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The cell undergoing collapse could belong to a grid [Rossignac 93], or a spatial subdivision such as an octree [Luebke 97], or could simply be defined as a volume in space [Low 97]. The single vertex to which the cell collapses could be chosen from one of the collapsed vertices or newly computed as some form of average of the collapsed vertices. We present the cell collapse operator here following the discussion in [Rossignac 93]. 7(a). The vertices of the mesh are placed in a regular grid. All the vertices that fall in the same grid cell are then unified into a single vertex.
There are several applications when simplification of the topology is undesirable and leads to unacceptable changes in the structure of the object. For example, topological structures are often of great interest in the study of protein structure and function. For instance, ion-transport channels are highly susceptible to small changes in side chains that border such channels. 19 with a channel. This channel is important for the transport of ions and water molecules across lipid membranes [Edelsbrunner 00].
The full-edge collapse operator has greater flexibility in determining the new vertex after edge collapse than the half-edge collapse operator, and in practice, this means that one can compute higher-fidelity simplifications using full-edge collapses than using half-edge collapses. However, the advantage of the half-edge collapse 28 Chapter 2 Mesh Simplification operator is that the vertices of the simplified mesh are a subset of the high-detail input mesh. This simplifies the bookkeeping associated with keeping track of the vertices and results in substantial storage savings since no new vertices must be stored.