public static DXY Circumcenter(DXY A, DXY B, DXY C)
{
double px = B.X - A.X;
double py = B.Y - A.Y;
double qx = C.X - A.X;
double qy = C.Y - A.Y;
double x = A.X + (qy * (px * px + py * py) - py * (qx * qx + qy * qy)) / (px * qy - py * qx) / 2;
double y = (py != 0)
? (px * (A.X + B.X - x - x) + py * (A.Y + B.Y)) / py / 2
: (qx * (A.X + C.X - x - x) + qy * (A.Y + C.Y)) / qy / 2;
return(new DXY(x, y));
/*
* double a = Length(B, C);
* double b = Length(C, A);
* double c = Length(A, B);
*
* double a2 = a * a;
* double b2 = b * b;
* double c2 = c * c;
*
* double denominator = a2 * (b2 + c2 - a2) + b2 * (a2 + c2 - b2) + c2 * (a2 + b2 - c2);
* double x = a2 * (b2 + c2 - a2) * A.X + b2 * (a2 + c2 - b2) * B.X + c2 * (a2 + b2 - c2) * C.X
* / denominator;
* double y = a2 * (b2 + c2 - a2) * A.Y + b2 * (a2 + c2 - b2) * B.Y + c2 * (a2 + b2 - c2) * C.Y
* / denominator;
*
* return new DXY(x, y);
*/
}
public static double Length(DXY p, DXY q)
{
double x = p.X - q.X;
double y = p.Y - q.Y;
return(Math.Sqrt(x * x + y * y));
}
public static bool IsOneLine(DXY a, DXY b, DXY c)
{
return(a.Y * (b.X - c.X) + b.Y * (c.X - a.X) + c.Y * (a.X - b.X) == 0);
}