基于C#的多边形冲突检测
Posted 王振耀
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之前在项目上碰到了一个多边形冲突检测的问题，经百度、bing、google，发现目前已有的方案，要么是场景覆盖不全，要么是通过第三方类库实现（而这些第三方类库几乎是无法逆向反编译的），而项目中禁止使用第三方类库，遂自己实现了此算法。
场景是这样的，有两个多边形，多边形A和多变型B，需要判断多边形B是否在多变型A内，即多边形B是否是多边形A的子多边形。
- B的点全部在A内
- A的点全部在B外
- A的线段与B的线段没有相交
接下来进行实现
第一步：创建多边形类
1 /// <summary> 2 /// 多边形 3 /// </summary> 4 public class Area_Dto 5 { 6 /// <summary> 7 /// 点的集合 8 /// </summary> 9 public List<Point_Dto> Points { get; set; } 10 /// <summary> 11 /// 线段的集合 12 /// </summary> 13 public List<LineSagement_Dto> LineSagements { get; set; } 14 }
第二步：创建点类
1 /// <summary> 2 /// 点 3 /// </summary> 4 public class Point_Dto 5 { 6 public Point_Dto(double x, double y) 7 { 8 this.X = x; 9 this.Y = y; 10 } 11 /// <summary> 12 /// 点的X坐标 13 /// </summary> 14 public double X { get; private set; } 15 /// <summary> 16 /// 点的Y坐标 17 /// </summary> 18 public double Y { get; private set; } 19 }
第三步：创建线段类
1 /// <summary> 2 /// 线段 3 /// </summary> 4 public class LineSagement_Dto 5 { 6 public LineSagement_Dto(Point_Dto start, Point_Dto end) 7 { 8 this.Start = start; 9 this.End = end; 10 GetFuncParam(this); 11 } 12 /// <summary> 13 /// 线段的起始点 14 /// </summary> 15 public Point_Dto Start { get; private set; } 16 /// <summary> 17 /// 线段的终止点 18 /// </summary> 19 public Point_Dto End { get; private set; } 20 /// <summary> 21 /// 线段的类型 22 /// </summary> 23 public LineType_Enum FunType { get; set; } 24 /// <summary> 25 /// 线段为斜线是才有实际作用 26 /// 线段的斜率及线段与Y轴的交点 27 /// </summary> 28 public List<double> Params { get; set; } = new List<double>(); 29 /// <summary> 30 /// 交点列表 31 /// </summary> 32 public List<Point_Dto> Intersection { get; set; } = new List<Point_Dto>(); 33 34 /// <summary> 35 /// 求当前线段的斜率，当当前线段为斜线时，同时是求出与Y轴的交点 36 /// </summary> 37 public void GetFuncParam(LineSagement_Dto lineSegment) 38 { 39 double x1 = this.Start.X; 40 double y1 = this.Start.Y; 41 double x2 = this.End.X; 42 double y2 = this.End.Y; 43 44 if (x1 == x2) 45 { 46 //type=2 47 this.FunType = LineType_Enum.XX; 48 this.Params.Add(x1); 49 50 } 51 else if (y1 == y2) 52 { 53 //type=1 54 this.FunType = LineType_Enum.YY; 55 this.Params.Add(y1); 56 } 57 else 58 { 59 //type=3 60 this.FunType = LineType_Enum.XnXYnY; 61 double a = (y2 - y1) / (x2 - x1);//斜率 62 double b = y1 - (x1 * ((y2 - y1) / (x2 - x1)));//与Y轴的交点 63 this.Params.Add(a); 64 this.Params.Add(b); 65 } 66 67 } 68 }
第四步：创建线段的类型枚举
1 /// <summary> 2 /// 线段的类型 3 /// </summary> 4 public enum LineType_Enum 5 { 6 /// <summary> 7 /// 竖线 8 /// </summary> 9 XX, 10 /// <summary> 11 /// 横线 12 /// </summary> 13 YY, 14 /// <summary> 15 /// 斜线 16 /// </summary> 17 XnXYnY 18 }
第五步：在多边形类中增加冲突检测方法
1 /// <summary> 2 /// 多边形冲突检测 3 /// </summary> 4 public bool CheckIfInArea(Area_Dto area) 5 { 6 if (area.LineSagements == null) 7 { 8 return true; 9 } 10 //若子点有在父外的则结束 11 foreach (Point_Dto point in this.Points) 12 { 13 if (!point.CheckIfInArea(area)) 14 return false; 15 } 16 //若父点有在子内的则结束 17 foreach (Point_Dto point in area.Points) 18 { 19 if (point.CheckIfInChildArea(this)) 20 return false; 21 } 22 //所有子线段与父线段没有相交则不冲突 23 if (WhetherPolygonIntersection(area)) 24 { 25 foreach (LineSagement_Dto edg in this.LineSagements) 26 { 27 if (edg.Intersection.Any()) 28 { 29 if (edg.FunType == LineType_Enum.XX) 30 { 31 List<Point_Dto> jiaodainList = edg.Intersection.OrderBy(m => m.Y).ToList(); 32 for (int i = 0; i < jiaodainList.Count - 1; i++) 33 { 34 Point_Dto start = jiaodainList[i]; 35 Point_Dto end = jiaodainList[i + 1]; 36 Point_Dto z = new Point_Dto(start.X, start.Y + ((end.Y - start.Y) / 2)); 37 if (z.CheckIfInArea(area)) 38 { 39 continue; 40 } 41 else 42 { 43 return false; 44 } 45 } 46 } 47 else if (edg.FunType == LineType_Enum.YY) 48 { 49 List<Point_Dto> jiaodainList = edg.Intersection.OrderBy(m => m.X).ToList(); 50 for (int i = 0; i < jiaodainList.Count - 1; i++) 51 { 52 Point_Dto start = jiaodainList[i]; 53 Point_Dto end = jiaodainList[i + 1]; 54 Point_Dto z = new Point_Dto(start.X + ((end.X - start.X) / 2), start.Y); 55 if (z.CheckIfInArea(area)) 56 { 57 continue; 58 } 59 else 60 { 61 return false; 62 } 63 } 64 } 65 else if (edg.FunType == LineType_Enum.XnXYnY) 66 { 67 if (edg.Start.Y <= edg.End.Y) 68 { 69 List<Point_Dto> jiaodainList = edg.Intersection.OrderBy(m => m.X).ThenBy(m => m.Y).ToList(); 70 for (int i = 0; i < jiaodainList.Count - 1; i++) 71 { 72 Point_Dto start = jiaodainList[i]; 73 Point_Dto end = jiaodainList[i + 1]; 74 Point_Dto z = new Point_Dto(start.X + ((end.X - start.X) / 2), start.Y + ((end.Y - start.Y) / 2)); 75 if (z.CheckIfInArea(area)) 76 { 77 continue; 78 } 79 else 80 { 81 return false; 82 } 83 } 84 } 85 else 86 { 87 List<Point_Dto> jiaodainList = edg.Intersection.OrderBy(m => m.X).ThenByDescending(m => m.Y).ToList(); 88 for (int i = 0; i < jiaodainList.Count - 1; i++) 89 { 90 Point_Dto start = jiaodainList[i]; 91 Point_Dto end = jiaodainList[i + 1]; 92 Point_Dto z = new Point_Dto(start.X + ((end.X - start.X) / 2), start.Y - ((start.Y - end.Y) / 2)); 93 if (z.CheckIfInArea(area)) 94 { 95 continue; 96 } 97 else 98 { 99 return false; 100 } 101 } 102 } 103 } 104 } 105 } 106 } 107 else 108 { 109 return true; 110 } 111 return true; 112 }
第六步：在点的类中增加点与线段关系的判断方法
1 /// <summary> 2 /// 此点向右引出的射线是否穿过sagement 3 /// 穿过的定义： 4 /// 此点在sagement的顶点上 5 /// 此点在sagement上 6 /// 此点不符合以上两种情况且此点引出的射线穿过sagement 7 /// </summary> 8 /// <param name="sagement"></param> 9 /// <returns>True:穿过线段 False:没有穿过线段</returns> 10 public PointWithLineSagementState_Enum CheckPointInLineSagement(LineSagement_Dto sagement) 11 { 12 double px = this.X; 13 double py = this.Y; 14 //bool flag = false; 15 16 17 Point_Dto pi = sagement.Start; 18 Point_Dto pj = sagement.End; 19 double sx = pi.X; double sy = pi.Y; 20 double tx = pj.X; double ty = pj.Y; 21 22 //点与线段顶点重合 23 bool psTf = (px == sx && py == sy); 24 bool ptTf = (px == tx && py == ty); 25 if (psTf || ptTf) 26 { 27 return PointWithLineSagementState_Enum.VertexOverlap; 28 } 29 switch (sagement.FunType) 30 { 31 case LineType_Enum.XX: 32 if (px == pi.X && ((py <= sy && py >= ty) || (py >= sy && py <= ty))) 33 return PointWithLineSagementState_Enum.OnLineSagement; 34 break; 35 case LineType_Enum.YY: 36 if (py == pi.Y && ((px >= sx && px <= tx) || (px <= sx && px >= tx))) 37 return PointWithLineSagementState_Enum.OnLineSagement; 38 break; 39 case LineType_Enum.XnXYnY: 40 default: 41 break; 42 } 43 //判断线段端点是否在射线两侧 44 if ((sy < py && ty >= py) || (sy >= py && ty < py)) 45 { 46 //线段上与射线Y坐标相同的点的X坐标 47 double x = sx + (py - sy) * (tx - sx) / (ty - sy); 48 //点在线段上 49 if (x == px) 50 { 51 return PointWithLineSagementState_Enum.OnLineSagement; 52 } 53 //射线穿过线段 54 if (x > px) 55 { 56 return PointWithLineSagementState_Enum.Cross; 57 } 58 } 59 return PointWithLineSagementState_Enum.UnCross; 60 } 61 62 /// <summary> 63 /// 点线的关系 64 /// </summary> 65 public enum PointWithLineSagementState_Enum 66 { 67 /// <summary> 68 /// 顶点重合 69 /// </summary> 70 VertexOverlap, 71 /// <summary> 72 /// 相交 73 /// </summary> 74 Cross, 75 /// <summary> 76 /// 不相交 77 /// </summary> 78 UnCross, 79 /// <summary> 80 /// 在线段上 81 /// </summary> 82 OnLineSagement 83 }
第七步：在点的类中实现子多边形的点是否在父多边形内的判断方法
1 /// <summary> 2 /// 子多边形的点是否在父多边形内 3 /// </summary> 4 /// <param name="theArea">父多边形</param> 5 /// <param name="vertexOverlap">当顶点重合时，是否算在图形内. 默认是算的</param> 6 /// <returns></returns> 7 public bool CheckIfInArea(Area_Dto theArea) 8 { 9 int cnt = 0; 10 foreach (LineSagement_Dto lineSagement in theArea.LineSagements) 11 { 12 switch (CheckPointInLineSagement(lineSagement)) 13 { 14 case PointWithLineSagementState_Enum.Cross: 15 cnt += 1; 16 break; 17 case PointWithLineSagementState_Enum.OnLineSagement: 18 return true; 19 case PointWithLineSagementState_Enum.VertexOverlap: 20 return true; 21 case PointWithLineSagementState_Enum.UnCross: 22 default: 23 break; 24 } 25 } 26 //射线穿过多边形边界的次数为奇数时点在多边形内 27 if (cnt % 2 == 1) 28 { 29 return true;//点在多边形内 30 } 31 else 32 { 33 return false;C#检测外键冲突的代码