  In this paper, we consider the orthogonal projection of a surface in
$\mathbb{R}^3$ for a given view direction. We then introduce and investigate
several invariants of the families of the plane curves that locally configure
the projection image of the surface. Using the invariants, we also show an
extension of d'Ocagne-Koenderink formula that associates a local behavior of
the projection image of a surface with Gaussian curvature of the surface.
