Ramer-Douglas-Peucker line simplification

Ramer-Douglas-Peucker line simplification is a draft programming task. It is not yet considered ready to be promoted as a complete task, for reasons that should be found in its talk page.

Ramer–Douglas–Peucker algorithm is a line simplification algorithm for reducing the number of points used to define its shape.

Task

Simplify the 2D line defined by the points (0,0),(1,0.1)(2,-0.1)(3,5)(4,6)(5,7)(6,8.1)(7,9)(8,9)(9,9) using the Ramer–Douglas–Peucker algorithm. The error threshold to use is 1.0. Display the remaining points.

C++

<lang cpp>#include <iostream>

1. include <cmath>
2. include <utility>
3. include <vector>
4. include <stdexcept>

using namespace std;

typedef std::pair<double, double> Point;

double PerpendicularDistance(const Point &pt, const Point &lineStart, const Point &lineEnd) { double dx = lineEnd.first - lineStart.first; double dy = lineEnd.second - lineStart.second;

//Normalise double mag = pow(pow(dx,2.0)+pow(dy,2.0),0.5); if(mag > 0.0) { dx /= mag; dy /= mag; }

double pvx = pt.first - lineStart.first; double pvy = pt.second - lineStart.second;

//Get dot product (project pv onto normalized direction) double pvdot = dx * pvx + dy * pvy;

//Scale line direction vector double dsx = pvdot * dx; double dsy = pvdot * dy;

//Subtract this from pv double ax = pvx - dsx; double ay = pvy - dsy;

return pow(pow(ax,2.0)+pow(ay,2.0),0.5); }

void RamerDouglasPeucker(const vector<Point> &pointList, double epsilon, vector<Point> &out) { if(pointList.size()<2) throw invalid_argument("Not enough points to simplify");

// Find the point with the maximum distance from line between start and end double dmax = 0.0; size_t index = 0; size_t end = pointList.size()-1; for(size_t i = 1; i < end; i++) { double d = PerpendicularDistance(pointList[i], pointList[0], pointList[end]); if (d > dmax) { index = i; dmax = d; } }

// If max distance is greater than epsilon, recursively simplify if(dmax > epsilon) { // Recursive call vector<Point> recResults1; vector<Point> recResults2; vector<Point> firstLine(pointList.begin(), pointList.begin()+index+1); vector<Point> lastLine(pointList.begin()+index, pointList.end()); RamerDouglasPeucker(firstLine, epsilon, recResults1); RamerDouglasPeucker(lastLine, epsilon, recResults2);

// Build the result list out.assign(recResults1.begin(), recResults1.end()-1); out.insert(out.end(), recResults2.begin(), recResults2.end()); if(out.size()<2) throw runtime_error("Problem assembling output"); } else { //Just return start and end points out.clear(); out.push_back(pointList[0]); out.push_back(pointList[end]); } }

int main() { vector<Point> pointList; vector<Point> pointListOut;

pointList.push_back(Point(0.0, 0.0)); pointList.push_back(Point(1.0, 0.1)); pointList.push_back(Point(2.0, -0.1)); pointList.push_back(Point(3.0, 5.0)); pointList.push_back(Point(4.0, 6.0)); pointList.push_back(Point(5.0, 7.0)); pointList.push_back(Point(6.0, 8.1)); pointList.push_back(Point(7.0, 9.0)); pointList.push_back(Point(8.0, 9.0)); pointList.push_back(Point(9.0, 9.0));

RamerDouglasPeucker(pointList, 1.0, pointListOut);

cout << "result" << endl; for(size_t i=0;i< pointListOut.size();i++) { cout << pointListOut[i].first << "," << pointListOut[i].second << endl; }

return 0; }</lang>

Output:

result
0,0
2,-0.1
3,5
7,9
9,9