385,308 research outputs found
Topological characterization of simple points by complex collapsibility
International audienceThinning is an image operation whose goal is to reduce object points in a "topology-preserving" way. Such points whose removal does not change the topology are called simple points and they play an important role in any thinning process. For efficient computation, local characterizations have been already studied based on the concept of point connectivity for two-and three-dimensional digital images. In this paper, we introduce a new topological characterization of simple points based on collapsibility of polyhedral complexes. We also study their topological characteristics and propose a linear thinning algorithm
Quadratic Volume Preserving Maps
We study quadratic, volume preserving diffeomorphisms whose inverse is also
quadratic. Such maps generalize the Henon area preserving map and the family of
symplectic quadratic maps studied by Moser. In particular, we investigate a
family of quadratic volume preserving maps in three space for which we find a
normal form and study invariant sets. We also give an alternative proof of a
theorem by Moser classifying quadratic symplectic maps.Comment: Ams LaTeX file with 4 figures (figure 2 is gif, the others are ps
Well-Centered Triangulation
Meshes composed of well-centered simplices have nice orthogonal dual meshes
(the dual Voronoi diagram). This is useful for certain numerical algorithms
that prefer such primal-dual mesh pairs. We prove that well-centered meshes
also have optimality properties and relationships to Delaunay and minmax angle
triangulations. We present an iterative algorithm that seeks to transform a
given triangulation in two or three dimensions into a well-centered one by
minimizing a cost function and moving the interior vertices while keeping the
mesh connectivity and boundary vertices fixed. The cost function is a direct
result of a new characterization of well-centeredness in arbitrary dimensions
that we present. Ours is the first optimization-based heuristic for
well-centeredness, and the first one that applies in both two and three
dimensions. We show the results of applying our algorithm to small and large
two-dimensional meshes, some with a complex boundary, and obtain a
well-centered tetrahedralization of the cube. We also show numerical evidence
that our algorithm preserves gradation and that it improves the maximum and
minimum angles of acute triangulations created by the best known previous
method.Comment: Content has been added to experimental results section. Significant
edits in introduction and in summary of current and previous results. Minor
edits elsewher
Linear Toric Fibrations
These notes are based on three lectures given at the 2013 CIME/CIRM summer
school. The purpose of this series of lectures is to introduce the notion of a
toric fibration and to give its geometrical and combinatorial
characterizations. Polarized toric varieties which are birationally equivalent
to projective toric bundles are associated to a class of polytopes called
Cayley polytopes. Their geometry and combinatorics have a fruitful interplay
leading to fundamental insight in both directions. These notes will illustrate
geometrical phenomena, in algebraic geometry and neighboring fields, which are
characterized by a Cayley structure. Examples are projective duality of toric
varieties and polyhedral adjunction theory
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