Task: Ramer-Douglas-Peucker line simplification
C#: using System;
using System.Collections.Generic;
using System.Linq;

namespace LineSimplification {
    using Point = Tuple<double, double>;

    class Program {
        static double PerpendicularDistance(Point pt, Point lineStart, Point lineEnd) {
            double dx = lineEnd.Item1 - lineStart.Item1;
            double dy = lineEnd.Item2 - lineStart.Item2;

            
            double mag = Math.Sqrt(dx * dx + dy * dy);
            if (mag > 0.0) {
                dx /= mag;
                dy /= mag;
            }
            double pvx = pt.Item1 - lineStart.Item1;
            double pvy = pt.Item2 - lineStart.Item2;

            
            double pvdot = dx * pvx + dy * pvy;

            
            double ax = pvx - pvdot * dx;
            double ay = pvy - pvdot * dy;

            return Math.Sqrt(ax * ax + ay * ay);
        }

        static void RamerDouglasPeucker(List<Point> pointList, double epsilon, List<Point> output) {
            if (pointList.Count < 2) {
                throw new ArgumentOutOfRangeException("Not enough points to simplify");
            }

            
            double dmax = 0.0;
            int index = 0;
            int end = pointList.Count - 1;
            for (int i = 1; i < end; ++i) {
                double d = PerpendicularDistance(pointList[i], pointList[0], pointList[end]);
                if (d > dmax) {
                    index = i;
                    dmax = d;
                }
            }

            
            if (dmax > epsilon) {
                List<Point> recResults1 = new List<Point>();
                List<Point> recResults2 = new List<Point>();
                List<Point> firstLine = pointList.Take(index + 1).ToList();
                List<Point> lastLine = pointList.Skip(index).ToList();
                RamerDouglasPeucker(firstLine, epsilon, recResults1);
                RamerDouglasPeucker(lastLine, epsilon, recResults2);

                
                output.AddRange(recResults1.Take(recResults1.Count - 1));
                output.AddRange(recResults2);
                if (output.Count < 2) throw new Exception("Problem assembling output");
            }
            else {
                
                output.Clear();
                output.Add(pointList[0]);
                output.Add(pointList[pointList.Count - 1]);
            }
        }

        static void Main(string[] args) {
            List<Point> pointList = new List<Point>() {
                new Point(0.0,0.0),
                new Point(1.0,0.1),
                new Point(2.0,-0.1),
                new Point(3.0,5.0),
                new Point(4.0,6.0),
                new Point(5.0,7.0),
                new Point(6.0,8.1),
                new Point(7.0,9.0),
                new Point(8.0,9.0),
                new Point(9.0,9.0),
            };
            List<Point> pointListOut = new List<Point>();
            RamerDouglasPeucker(pointList, 1.0, pointListOut);
            Console.WriteLine("Points remaining after simplification:");
            pointListOut.ForEach(p => Console.WriteLine(p));
        }
    }
}

Python: from __future__ import print_function
from shapely.geometry import LineString
 
if __name__=="__main__":
	line = LineString([(0,0),(1,0.1),(2,-0.1),(3,5),(4,6),(5,7),(6,8.1),(7,9),(8,9),(9,9)])
	print (line.simplify(1.0, preserve_topology=False))