//获取点集中，与指定点距离最大的点下标
private int GetMaxDistancePointIndex(ShootPoint P, ref List <ShootPoint> Points)
{
//构造间距（平方）序列
double[] Mat = new double[Points.Count];
//中间变量
ShootPoint TempPoint;
double DeltaX = 0;
double DeltaY = 0;
//填充序列
for (int i = 0; i < Points.Count; i++)
{
//获取对应的点
TempPoint = Points.ElementAt(i);
//计算坐标增量
DeltaX = TempPoint.X_Pos - P.X_Pos;
DeltaY = TempPoint.Y_Pos - P.Y_Pos;
//获取两点间距的平方（因为最终只是比大小，所以省去了开方这一步骤用以节省运算量）
Mat[i] = DeltaX * DeltaX + DeltaY * DeltaY;
}
//遍历间距序列，找到值最大的元素
return(Array.IndexOf(Mat, Mat.Max()));
}
//判断某点是否在圆范围内（在圆上和在圆内都算在圆范围内）
public bool isInThisCircle(ShootPoint Point)
{
double DeltaX = Point.X_Pos - Center.X_Pos;
double DeltaY = Point.Y_Pos - Center.Y_Pos;
//忽略0.01mm以内的偏差，防止出现边界情况导致错误
return((this.radius * this.radius + 1e-04) >= (DeltaX * DeltaX + DeltaY * DeltaY));
}
//以两点连线作为直径构造圆
public Circle(ShootPoint Point1, ShootPoint Point2)
{
//获取圆心坐标
double Center_X = (Point1.X_Pos + Point2.X_Pos) / 2;
double Center_Y = (Point1.Y_Pos + Point2.Y_Pos) / 2;
center = new ShootPoint(Center_X, Center_Y);
//计算半径
double DeltaX = center.X_Pos - Point2.X_Pos;
double DeltaY = center.Y_Pos - Point2.Y_Pos;
radius = Math.Sqrt(DeltaX * DeltaX + DeltaY * DeltaY);
}
//画一个点(此单位为mm，将在内部进行转换)
private void DrawPoint(ShootPoint P, Color color)
{
//申请一个蓝画刷
Pen pen = new Pen(color);
Graphics Grphc = this.GrphcBuf.Graphics;
//反向映射
int Point_X = (int)(P.X_Pos / mm_PixelRate_X);
int Point_Y = (int)(P.Y_Pos / mm_PixelRate_Y);
//获得外框矩形参数
Rectangle RecCenter = new Rectangle(Point_X - 4, Point_Y - 4, 8, 8);
//画圆心
Grphc.FillEllipse(pen.Brush, RecCenter);
//从缓冲区输出至图框
this.GrphcBuf.Render();
}
//以三个不共线的点确定的三角形构造圆，此时圆为三角形的外接圆
//若共线，则按照无参数方式构造空圆
public Circle(ShootPoint Point1, ShootPoint Point2, ShootPoint Point3)
{
//求从点1出发指向点2、3的向量
Vector2 Vec_1 = new Vector2(Point1, Point2);
Vector2 Vec_2 = new Vector2(Point1, Point3);
//如果斜率差小于一定阈值，则认为是一条直线
if (Vec_1.isCollinear(Vec_2))
{
center = new ShootPoint(0, 0);
radius = 0;
}
else
{
//求从点1出发指向点2、3向量的正交向量，作为其连线中垂线的方向向量
Vector2 Vector_1 = Vec_1.GetOrthogonalVector();
Vector2 Vector_2 = Vec_2.GetOrthogonalVector();
//获取两直线中点
ShootPoint CenterPoint1 = new ShootPoint((Point1.X_Pos + Point2.X_Pos) / 2, (Point1.Y_Pos + Point2.Y_Pos) / 2);
ShootPoint CenterPoint2 = new ShootPoint((Point1.X_Pos + Point3.X_Pos) / 2, (Point1.Y_Pos + Point3.Y_Pos) / 2);
///则直线参数方程可以是：直线上某点P = CenterPoint + k * Vector_1.其中，k为任意实数。
//据参数方程求中垂线交点参数
double k1 = (Vector_2.X * (CenterPoint1.Y_Pos - CenterPoint2.Y_Pos)
+ Vector_2.Y * (CenterPoint2.X_Pos - CenterPoint1.X_Pos))
/ (Vector_1.X * Vector_2.Y - Vector_2.X * Vector_1.Y);
//求得交点坐标,即为圆心坐标
center = new ShootPoint(new Vector2(CenterPoint1) + k1 * Vector_1);
///验证正确性用
//double k2 = (k1 * Vector_1.Y + CenterPoint1.Y_Pos - CenterPoint2.Y_Pos) / Vector_2.Y;
//ShootPoint CheckCenter = new ShootPoint(new Vector2(CenterPoint2) + k2 * Vector_2);
//计算半径
double DeltaX = Point1.X_Pos - Center.X_Pos;
double DeltaY = Point1.Y_Pos - Center.Y_Pos;
radius = Math.Sqrt(DeltaX * DeltaX + DeltaY * DeltaY);
}
}
public Vector2(ShootPoint Src, ShootPoint Aim)
{
x = Aim.X_Pos - Src.X_Pos;
y = Aim.Y_Pos - Src.Y_Pos;
}
public Vector2(ShootPoint Point)
{
x = Point.X_Pos;
y = Point.Y_Pos;
}
//构造空圆
public Circle()
{
center = new ShootPoint(0, 0);
radius = 0;
}
//以圆心和半径构造圆
public Circle(ShootPoint Center, double R)
{
center = Center;
radius = R;
}
//从已经确定在圆上的一点和其他三点中确定最小包络圆
private Circle GetNewCircle(ShootPoint P_Certain, ref List <ShootPoint> CirclePoints)
{
List <ShootPoint> Points = new List <ShootPoint>();
List <ShootPoint> AllPoints = CirclePoints.GetRange(0, CirclePoints.Count);
//添加必在圆上的点到点集中
Points.Add(P_Certain);
AllPoints.Add(P_Certain);
//第一轮尝试
Points.Add(CirclePoints.ElementAt(0));
Points.Add(CirclePoints.ElementAt(1));
//求出此三点的最小包络圆
Circle MinCircle = GetMinCircleOf3Points(ref Points);
//判断是否包含所有点
if (isAllPointsInCircle(ref AllPoints, MinCircle))
{
//仅保留在圆上的点，用于优化算法运行速度
CirclePoints = Points;
return(MinCircle);
}
else if (CirclePoints.Count < 3)
{
//如果在圆上的点比3小，就说明用于输入函数的点一定全拿来生成新圆了
//如此还没通过上面的条件，那么一定是前面的运算中哪里算错了。
return(new Circle());
}
//第二轮尝试
if (Points.Count == 3)
{
//如果在生成上一个圆时，三个点都在圆上，拿掉最后面的点。
Points.RemoveAt(2);
}
Points.Add(CirclePoints.ElementAt(2));
//求出此三点的最小包络圆
MinCircle = GetMinCircleOf3Points(ref Points);
//判断是否包含所有点
if (isAllPointsInCircle(ref AllPoints, MinCircle))
{
//仅保留在圆上的点，用于优化算法运行速度
CirclePoints = Points;
return(MinCircle);
}
//最后一轮尝试
if (Points.Count == 3)
{
//如果在生成上一个圆时，三个点都在圆上，拿掉1点。
Points.RemoveAt(1);
}
Points.Add(CirclePoints.ElementAt(1));
//求出此三点的最小包络圆
MinCircle = GetMinCircleOf3Points(ref Points);
//判断是否包含所有点
if (isAllPointsInCircle(ref AllPoints, MinCircle))
{
//仅保留在圆上的点，用于优化算法运行速度
CirclePoints = Points;
return(MinCircle);
}
//按道理讲不会到这里，若到了这里，说明出现了输入上的问题。
return(new Circle());
}
