MSNANAMar 27, 2019

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

arXiv:1807.0141711 citationsh-index: 105
Originality Synthesis-oriented
AI Analysis

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.

Foundations

The foundational work for this paper's niche, ranked by how specifically the neighbourhood builds on it — not by global fame.

Your Notes