Felix Effenberger
Finding and Classifying Critical Points of 2D Vector Fields: A Cell-Oriented Approach Using Group Theory.
Tue, 04/27/2010 - 15:02 — SomNambulAuthors: Felix Effenberger, Daniel Weiskopf
Subjects: Graphics
AbstractWe present a novel approach to finding critical points in cell-wise
barycentrically or bilinearly interpolated vector fields on surfaces. The
Poincar\e index of the critical points is determined by investigating the
qualitative behavior of 0-level sets of the interpolants of the vector field
components in parameter space using precomputed combinatorial results, thus
avoiding the computation of the Jacobian of the vector field at the critical
points in order to determine its index. The locations of the critical points
within a cell are determined analytically to achieve accurate results.simpcomp -- A GAP toolbox for simplicial complexes.
Fri, 04/09/2010 - 15:01 — SomNambulAuthors: Jonathan Spreer, Felix Effenberger
Subjects: Combinatorics
Abstractsimpcomp is an extension (a so called package) to GAP, the well known system
for computational discrete algebra. The package enables the user to compute
numerous properties of (abstract) simplicial complexes, provides functions to
construct new complexes from existing ones and an extensive library of
triangulations of manifolds.Stacked polytopes and tight triangulations of manifolds.
Mon, 11/30/2009 - 16:01 — SomNambulAuthors: Felix Effenberger
Subjects: Geometric Topology
AbstractTightness of a triangulated manifold is a topological condition, roughly
meaning that any simplexwise linear embedding of the triangulation into
euclidean space is ``as convex as possible''. It can thus be understood as a
generalization of the concept of convexity. In even dimensions,
super-neighborliness is known to be a purely combinatorial condition which
implies the tightness of a triangulation.
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