If yu' [member of] E(G) and u' is an intermediate vertex, or y'u [member of] E(G) and y' is an intermediate vertex, then x sends 1/3 to w through yz and yu.

Furthermore, x'y is incident with another 3-face x'yu such that u [not equal to] y' and u is an intermediate vertex by R7.

Suppose that v is an intermediate vertex. Then v sends out charges only by R1, which implies that w'(v) [greater than or equal to] w(v) - 1/3d(v) = 2d(v) - 10 - 1/3d(v) = 5d(v.)-3[degrees] / 3 [greater than or equal to] 0 for d(v) [greater than or equal to] 6.

However, there is no edge from vertex 2 to vertex 4 (into which vertex 1 was coalesced) over which to send the update [U.sup.4.sub.2], nor can the edge 2 [??] 4 be length-two reduced (which would allow that update to be sent to an

intermediate vertex).

If the edge has no successor edge (null pointer), then it is considered a local maximum, otherwise it is an intermediate vertex. Processing at each vertex depends on the class of a given vertex as follows:

Left and right intermediate: When an intermediate vertex is found, the vertex need be added only to the left end or to the right end of the vertex list of the polygon assigned to the edge, depending on whether the edge side is left or right.

Whenever a local maximum, left intermediate or right intermediate vertex is encountered, a trapezoid should be output.