Validation of CG Models - An Introduction to Computer Graphics for Artists - page 122

Fig. 9.9 The bow-tie face on the left cannot be triangulated without drastically changing the shape
of the polygon. On right , an edge has been made at the bottom of the polygon to correct it

Fig. 9.10 Convex quad on left , concave on right . Triangulation options for each polygon shown
with a dashed line . One of the two triangulation options for the concave polygon causes it to be
coincident with itself (Sect. 9.4.2 )

To fi x a face of this type, it is often easiest to triangulate it (Fig. 9.9 ). If this
doesn't give you the result you want, you can delete the face and then rebuild it.
You should not have any bow-tie faces in your model. You should check for
these and eliminate any you fi nd before delivery. They are a problem because a
renderer will behave unpredictably regarding these faces. Depending on how the
renderer is designed, it may subdivide the face for rendering in such a way that
half of it is invisible, the other half visible, it may make the entire face invisible
or visible, or it may fl icker as it tries to determine which part of it is facing the
camera.

9.3.4 Concave Face

A concave face has four or more sides and at least one vertex that reverses the angle
of the edges it is connected to relative to other vertices. This is a technical error
because it is possible to subdivide a concave face so that it self-intersects (Fig. 9.10 ).