# Valence-Driven Conquest

### vertex degree tip vertices

**Definition:** Alliez’s VD (Valence-Driven Conquest) reduces the number of triangles by

*checking the degree of the tip vertex.*

It removes the tip vertices with valence more than 3 and tags the remaining vertices. Because the decimation follows a systematic traversal, the decompression can reverse it and reconstruct the meshes. The connectivity can be compressed to 3.7 bits per vertex and the geometry encoding takes 12 bits per vertex. The geometric data contains the error vector between the predicted and the real vertex positions. However, the selection of the vertices to be removed at each batch is only based on the connectivity, and it thus produces less accurate intermediate models than CPM.

The transformations at compression for Valence-driven conquest are “vertex removal” and “retriangulation”. A degree-d “patch” is a set of faces incident to valence-d vertex. This valence-d vertex is the “tip-vertex” of this patch. Figure 1 shows how a degree-5 tip-vertex V is removed, and then how the patch is retriangulated and tagged with “+” and “-” signs. The inverse transformations at decompression are “patch discovery” and “vertex insertion”. The decoder uses the received degree information and the current tags to discover the border of the patch and insert the new vertex.

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