                    "right border must be necessary"
                );

                if(input_geometry[right_border].necessary) {
                    recursion_stack.push(std::make_pair(left_border, right_border));
                    left_border = right_border;
                }
                ++right_border;
            } while( right_border < input_geometry.size());
        }
        while(!recursion_stack.empty()) {
            //pop next element
            const PairOfPoints pair = recursion_stack.top();
            recursion_stack.pop();
            BOOST_ASSERT_MSG(
                input_geometry[pair.first].necessary,
                "left border mus be necessary"
            );
            BOOST_ASSERT_MSG(
                input_geometry[pair.second].necessary,
                "right border must be necessary"
            );
            BOOST_ASSERT_MSG(
                pair.second < input_geometry.size(),
                "right border outside of geometry"
            );
            BOOST_ASSERT_MSG(
                pair.first < pair.second,
                "left border on the wrong side"
            );
            int max_distance = INT_MIN;

            std::size_t farthest_element_index = pair.second;
            //find index idx of element with max_distance
            for(std::size_t i = pair.first+1; i < pair.second; ++i){
                const int temp_dist = fastDistance(
                                        input_geometry[i].location,
                                        input_geometry[pair.first].location,
                                        input_geometry[pair.second].location
                                    );
                const double distance = std::fabs(temp_dist);
                if(
                    distance > DouglasPeuckerThresholds[zoom_level] &&
                    distance > max_distance
                ) {
                    farthest_element_index = i;
                    max_distance = distance;
                }
            }
            if (max_distance > DouglasPeuckerThresholds[zoom_level]) {
                //  mark idx as necessary
                input_geometry[farthest_element_index].necessary = true;
                if (1 < (farthest_element_index - pair.first) ) {
                    recursion_stack.push(
                        std::make_pair(pair.first, farthest_element_index)
                    );
                }
                if (1 < (pair.second - farthest_element_index) ) {
                    recursion_stack.push(
                        std::make_pair(farthest_element_index, pair.second)
                    );
                }
            }
        }
    }
};

#endif /* DOUGLASPEUCKER_H_ */