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The Implementation of the Colored Abstract Simplicial Complex and its Application to Mesh Generation.

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Area of Science:

  • Computational geometry
  • Data structures
  • Topological data analysis

Background:

  • Abstract simplicial complexes (ASC) are fundamental in computational topology.
  • Representing ASCs with user-defined data requires efficient and flexible data structures.
  • Existing libraries may lack support for arbitrary dimensions or direct data integration.

Purpose of the Study:

  • Introduce CASC, a novel C++ library for abstract simplicial complexes (ASC).
  • Provide a header-only, modern C++ solution for representing ASCs with user-defined data.
  • Decouple topological representation from user data interaction for enhanced flexibility.

Main Methods:

  • Utilize C++11 variadic template parameters and C++14 automatic return type deduction.
  • Implement a data structure storing user-defined classes directly on simplices.
  • Develop a metadata-aware decimation algorithm for general simplex collapsing.

Main Results:

  • CASC offers a flexible and efficient representation of arbitrary-dimension ASCs.
  • The library decouples topology from user data, simplifying complex analyses.
  • A metadata-aware decimation algorithm is presented and demonstrated.

Conclusions:

  • CASC provides a powerful new tool for computational topology and data analysis.
  • The library's design facilitates advanced applications, such as surface mesh representation.
  • Modern C++ features enable efficient and adaptable ASC data structures.