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

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 Trans. Math. Softw. 45.3 (August 2019), pp. 1--20