參考資料：

https://download.csdn.net/download/u010991835/10223982

http://www.cnblogs.com/HolyChen/p/5982184.html

傳進來點集，輸出凸包的點集：

#region 計算點的凸包，並返回凸包的點集
		public static List<XYZ> GetConvexHullPoints(List<XYZ> points)
		{
			List<Segment> segments = new List<Segment>();
			segments = GetAllSegments(points);
			List<XYZ> ProcessingPoints = new List<XYZ>();
			int i = 0;
			int j = 0;
			for (i = 0; i < segments.Count; )
			{
				//ProcessingPoints will be the points that are not in the current segment
				ProcessingPoints = new List<XYZ>(points);

				for (j = 0; j < ProcessingPoints.Count; )
				{

					if (segments[i].contains(ProcessingPoints[j]))
					{
						ProcessingPoints.Remove(ProcessingPoints[j]);
						j = 0;
						continue;
					}
					j++;

				}

				if (!isEdge(ProcessingPoints, segments[i]))
				{
					segments.Remove(segments[i]);
					i = 0;
					continue;
				}
				else
				{ i++; }
			}
			return segments.Select(x => x.p).ToList();
		}

		private static bool isEdge(List<XYZ> processingPoints, Segment edge)
		{
			for (int k = 0; k < processingPoints.Count; k++)
			{
				if (IsLeft(edge, processingPoints[k]))
				{
					return false;
				}
			}
			return true;
		}
		private static bool IsLeft(Segment segment, XYZ r)
		{
			double D = 0;
			double px, py, qx, qy, rx, ry = 0;
			//The determinant
			// | 1 px py |
			// | 1 qx qy |
			// | 1 rx ry |
			//if the determinant result is positive then the point is left of the segment
			px = segment.p.X;
			py = segment.p.Y;
			qx = segment.q.X;
			qy = segment.q.Y;
			rx = r.X;
			ry = r.Y;

			D = ((qx * ry) - (qy * rx)) - (px * (ry - qy)) + (py * (rx - qx));

			if (D <= 0)
				return false;

			return true;
		}
		private static List<Segment> GetAllSegments(List<XYZ> points)
		{
			List<Segment> segments = new List<Segment>();
			//Initialize all possible segments from the picked points
			for (int i = 0; i < points.Count; i++)
			{
				for (int j = 0; j < points.Count; j++)
				{
					if (i != j)
					{
						Segment op = new Segment();
						XYZ p1 = points[i];
						XYZ p2 = points[j];
						op.p = p1;
						op.q = p2;

						segments.Add(op);
					}
				}
			}
			return segments;
		}
		public struct Segment
		{
			public XYZ p;
			public XYZ q;

			public bool contains(XYZ point)
			{
				if (p.IsAlmostEqualTo(point) || q.IsAlmostEqualTo(point))
					return true;
				return false;
			}

		}

		#endregion
 

進一步改進演算法，這裡的segement點不是按照順序連起來的，那麼需要讓點按照順序串聯起來需要進一步判斷。

public static List<XYZ> GetConvexHullPoints(List<XYZ> points)
		{
			List<Segment> segments = new List<Segment>();
			segments = GetAllSegments(points);
			List<XYZ> ProcessingPoints = new List<XYZ>();
			int i = 0;
			int j = 0;
			for (i = 0; i < segments.Count; )
			{
				//ProcessingPoints will be the points that are not in the current segment
				ProcessingPoints = new List<XYZ>(points);

				for (j = 0; j < ProcessingPoints.Count; )
				{

					if (segments[i].contains(ProcessingPoints[j]))
					{
						ProcessingPoints.Remove(ProcessingPoints[j]);
						j = 0;
						continue;
					}
					j++;

				}

				if (!isEdge(ProcessingPoints, segments[i]))
				{
					segments.Remove(segments[i]);
					i = 0;
					continue;
				}
				else
				{ i++; }
			}
			List<XYZ> xyzList = new List<XYZ>();
			xyzList.Add(segments[0].StartPoint);
			xyzList.Add(segments[0].EndPoint);
			segments.RemoveAt(0);
			while(segments.Count!=0)
			{
				bool hasContinuePoint = false;
				for (int ii=0;ii<segments.Count;ii++)
				{
					if (xyzList.Last().IsAlmostEqualTo(segments[ii].StartPoint))
					{
						xyzList.Add(segments[ii].EndPoint);
						hasContinuePoint = true;
						segments.RemoveAt(ii);
						break;
					}
					if (hasContinuePoint == false && xyzList.Last().IsAlmostEqualTo(segments[ii].EndPoint))
					{
						xyzList.Add(segments[ii].StartPoint);
						segments.RemoveAt(ii);
						break;
					}
				}
			}

			return xyzList;
		}