/// <summary>
/// Calculates the rotational inertia for a polygon with a given mass
/// Passed in polygon does not need to be in local space
/// </summary>
/// <param name="polygon"></param>
/// <param name="mass"></param>
/// <returns></returns>
public static float GetInertiaForPolygon(gxtPolygon polygon, float mass)
{
gxtDebug.Assert(polygon.NumVertices >= 3);
// perform a deep copy so we don't corrupt the values of the polygon
Vector2[] vertices = new Vector2[polygon.NumVertices];
for (int i = 0; i < vertices.Length; ++i)
{
vertices[i] = polygon.v[i];
}
Vector2 centroid = polygon.GetCentroid();
if (centroid != Vector2.Zero)
{
for (int i = 0; i < vertices.Length; ++i)
{
vertices[i] -= centroid;
}
//polygon.Translate(-centroid);
}
float denom = 0.0f;
float numer = 0.0f;
for (int j = vertices.Length - 1, i = 0; i < vertices.Length; j = i, i++)
{
float a = vertices[i].LengthSquared();
float b = Vector2.Dot(vertices[i], vertices[j]);
float c = vertices[j].LengthSquared();
float d = gxtMath.Abs(gxtMath.Cross2D(vertices[j], vertices[i]));
numer += d;
denom += (a + b + c) * d;
}
return denom / (numer * 6.0f);
}
