Simplicial maps for progressive transmission of polygonal surfaces
Andre P. Gueziec, Gabriel Taubin, Francis Lazarus, William Horn · 1998
We present a new method for (1) automatically gener-'.ating multiple Levels Of Detail (LODs) of a polygohal surface, (2) progressively loading, or transmitting, and displaying a surface, and for (3) changing interactively the LOD when displaying.We build the LODs using any algorithm that performs edge collapses and certain vertex removals to simplify surfaces, and provides an ordered list of ordered vertex pairs (edge collapse specifications).We propose a Surface Partition for encodirig surfa& LODs: we define vertex and triangle levels during simplification; vertices and triangles are partitioned and sorted according to their level, and are passed to the display algorithm in decreasing level order, one level at a time, together with a vertex repre- senmives array.Each level of vertices and triangles, together with higher levels and the vertex representatives, form a valid surface.The vertex representatives array encodes a succession of simplicial maps between the highest resolution LOD and other LODs.We propose a data structure using a Directed Acyclic Graph (DAG) forrecording a partial ordering among edge collapses, and varyirig the LODs across the surface.We describe an implementation of our method in VRML.