opencvsharp 通过3点坐标计算半径,弧度,圆形
时间: 2023-07-28 07:13:33 浏览: 59
通过3点坐标计算圆形的方法是使用三角形相似性质和勾股定理,具体步骤如下:
1. 计算出三个点之间的距离,即AB、BC、CA的长度。
2. 判断三个点是否共线,如果共线则无法构成圆形,返回错误信息。
3. 计算出三角形ABC三边的中垂线交点O(即圆心)的坐标,可以使用向量法计算,具体可参考以下代码:
```csharp
// 计算向量AB和BC的中垂线的法向量
float ABx = b.X - a.X;
float ABy = b.Y - a.Y;
float ABz = b.Z - a.Z;
float BCx = c.X - b.X;
float BCy = c.Y - b.Y;
float BCz = c.Z - b.Z;
float ABBCx = ABy * BCz - ABz * BCy;
float ABBCy = ABz * BCx - ABx * BCz;
float ABBCz = ABx * BCy - ABy * BCx;
// 计算向量OA和OB的中点坐标
float OAx = (a.X + b.X) / 2;
float OAy = (a.Y + b.Y) / 2;
float OAz = (a.Z + b.Z) / 2;
float OBx = (b.X + c.X) / 2;
float OBy = (b.Y + c.Y) / 2;
float OBz = (b.Z + c.Z) / 2;
// 计算直线AB和BC的交点O
float t = (ABBCx * (OAx - OBx) + ABBCy * (OAy - OBy) + ABBCz * (OAz - OBz))
/ (ABBCx * ABBCx + ABBCy * ABBCy + ABBCz * ABBCz);
float Ox = OAx + ABBCx * t;
float Oy = OAy + ABBCy * t;
float Oz = OAz + ABBCz * t;
```
4. 计算出圆心到任意一点的距离即为半径R,可以使用勾股定理计算,具体可参考以下代码:
```csharp
float ABx = b.X - a.X;
float ABy = b.Y - a.Y;
float ABz = b.Z - a.Z;
float ACx = c.X - a.X;
float ACy = c.Y - a.Y;
float ACz = c.Z - a.Z;
float AB2 = ABx * ABx + ABy * ABy + ABz * ABz;
float AC2 = ACx * ACx + ACy * ACy + ACz * ACz;
float BC2 = (b.X - c.X) * (b.X - c.X) + (b.Y - c.Y) * (b.Y - c.Y) + (b.Z - c.Z) * (b.Z - c.Z);
float R = (float)Math.Sqrt(AB2 * AC2 * BC2) / (2 * Math.Sqrt((AB2 + AC2 + BC2) * (AC2 + BC2 - AB2) * (AB2 + BC2 - AC2)));
```
5. 计算圆心到任意一点的向量和X轴正方向的夹角即为弧度,可以使用反正切函数计算,具体可参考以下代码:
```csharp
float dx = b.X - Ox;
float dy = b.Y - Oy;
float radian = (float)Math.Atan2(dy, dx);
```
至此,我们已经完成了通过3点坐标计算圆形的过程。