1. Progressive Meshes
Copyright, 1996 © Dale Carnegie & Associates, Inc.

2. The Mesh Definition A Mesh is a tuple M=(K,V,D,S)
V = {v1,…, vm} the set of vertices defining mesh shape in R3
K  Rm is the parametric domain, defining the mesh as the image øv(K) : Rm  R3
D = {df : df is the discrete attribute of face f }
S = {sf : sf is the scalar attribute of face corner (v,f) }

3. Edge Collapse/Vertex Split
An initial Mesh M’ = Mn is simplified to a coarser mesh M0
Vertex split and edge collapse are invertible

4. Progressive Mesh
A vsplit(s,l,r,t,A) adds near vertex vs a new vertex vt and two new faces {vs,vl,vr} and {vs,vl,vr}. The attribute information is carried by A.
Any arbitary mesh M’ can be represented as a simple mesh M0 with a sequence of n vsplit records.
(M0,{vsplit0,…,vsplitn-1}) is a progressive mesh

5. Geomorphs An intermediate mesh MG() = (Ki+1, VG())
is determined with 0   1, such that MG(0) looks like Mi and MG(1) looks like Mi+1. MG() has connectivity of of Mi+1 with vertex position being linearly interpolated.

6. Progressive Transmission
The compact mesh M0 is transmitted first followed by a stream of vspliti records. The receiver incrementally rebuilds M’ and animates the changing mesh using geomorphs.
The original mesh M’ is exactly recovered atfer n records : PM is a lossless representation.

7. Selective Refinement
An initial mesh Mc is selectively refined by iterating through {vsplit0,…,vsplitn-1}, but selectively performing vsplit if :
all 3 vertices are present in the mesh
REFINE(vsi) is TRUE.
Selective refinement also allows a particular Level of Detail (LOD) of a mesh

8. Mesh Compression
A compact representation of the vsplit(si,li,ri) records enables to store the mesh in a compressed notation.
si is stored directly
Remaining 2 adjacent vertices can be stored in app 5 bits
Scalar and discrete attributes of Mi+1 can be predicted from Mi. Hence a delta encoding can reduce storage.