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Medial Axis and Singularities.

Lev Birbrair1, Maciej P Denkowski2

  • 11Universidade Federal do Ceará, Fortaleza, Brazil.

Journal of Geometric Analysis
|March 7, 2019
PubMed
Summary
This summary is machine-generated.

This study investigates medial axes in polynomially bounded o-minimal structures, identifying points on a set

Keywords:
Central setMedial axisSingularitiesSkeletono-Minimal geometry

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Area of Science:

  • Computational geometry
  • Singularity theory
  • Real algebraic geometry

Background:

  • Medial axes are fundamental geometric objects.
  • Polynomially bounded o-minimal structures offer a framework for studying complex sets.
  • Singularity theory provides tools for analyzing complex shapes and their properties.

Purpose of the Study:

  • To study the medial axes of sets definable in polynomially bounded o-minimal structures.
  • To characterize singular points on definable, closed sets that are part of the medial axis.

Main Methods:

  • Utilizing concepts from singularity theory.
  • Leveraging properties of polynomially bounded o-minimal structures.
  • Analyzing the definition of medial axes as points with multiple closest points.

Main Results:

  • Characterization of singular points reached by the medial axis.
  • Gathering basic results for a self-contained study.
  • Establishing a connection between medial axes and singularity theory in these structures.

Conclusions:

  • The medial axis of definable sets in these structures can be effectively studied using singularity theory.
  • Understanding these singular points is key to characterizing the medial axis.
  • This work provides foundational results for further research in this area.