Illustrate the Back Face Detection Method

A single polyhedron is a convex solid, which has no external angle between faces less  than 180° and there is a simple object space method to determine which faces are the  visible front faces, and which are the hidden back faces.

The faces are characterized by their outward normals, and for this reason, the method is  also known as the Outward Normal Method.  The outward normal for every face of the convex solid is determined by taking the  cross-product of any two adjacent sides of the face. For consistency in checking, when  the viewer looks directly at the face under consideration, the vertex numbering (naming)  scheme for all faces must be in the same direction, say counter-clockwise. We need to start with a single polygon numbered in the proper order. There are analytical methods for doing this, but where user has control over the input, it is much easier to number the first polygon counter-clockwise when visible to the viewer.

Once this is done, any adjacent polygon will have the common edge traversed in the opposite direction, and hence no further decision-making will be necessary regarding the direction of numbering. This logic is particularly helpful in naming the faces away from the observer and those that are approximately horizontal, eliminating the need for the observer to imagine himself at all sorts of odd viewing angles.