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Open Access Publications from the University of California

Simplification of three-dimensional density maps

  • Author(s): Natarajan, Vijay
  • Edelsbrunner, Herbert
  • Editor(s): Ebert, David S.
  • et al.

We present an algorithm for the simplification of density maps in 3D. We assume that an input function specified at vertices of a triangulation and linearly interpolated within the tetrahedra. The fundamental operation in the simplification procedure is a topology preserving edge contraction. We describe simple and local conditions that can be used to check if an edge contraction preserves topology. These conditions are derived from the generic link conditions for 3-complexes described by Dey et. al. Besides providing a good approximation of the density map, the algorithm also aims to generate a mesh with good quality elements. We achieve this additional goal using a novel extension of the quadric error metric. We visualize isosurfaces extracted from the simplified density maps and use them along with an approximation error computation to evaluate the algorithm. We also develop validation tools to test the correctness of the simplified model and perform statistical measurements on the critical points of the density map to study the relationship between geometric and topological simplification.

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