The vertex-and-face-table representation could be enhanced with an edge-table representation;…

The vertex-and-face-table representation could be enhanced with an edge-table representation; each row of the edge table would contain indices of two vertices that were to be joined by an edge. In this exercise, we’ll examine the consequences of introducing an edge table.

(a) Assuming that the edges in a mesh are exactly those that are part of the boundary of a face, describe an algorithm for deleting a face from a mesh.

(b) Suppose that edges are to be treated as directed, that is, the edge (3, 11) is different from the edge (11, 3), and that the same is true for faces. The boundary of the face (3, 5, 8) consists of the three directed edges (3, 5), (5, 8), and (8, 3). Assuming that we agree that the shapes we represent are all to be polygonal surfaces, discuss face deletion again. Make a Möbius strip from five triangles, and check whether your deletion algorithm works for the deletion of each triangle.

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