/// <summary>
/// Returns a value suitable for comparing the relative area of two triangles. (E.g.
/// Is triangle A larger than triangle B.)
/// </summary>
/// <remarks>
/// <para>
/// The value returned by this method can be converted to an area as follows:
/// <c>Area = Math.sqrt(value) / 2</c>
/// </para>
/// <para>
/// Useful for cheaply comparing the size of triangles.
/// </para>
/// </remarks>
/// <param name="a">Vertex A of triangle ABC.</param>
/// <param name="b">Vertex B of triangle ABC.</param>
/// <param name="c">Vertex C of triangle ABC.</param>
/// <returns>A value suitable for comparing the relative area of two triangles.</returns>
public static float GetAreaComp(Vector3 a, Vector3 b, Vector3 c)
{
// References:
// http://softsurfer.com/Archive/algorithm_0101/algorithm_0101.htm#Modern%20Triangles
// Get directional vectors.
Vector3 u = b - a; // A -> B
Vector3 v = c - a; // A -> C
// Cross product.
Vector3 n = new Vector3(u.y * v.z - u.z * v.y
, -u.x * v.z + u.z * v.x
, u.x * v.y - u.y * v.x);
return(Vector3Util.GetLengthSq(n));
}