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Optimal-time dynamic mesh refinement: preliminary results Umut A. Acar
 

Summary: Optimal-time dynamic mesh refinement: preliminary results
Umut A. Acar
Beno^it Hudson
Abstract
We present early results on a dynamic mesh re-
finement algorithm. Using a variant of the Sparse
Voronoi Refinement algorithm and applying the tech-
nique of Self-Adjusting Computation, we find that
we expect to run in O(polylog n) time per update
on points sets in arbitrary dimension. This is based
on some theoretical results, along with experimental
results from an implementation.
1 Sparse Voronoi Refinement
Mesh refinement solves the following problem: given
a point set P Rd
, add additional Steiner points
such that the Delaunay tessellation of the augmented
set creates only simplices of good quality. The quality
metric usually used, because it is tractable to theoret-
ical analysis, is the radius-edge condition: given the

  

Source: Acar, Umut - Programming Languages and Systems Group, Max-Planck Institute for Software Systems

 

Collections: Computer Technologies and Information Sciences