/// <summary>Creates a unit vector perpendicular to the plane described by three spatial coordinates, suitable for being a surface normal.</summary>
/// <param name="a">The first spatial coordinate.</param>
/// <param name="b">The second spatial coordinate.</param>
/// <param name="c">The third spatial coordinate.</param>
/// <param name="normal">On success, receives the vector perpendicular to the described plane. On failure, receives Vector3f.Up.</param>
/// <returns>The success of the operation. This operation fails if the specified three vectors are colinear.</returns>
public static bool CreateNormal(Vector3f a, Vector3f b, Vector3f c, out Vector3f normal)
{
normal = Vector3f.Cross(b - a, c - a);
double norm = normal.X * normal.X + normal.Y * normal.Y + normal.Z * normal.Z;
if (norm != 0.0)
{
normal *= 1.0 / System.Math.Sqrt(norm);
return(true);
}
else
{
normal = Vector3f.Up;
return(false);
}
}
/// <summary>Checks whether three spatial coordinates are colinear.</summary>
/// <param name="a">The first spatial coordinate.</param>
/// <param name="b">The second spatial coordinate.</param>
/// <param name="c">The third spatial coordinate.</param>
/// <returns>A boolean indicating whether the three spatial coordinates are colinear.</returns>
public static bool AreColinear(Vector3f a, Vector3f b, Vector3f c)
{
Vector3f normal = Vector3f.Cross(b - a, c - a);
return(IsNullVector(normal));
}
