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

Published: less than 1 minute read  Links: DOI arXiv

We introduce the Colored Abstract Simplicial Complex library (CASC): a new, modern, and header-only C++ library that provides a data structure to represent arbitrary dimension abstract simplicial complexes (ASC) with user-defined classes stored directly on the simplices at each dimension. This is accomplished by using the latest C++ language features including variadic template parameters introduced in C++11 and automatic function return type deduction from C++14. Effectively, CASC decouples the representation of the topology from the interactions of user data. We present the innovations and design principles of the data structure and related algorithms. This includes a metadata-aware decimation algorithm, which is general for collapsing simplices of any dimension. We also present an example application of this library to represent an orientable surface mesh.

Recommended citation: C. T. Lee†,$, J. B. Moody, R. E. Amaro, J. A. McCammon, and M. J. Holst "The Implementation of The Colored Abstract Simplicial Complex and its Application to Mesh Generation". ACM Transactions on Mathematical Software 45.3 (August 2019), pp. 1–20.