基於C#實現的多邊形沖突檢測實例
前言
之前在項目上碰到瞭一個多邊形沖突檢測的問題，經百度、bing、google，發現目前已有的方案，要麼是場景覆蓋不全，要麼是通過第三方類庫實現（而這些第三方類庫幾乎是無法逆向反編譯的），而項目中禁止使用第三方類庫，遂自己實現瞭此算法。
場景是這樣的，有兩個多邊形，多邊形A和多變型B，需要判斷多邊形B是否在多變型A內，即多邊形B是否是多邊形A的子多邊形。
- B的點全部在A內
- A的點全部在B外
- A的線段與B的線段沒有相交
接下來進行實現
第一步：創建多邊形類
1 /// <summary>
2 /// 多邊形
3 /// </summary>
4 public class Area_Dto
5 {
6 /// <summary>
7 /// 點的集合
8 /// </summary>
9 public List<Point_Dto> Points { get; set; }
10 /// <summary>
11 /// 線段的集合
12 /// </summary>
13 public List<LineSagement_Dto> LineSagements { get; set; }
14 }
多邊形
第二步：創建點類
1 /// <summary>
2 /// 點
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 /// 點的X坐標
13 /// </summary>
14 public double X { get; private set; }
15 /// <summary>
16 /// 點的Y坐標
17 /// </summary>
18 public double Y { get; private set; }
19 }
點
第三步：創建線段類
1 /// <summary>
2 /// 線段
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 /// 線段的起始點
14 /// </summary>
15 public Point_Dto Start { get; private set; }
16 /// <summary>
17 /// 線段的終止點
18 /// </summary>
19 public Point_Dto End { get; private set; }
20 /// <summary>
21 /// 線段的類型
22 /// </summary>
23 public LineType_Enum FunType { get; set; }
24 /// <summary>
25 /// 線段為斜線是才有實際作用
26 /// 線段的斜率及線段與Y軸的交點
27 /// </summary>
28 public List<double> Params { get; set; } = new List<double>();
29 /// <summary>
30 /// 交點列表
31 /// </summary>
32 public List<Point_Dto> Intersection { get; set; } = new List<Point_Dto>();
33
34 /// <summary>
35 /// 求當前線段的斜率，當當前線段為斜線時，同時是求出與Y軸的交點
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)));//與Y軸的交點
63 this.Params.Add(a);
64 this.Params.Add(b);
65 }
66
67 }
68 }
線段
第四步：創建線段的類型枚舉
/// <summary>
/// 線段的類型
/// </summary>
public enum LineType_Enum
{
/// <summary>
/// 豎線
/// </summary>
XX,
/// <summary>
/// 橫線
/// </summary>
YY,
/// <summary>
/// 斜線
/// </summary>
XnXYnY
}
第五步：在多邊形類中增加沖突檢測方法
1 /// <summary>
2 /// 多邊形沖突檢測
3 /// </summary>
4 public bool CheckIfInArea(Area_Dto area)
5 {
6 if (area.LineSagements == null)
7 {
8 return true;
9 }
10 //若子點有在父外的則結束
11 foreach (Point_Dto point in this.Points)
12 {
13 if (!point.CheckIfInArea(area))
14 return false;
15 }
16 //若父點有在子內的則結束
17 foreach (Point_Dto point in area.Points)
18 {
19 if (point.CheckIfInChildArea(this))
20 return false;
21 }
22 //所有子線段與父線段沒有相交則不沖突
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 }
多邊形沖突檢測
第六步：在點的類中增加點與線段關系的判斷方法
1 /// <summary>
2 /// 此點向右引出的射線是否穿過sagement
3 /// 穿過的定義：
4 /// 此點在sagement的頂點上
5 /// 此點在sagement上
6 /// 此點不符合以上兩種情況且此點引出的射線穿過sagement
7 /// </summary>
8 /// <param name="sagement"></param>
9 /// <returns>True:穿過線段 False:沒有穿過線段</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 //點與線段頂點重合
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 //判斷線段端點是否在射線兩側
44 if ((sy < py && ty >= py) || (sy >= py && ty < py))
45 {
46 //線段上與射線Y坐標相同的點的X坐標
47 double x = sx + (py - sy) * (tx - sx) / (ty - sy);
48 //點在線段上
49 if (x == px)
50 {
51 return PointWithLineSagementState_Enum.OnLineSagement;
52 }
53 //射線穿過線段
54 if (x > px)
55 {
56 return PointWithLineSagementState_Enum.Cross;
57 }
58 }
59 return PointWithLineSagementState_Enum.UnCross;
60 }
61
62 /// <summary>
63 /// 點線的關系
64 /// </summary>
65 public enum PointWithLineSagementState_Enum
66 {
67 /// <summary>
68 /// 頂點重合
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 /// 在線段上
81 /// </summary>
82 OnLineSagement
83 }
點與線段關系的判斷
第七步：在點的類中實現子多邊形的點是否在父多邊形內的判斷方法
1 /// <summary>
2 /// 子多邊形的點是否在父多邊形內
3 /// </summary>
4 /// <param name="theArea">父多邊形</param>
5 /// <param name="vertexOverlap">當頂點重合時，是否算在圖形內. 默認是算的</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 //射線穿過多邊形邊界的次數為奇數時點在多邊形內
27 if (cnt % 2 == 1)
28 {
29 return true;//點在多邊形內
30 }
31 else
32 {
33 return false;//點不在多邊形內
34 }
35 }
子多邊形的點是否在父多邊形內
第八步：在點的類中實現父多邊形的點是否在子多邊形內的判斷方法
1 /// <summary>
2 /// 父多邊形的點是否在子多邊形內
3 /// </summary>
4 /// <param name="theArea"></param>
5 /// <returns></returns>
6 public bool CheckIfInChildArea(Area_Dto theArea)
7 {
8 int cnt = 0;
9 foreach (LineSagement_Dto lineSagement in theArea.LineSagements)
10 {
11 switch (CheckPointInLineSagement(lineSagement))
12 {
13 case PointWithLineSagementState_Enum.Cross:
14 cnt += 1;
15 break;
16 case PointWithLineSagementState_Enum.OnLineSagement:
17 return false;
18 case PointWithLineSagementState_Enum.VertexOverlap:
19 return false;
20 case PointWithLineSagementState_Enum.UnCross:
21 default:
22 break;
23 }
24 }
25 //射線穿過多邊形邊界的次數為奇數時點在多邊形內
26 if (cnt % 2 == 1)
27 {
28 return true;//點在多邊形內
29 }
30 else
31 {
32 return false;//點不在多邊形內
33 }
34 }
父多邊形的點是否在子多邊形內
第九步：在多邊形的類中實現多邊形自身的線段是否與另外一個多邊形的所有線段相交的方法
1 /// <summary>
2 /// 線段是否與多邊形的所有線段有相交
3 /// True:是
4 /// False:否
5 /// </summary>
6 public bool WhetherPolygonIntersection(Area_Dto father)
7 {
8 List<LineSagement_Dto> childEdgeXfatherEdge_List = new List<LineSagement_Dto>();
9 foreach (LineSagement_Dto edg in this.LineSagements)
10 {
11 Point_Dto a = edg.Start;
12 Point_Dto b = edg.End;
13 foreach (LineSagement_Dto fatherEdge in father.LineSagements)
14 {
15 Point_Dto c = fatherEdge.Start;
16 Point_Dto d = fatherEdge.End;
17
18 double denominator = (b.Y - a.Y) * (d.X - c.X) - (a.X - b.X) * (c.Y - d.Y);
19 // 如果分母為0 則平行或共線, 不相交
20 if (denominator == 0)
21 {
22 //豎線
23 if (edg.FunType == LineType_Enum.XX)
24 {
25 //共線
26 if (edg.Start.X == fatherEdge.Start.X)
27 {
28 //不重疊
29 if (b.Y > c.Y || a.Y < d.Y)
30 {
31 continue;
32 }
33 //完全重疊
34 if (a.Y == c.Y && b.Y == d.Y)
35 {
36 continue;
37 }
38 //上跨立（包含兩線相接）
39 if (a.Y > c.Y && b.Y <= c.Y && b.Y >= d.Y)
40 {
41 edg.Intersection.Add(c);
42 continue;
43 }
44 //下跨立（包含兩線相接）
45 if (a.Y <= c.Y && a.Y >= d.Y && b.Y < d.Y)
46 {
47 edg.Intersection.Add(d);
48 continue;
49 }
50 //父包子
51 if (c.Y >= a.Y && d.Y <= b.Y)
52 {
53 continue;
54 }
55 //子包父
56 if (a.Y >= c.Y && b.Y <= d.Y)
57 {
58 edg.Intersection.Add(c);
59 edg.Intersection.Add(d);
60 continue;
61 }
62 }
63 //平行
64 else
65 {
66 continue;
67 }
68 }
69
70 //橫線
71 else if (edg.FunType == LineType_Enum.YY)
72 {
73 //共線
74 if (edg.Start.Y == fatherEdge.Start.Y)
75 {
76 //不重疊
77 if (b.X < c.X || a.X > d.X)
78 {
79 continue;
80 }
81 //完全重疊
82 if (a.X == c.X && b.X == d.X)
83 {
84 continue;
85 }
86 //左跨立（包含兩線相接）
87 if (a.X < c.X && b.X >= c.X && b.X <= d.X)
88 {
89 edg.Intersection.Add(c);
90 continue;
91 }
92 //右跨立（包含兩線相接）
93 if (b.X > d.X && a.X >= c.X && a.X <= d.X)
94 {
95 edg.Intersection.Add(d);
96 continue;
97 }
98 //父包子
99 if (c.X <= a.X && d.X >= b.X)
100 {
101 continue;
102 }
103 //子包父
104 if (a.X <= c.X && b.X >= d.X)
105 {
106 edg.Intersection.Add(c);
107 edg.Intersection.Add(d);
108 continue;
109 }
110 }
111 //平行
112 else
113 {
114 continue;
115 }
116 }
117 //斜線
118 else if (edg.FunType == LineType_Enum.XnXYnY)
119 {
120 //共線
121 if (edg.Params.First().Equals(fatherEdge.Params.First()) && edg.Params.Last().Equals(fatherEdge.Params.Last()))
122 {
123 //不重疊
124 if ((a.X < c.X && b.X < c.X)
125 || (a.X > d.X && b.X > d.X))
126 {
127 continue;
128 }
129 //完全重疊
130 if (a.X == c.X && a.Y == c.Y && b.X == d.X && b.Y == d.Y)
131 {
132 continue;
133 }
134 //跨立（包含兩線相接）
135 if (a.X < c.X && b.X >= c.X && b.X <= d.X)
136 {
137 edg.Intersection.Add(c);
138 continue;
139 }
140 //跨立（包含兩線相接）
141 if (a.X >= c.X && a.X <= d.X && b.X > d.X)
142 {
143 edg.Intersection.Add(d);
144 continue;
145 }
146 //父包子
147 if (a.X >= c.X && a.X <= d.X && b.X >= c.X && b.X <= d.X)
148 {
149 continue;
150 }
151 //子包父
152 if (a.X <= c.X && b.X >= d.X)
153 {
154 edg.Intersection.Add(c);
155 edg.Intersection.Add(d);
156 continue;
157 }
158 }
159 //平行
160 else
161 {
162 continue;
163 }
164 }
165 }
166 // 線段所在直線的交點坐標 (x , y)
167 double x = ((b.X - a.X) * (d.X - c.X) * (c.Y - a.Y)
168 + (b.Y - a.Y) * (d.X - c.X) * a.X
169 - (d.Y - c.Y) * (b.X - a.X) * c.X) / denominator;
170 double y = -((b.Y - a.Y) * (d.Y - c.Y) * (c.X - a.X)
171 + (b.X - a.X) * (d.Y - c.Y) * a.Y
172 - (d.X - c.X) * (b.Y - a.Y) * c.Y) / denominator;
173 // 判斷交點是否在兩條線段上
174 if (
175 // 交點在線段1上
176 (x - a.X) * (x - b.X) <= 0 && (y - a.Y) * (y - b.Y) <= 0
177 // 且交點也在線段2上
178 && (x - c.X) * (x - d.X) <= 0 && (y - c.Y) * (y - d.Y) <= 0)
179 {
180 edg.Intersection.Add(new Point_Dto(x, y));
181 }
182 else
183 {
184 continue;
185 }
186 }
187 }
188 if (this.LineSagements.Where(m => m.Intersection.Any()).Any())
189 {
190 return true;
191 }
192 else
193 {
194 return false;
195 }
196 }
線段是否與多邊形的所有線段有相交
總結
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