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));
        }
    }
}

PHP: function perpendicular_distance(array $pt, array $line) {

  $dx = $line[1][0] - $line[0][0];
  $dy = $line[1][1] - $line[0][1];
  $mag = sqrt($dx * $dx + $dy * $dy);
  if ($mag > 0) {
    $dx /= $mag;
    $dy /= $mag;
  }

  $pvx = $pt[0] - $line[0][0];
  $pvy = $pt[1] - $line[0][1];
  $pvdot = $dx * $pvx + $dy * $pvy;

  $dsx = $pvdot * $dx;
  $dsy = $pvdot * $dy;
  $ax = $pvx - $dsx;
  $ay = $pvy - $dsy;

  return sqrt($ax * $ax + $ay * $ay);
}

function ramer_douglas_peucker(array $points, $epsilon) {
  if (count($points) < 2) {
    throw new InvalidArgumentException('Not enough points to simplify');
  }

  $dmax = 0;
  $index = 0;
  $end = count($points) - 1;
  $start_end_line = [$points[0], $points[$end]];
  for ($i = 1; $i < $end; $i++) {
    $dist = perpendicular_distance($points[$i], $start_end_line);
    if ($dist > $dmax) {
      $index = $i;
      $dmax = $dist;
    }
  }

  if ($dmax > $epsilon) {
    $new_start = ramer_douglas_peucker(array_slice($points, 0, $index + 1), $epsilon);
    $new_end = ramer_douglas_peucker(array_slice($points, $index), $epsilon);
    array_pop($new_start);
    return array_merge($new_start, $new_end);
  }


  return [ $points[0], $points[$end]];
}

$polyline = [
  [0,0],
  [1,0.1],
  [2,-0.1],
  [3,5],
  [4,6],
  [5,7],
  [6,8.1],
  [7,9],
  [8,9],
  [9,9],
];

$result = ramer_douglas_peucker($polyline, 1.0);
print "Result:\n";
foreach ($result as $point) {
  print $point[0] . ',' . $point[1] . "\n";
}