「C#学习笔记」三点定位算法

自己写的，可能还有很多不足，看着哪里不对的求提出，我改~

先上代码，然后解释我的想法

 1 namespace ThreePointOrientation
 2 {
 3     class Program
 4     {
 5         struct Point
 6         {
 7             public int x;
 8             public int y;
 9         }
10         static Point ThreePointOrientation(Point A, Point B, Point C, int lenAZ, int lenBZ, int lenCZ)
11         {
12             Point A1, B1, C1, Min, B2, Z2, Z1, ZZ1, inA1B1;14             //1
15             if (A.x <= B.x && A.x <= C.x)
16             { A1 = A; B1 = B; C1 = C; }
17             else if (B.x <= A.x && B.x <= C.x)
18             { A1 = B; B1 = C; C1 = A; }
19             else
20             { A1 = C; B1 = A; C1 = B; }
21             Min = A1;
22             //2
23             A1.x = 0; A1.y = 0;
24             B1.x -= Min.x; B1.y -= Min.y;
25             C1.x -= Min.x; C1.y -= Min.y;
26             //3
27             int lenAB = (int)System.Math.Sqrt(B1.x*B1.x + B1.y*B1.y);32             B2.x = lenAB; B2.y = 0;
33             //4
34             Z2.x = (lenAZ * lenAZ + lenAB * lenAB - lenBZ * lenBZ) / (2 * lenAB);
35             Z2.y = (int)System.Math.Sqrt(lenAZ*lenAZ-Z2.x*Z2.x);
36             //5
37             float tanBAB = (float)B1.y / (float)B1.x;
38             float tanCAC = (float)Z2.y / (float)Z2.x;
39             float tanCAB2;
40             if (B1.y >= 0)
41                 tanCAB2 = (tanBAB+tanCAC)/(1-tanBAB*tanCAC);
42             else
43                 tanCAB2 = (tanCAC-tanBAB)/(1+tanCAC*tanBAB);
44             //6
45             Z1.x = (int)((float)lenAZ / (System.Math.Sqrt(tanCAB2 * tanCAB2 + 1)));
46             Z1.y = (int)(tanCAB2 * Z1.x);
47             //7
48             inA1B1.x = (A1.x + B1.x) / 2;
49             inA1B1.y = (A1.y + B1.y) / 2;
50             //8
51             ZZ1.x = inA1B1.x * 2 - Z1.x;
52             ZZ1.y = inA1B1.y * 2 - Z1.y;
53             //9
54             int lenZZ1C1 = (int)System.Math.Sqrt(System.Math.Pow(ZZ1.x - C1.x, 2) + System.Math.Pow(ZZ1.y - C1.y, 2));
55             int lenZ1C1 = (int)System.Math.Sqrt(System.Math.Pow(Z1.x - C1.x, 2) + System.Math.Pow(Z1.y - C1.y, 2));
56             if((lenZZ1C1-lenCZ)<(lenZ1C1-lenCZ))
57                 Z1 = ZZ1;
58             //10
59             Z1.x += Min.x;
60             Z1.y += Min.y;
61 
62             return Z1;
63         }
64         static void Main(string[] args)
65         {
66             Point a, b, c, z;
67             int az, bz, cz;
68             a.x = -5;
69             a.y = -5;
70             b.x = 47;
71             b.y = 25;
72             c.x = -5;
73             c.y = 55;
74             az = 34;
75             bz = 34;
76             cz = 34;
77             z = ThreePointOrientation(a, b, c, az, bz, cz);
78             Console.WriteLine("x = {0}, y = {1}
", z.x, z.y);
79             Console.ReadKey();
80         }
81     }
82 }

主要就是函数Point ThreePointOrientation(Point A, Point B, Point C, int lenAZ, int lenBZ, int lenCZ);

A,B,C是已知的三点，lenAZ,lenBZ,lenCZ分别是三点到要求的点的距离，函数返回要求的点的坐标。

我的想法......

1.把ABC三点中x值最小的赋值给A1，另外两点分别给B1和C1，并记录A1的值给Min

2.把A1B1C1这个三角形平移至A1在原点处（即三个点分别减去Min）

3.计算A1B1距离lenAB，记B2(lenAB, 0)。（相当于把边A1B1旋转到与x轴重合，得到A1B2）

4.根据A1B2的坐标和lenAZ、lenBZ的值可以很容易算出Z2的坐标（Z2为经过平移和旋转之后的要求的点）

5.6.利用公式求得Z1（其实通过A1、B1两点及AZ、BZ两条边能确定的点有两个，如图的Z1和ZZ1）

7.8.9.求出另一个点ZZ1，判断C1Z1、C1ZZ1哪个与CZ更相近，把相近的点赋值给Z1

10.把Z1点平移回去（加上Min）即得Z