S.A.Coons points out that the normal to a polygon is the vector of its projected areas. Check that this is the sum of its cross-product normals. The normal is also a differentiation. The normal to a surface is the limit of the normal of a shrinking interpolating polygon. Large should mean less influence. Glassner points out that the normal to a quad is the cross-product of its diagonals. 2D area by accumulation of trapezoids is standard civil engineering. A vertex normal as the projected area of a surrounding polygon where each edge is scaled by the inverse square of its norm produces smoother pictures. Not differentiation consistent is used for art direction. A smoother normal estimate will destroy the look of faceted geometry.