The Implementation of the Colored Abstract Simplicial Complex and its Application to Mesh Generation
Provides a flexible, modern data structure for topological computation, but is an incremental implementation of existing concepts.
CASC is a new C++ library for representing abstract simplicial complexes with user-defined data on simplices, enabling a metadata-aware decimation algorithm for collapsing simplices of any dimension. It was applied to represent orientable surface meshes.
We introduce CASC: a new, modern, and header-only C++ library which 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.