Task: Ramer-Douglas-Peucker line simplification


C++: #include <iostream>
#include <cmath>
#include <utility>
#include <vector>
#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;

	
	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;

	
	double pvdot = dx * pvx + dy * pvy;

	
	double dsx = pvdot * dx;
	double dsy = pvdot * dy;

	
	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");

	
	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(dmax > epsilon)
	{
		
		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);
 
		
		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 
	{
		
		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;
}



Go: package main

import (
    "fmt"
    "math"
)

type point struct{ x, y float64 }

func RDP(l []point, ε float64) []point {
    x := 0
    dMax := -1.
    last := len(l) - 1
    p1 := l[0]
    p2 := l[last]
    x21 := p2.x - p1.x
    y21 := p2.y - p1.y
    for i, p := range l[1:last] {
        if d := math.Abs(y21*p.x - x21*p.y + p2.x*p1.y - p2.y*p1.x); d > dMax {
            x = i + 1
            dMax = d
        }
    }
    if dMax > ε {
        return append(RDP(l[:x+1], ε), RDP(l[x:], ε)[1:]...)
    }
    return []point{l[0], l[len(l)-1]}
}

func main() {
    fmt.Println(RDP([]point{{0, 0}, {1, 0.1}, {2, -0.1},
        {3, 5}, {4, 6}, {5, 7}, {6, 8.1}, {7, 9}, {8, 9}, {9, 9}}, 1))
}