/// <summary> Attempts to calculate a sphere with center in 'c' and radius 'r' from four points </summary>
public static bool TryCreate(Vector3 v0, Vector3 v1, Vector3 v2, Vector3 v3, out Vector3 c, out float r)
{
c = default;
r = default;
var p = new float[4, 4]
{
{ v0.x, v0.y, v0.z, 1.0f },
{ v1.x, v1.y, v1.z, 1.0f },
{ v2.x, v2.y, v2.z, 1.0f },
{ v3.x, v3.y, v3.z, 1.0f }
};
var a = new float[4, 4];
// Find minor 1, 1.
for (int i = 0; i < 4; i++)
{
a[i, 0] = p[i, 0];
a[i, 1] = p[i, 1];
a[i, 2] = p[i, 2];
}
float detM11 = Mathx.Determinant(a);
if (Mathx.IsZero(detM11))
{
return(false);
}
for (int i = 0; i < 4; i++)
{
a[i, 0] = p[i, 0] * p[i, 0] + p[i, 1] * p[i, 1] + p[i, 2] * p[i, 2];
}
for (int i = 0; i < 4; i++)
{
a[i, 1] = p[i, 1];
a[i, 2] = p[i, 2];
}
float detM12 = Mathx.Determinant(a);
for (int i = 0; i < 4; i++)
{
a[i, 1] = p[i, 0];
a[i, 2] = p[i, 2];
}
float detM13 = Mathx.Determinant(a);
for (int i = 0; i < 4; i++)
{
a[i, 1] = p[i, 0];
a[i, 2] = p[i, 1];
}
float detM14 = Mathx.Determinant(a);
for (int i = 0; i < 4; i++)
{
a[i, 1] = p[i, 0];
a[i, 2] = p[i, 1];
a[i, 3] = p[i, 2];
}
float detM15 = Mathx.Determinant(a);
c.x = 0.5f * detM12 / detM11;
c.y = -0.5f * detM13 / detM11;
c.z = 0.5f * detM14 / detM11;
r = Mathf.Sqrt(c.x * c.x + c.y * c.y + c.z * c.z - detM15 / detM11);
return(true);
}
