C# 求点集的最小包围矩形，供大家参考，具体内容如下

思路：

1、求点集的中心点
2、将点集绕矩形进行一系列角度的旋转，并求记录旋转点集的包围矩形的面积和旋转角度；
3、将面积最小的矩形绕点集中心点旋转回去。

// 1.寻找多边形的中心 public XYZ GetCenter(List<XYZ> pts) { double sumx = 0; double sumy = 0; foreach (var p in pts) { sumx = sumx + p.X; sumy = sumy + p.Y; } var pt = new XYZ(sumx/pts.Count(),sumy/pts.Count(),0); return pt; } // 2.旋转多边形，针对每个点实现绕中心点旋转 public XYZ RotatePt(XYZ inpt ,XYZ centerPt ,double theta) { double ix = inpt.X; double iy = inpt.Y; double cx = centerPt.X; double cy = centerPt.Y; double Q = theta / 180 * 3.1415926; //角度 double ox, oy; ox = (ix - cx) * Math.Cos(Q) - (iy - cy) * Math.Sin(Q) + cx; //旋转公式 oy = (ix - cx) * Math.Sin(Q) + (iy - cy) * Math.Cos(Q) + cy; var outpt = new XYZ(ox,oy,0); return outpt; } // 3.多边形旋转后求简单外接矩形 public List<XYZ> GetRect(List<XYZ> inpts) { var outpts =new List<XYZ>(); int size = inpts.Count(); if (size == 0) return null; else { var tempx = new List<double>(); var tempy = new List<double>(); for (int i = 0; i < size; i++) { tempx.Add(inpts[i].X); tempy.Add(inpts[i].Y); } XYZ endpoint0 = new XYZ(tempx.Min(), tempy.Max(), 0); XYZ endpoint1 = new XYZ(tempx.Max(), tempy.Max(), 0); XYZ endpoint2 = new XYZ(tempx.Max(), tempy.Min(), 0); XYZ endpoint3 = new XYZ(tempx.Min(), tempy.Min(), 0); outpts.Add(endpoint0); outpts.Add(endpoint1); outpts.Add(endpoint2); outpts.Add(endpoint3); return outpts; } } // 4.存储每个旋转角度下多边形的外接矩形，记录外接矩形的顶点坐标、面积和此时多边形的旋转角度 public class RectData { public List<XYZ> boundary { get;set;} public XYZ center { get; set; } public double theta { get; set; } public double area { get; set; } } public RectData GetRotateRectDatas(List<XYZ> inpts, double theta) { XYZ center = GetCenter(inpts); var tempvertices = new List<XYZ>(); for (int i=0; i<inpts.Count();i++) { XYZ temp = RotatePt(inpts[i], center, theta); tempvertices.Add(temp); } List<XYZ> vertices = GetRect(tempvertices); double deltaX, deltaY; //求每个外接矩形的面积 deltaX = vertices[0].X - vertices[2].X; deltaY = vertices[0].Y - vertices[2].Y; var polygen = new RectData { area=Math.Abs(deltaY * deltaX), center= center, theta = theta, boundary= vertices }; return polygen; } //获取所有新的矩形 public List<RectData> GetAllNewRectDatas(List<XYZ> inpts) { var polygens =new List<RectData>(); for (int theta = 0; theta <= 90;) { polygens.Add(GetRotateRectDatas(inpts, theta)); theta = theta + 5; } return polygens; } //获取新的矩形 public RectData GetMinAreaRect(List<RectData> polygons) { double minarea = 100000000; int N =0; for ( int i=0; i< polygons.Count(); i++) { if (minarea > polygons[i].area) { minarea = polygons[i].area; N = i; } } var polygon = new RectData(); polygon = polygons[N]; //旋转到最小面积的方向 XYZ centerPt = GetCenter(polygon.boundary); var boundary = new List<XYZ>(); foreach(var bound in polygon.boundary) { XYZ pt = RotatePt(bound, polygon.center, -polygon.theta); boundary.Add(pt); } var outpolygon = new RectData { center= polygon.center, area = polygon.area, theta = polygon.theta, boundary = boundary }; return outpolygon;}

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