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

TL;DR

This paper introduces CASC, a modern C++ library for representing arbitrary dimension abstract simplicial complexes, enabling flexible topology-data decoupling and supporting applications like mesh generation.

Contribution

CASC is a novel, header-only C++ library that efficiently represents complex topologies with user-defined data, using advanced language features for flexibility and decoupling.

Findings

CASC effectively decouples topology from user data.

The library supports a metadata-aware decimation algorithm.

Application demonstrated on orientable surface mesh.

Abstract

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.