public static float Orient(Vertex a,
Vertex b,
Vertex c)
{
Matrix3 m = new Matrix3(a.x, a.y, 1,
b.x, b.y, 1,
c.x, c.y, 1);
return m.Determinant();
}
public bool CircumCircle(List<Vertex> verts, out Vertex center, out float radius)
{
// Calculate the circle that passes through 3 coplanar points
// http://mathworld.wolfram.com/Circle.html
Vertex p0 = verts[vertices[0]];
Vertex p1 = verts[vertices[1]];
Vertex p2 = verts[vertices[2]];
Matrix3 ma = new Matrix3(p0.x, p0.y, 1,
p1.x, p1.y, 1,
p2.x, p2.y, 1);
float a = ma.Determinant();
if (Math.Abs(a) < 1e-5f)
{
center = new Vertex(0, 0);
radius = 0;
return false;
}
Matrix3 md = new Matrix3(p0.x * p0.x + p0.y * p0.y, p0.y, 1,
p1.x * p1.x + p1.y * p1.y, p1.y, 1,
p2.x * p2.x + p2.y * p2.y, p2.y, 1);
float d = -md.Determinant();
Matrix3 me = new Matrix3(p0.x * p0.x + p0.y * p0.y, p0.x, 1,
p1.x * p1.x + p1.y * p1.y, p1.x, 1,
p2.x * p2.x + p2.y * p2.y, p2.x, 1);
float e = me.Determinant();
Matrix3 mf = new Matrix3(p0.x * p0.x + p0.y * p0.y, p0.x, p0.y,
p1.x * p1.x + p1.y * p1.y, p1.x, p1.y,
p2.x * p2.x + p2.y * p2.y, p2.x, p2.y);
float f = -mf.Determinant();
center = new Vertex(-d / (2 * a), -e / (2 * a));
radius = (float)Math.Sqrt((d * d + e * e) / (4 * a * a) - f / a);
return true;
}