/// <summary>
/// 判断是否为凸多边形
/// </summary>
/// <param name="PG">PG多边形</param>
/// <returns>如果是凸多边形返回True，否则返回False。</returns>
public static Boolean IsConvexPolygon(PolygonI PG)
{
if (PG.Vertex == null)
{
return(false);
}
if (PG.Vertex.Count < 4)
{
return(true);
}
for (Int32 i = 0; i < PG.Vertex.Count; ++i)
{
LineD line = new LineD(PG.Vertex[i], PG.Vertex[(i + 1) % PG.Vertex.Count]);
Double flag = 0;
for (Int32 j = 0; j < PG.Vertex.Count; ++j)
{
Double result = LineAlgorithm.Position(line, PG.Vertex[j]);
if ((flag * result) < 0)//点在线的两侧则返回失败。
{
return(false);
}
if (result != 0)
{
flag = result;
}
}
}
return(true);
}
/// <summary>
/// 根据点P,Q,R三点确定一个圆,注意三点不能共线
/// </summary>
/// <param name="P">点P</param>
/// <param name="Q">点Q</param>
/// <param name="R">点R</param>
/// <returns>返回圆，如果圆不存在则返回null.</returns>
public static CircleD?CreateCircle(PointI P, PointI Q, PointI R)
{
if (DoubleAlgorithm.Equals(LineAlgorithm.Position(P, Q, R), 0))
{
return(null); //三点共线无法确定圆
}
//formula
//(x-a)^2+(y-b)^2=r^2
//f1:(x1-a)^2 + (y1-b)^2 = r^2
//f2:(x2-a)^2 + (y2-b)^2 = r^2
//f3:(x3-a)^2 + (y3-b)^2 = r^2
//f1=f2: x1^2-2ax1+y1^2-2by1= x2^2-2ax2+y2^2-2by2;
//a=(((X(1)^2-X(2)^2+Y(1)^2-Y(2)^2)*(Y(2)-Y(3)))-((X(2)^2-X(3)^2+Y(2)^2-Y(3)^2)*(Y(1)-Y(2))))/(2*(X(1)-X(2))*(Y(2)-Y(3))-2*(X(2)-X(3))*(Y(1)-Y(2)))
//b=(((X(1)^2-X(2)^2+Y(1)^2-Y(2)^2)*(X(2)-X(3)))-((X(2)^2-X(3)^2+Y(2)^2-Y(3)^2)*(X(1)-X(2))))/(2*(Y(1)-Y(2))*(X(2)-X(3))-2*(Y(2)-Y(3))*(X(1)-X(2)))
Double a = (Double)(((P.X * P.X - Q.X * Q.X + P.Y * P.Y - Q.Y * Q.Y) * (Q.Y - R.Y)) - ((Q.X * Q.X - R.X * R.X + Q.Y * Q.Y - R.Y * R.Y) * (P.Y - Q.Y))) / (Double)(2 * (P.X - Q.X) * (Q.Y - R.Y) - 2 * (Q.X - R.X) * (P.Y - Q.Y));
Double b = (Double)(((P.X * P.X - Q.X * Q.X + P.Y * P.Y - Q.Y * Q.Y) * (Q.X - R.X)) - ((Q.X * Q.X - R.X * R.X + Q.Y * Q.Y - R.Y * R.Y) * (P.X - Q.X))) / (Double)(2 * (P.Y - Q.Y) * (Q.X - R.X) - 2 * (Q.Y - R.Y) * (P.X - Q.X));
Double r = PointAlgorithm.Distance(P, new PointD(a, b));
return(new CircleD(a, b, r));
}
