PointReducer.cs

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;

namespace ReducePoints
{
    public class PointReducer
    {
        private readonly List<XYPoint> _input;

        public PointReducer(IEnumerable<XYPoint> input)
        {
            _input = input.ToList();
        }

        public IEnumerable<XYPoint> Reduce(double start, double end, int restrict)
        {
            var counter = 0;
            foreach (var range in EnumrateRestrictedRangeCollection(start, end, restrict))
            {
                var tempList = new List<XYPoint>();

                while ( counter < _input.Count && _input[counter].X < range)
                {
                    tempList.Add( _input[counter]);
                    counter++;
                }

                foreach (var xyPoint in EnumrateReducedList(tempList))
                {
                    yield return xyPoint;
                }
            }
        }

        private static IEnumerable<XYPoint> EnumrateReducedList(List<XYPoint> tempList)
        {
            if (tempList.Count <= 0)
            {
                yield break;
            }

            var orderedTempList = tempList.OrderBy(point => point.Y);
            var returnArray = new[]
                                  {
                                      tempList.First(),
                                      tempList.Last(),
                                      orderedTempList.First(),
                                      orderedTempList.Last(),
                                  }.Distinct().OrderBy(point => point.X);

            foreach (var xyPoint in returnArray)
            {
                yield return xyPoint;
            }
        }

        IEnumerable<double> EnumrateRestrictedRangeCollection(double start, double end, int restrict)
        {
            var distance = (end - start) / restrict;

            for (var i = 1; i < restrict; i++)
            {
                yield return start + distance * i;
            }
            yield return end;
        }
    }
}