Colored Abstract Simplicial Complex (CASC)

Colored Abstract Simplicial Complex (CASC) represents and manipulates arbitrary-dimensional abstract simplicial complexes, enabling storage of user-defined classes on simplices at each dimension and topology-aware operations such as metadata-aware decimation.

Key Features:

• Header-only C++ library: Implemented as a header-only C++ library to provide compile-time composition of types and templates.
• Arbitrary-Dimensional Representation: Represents abstract simplicial complexes (ASCs) in arbitrary dimensions.
• User-Defined Data Storage: Stores user-defined classes directly on simplices at each dimension.
• C++11 and C++14 language features: Uses variadic templates from C++11 and automatic function return type deduction from C++14 to enable flexible type and API composition.
• Decoupled Topology and User Data: Employs metatemplate programming to separate topology representation from user data and interactions.
• Metadata-Aware Decimation Algorithm: Provides a decimation algorithm that can collapse simplices of any dimension while respecting stored metadata.
• Hasse Diagram Topology Storage: Stores full combinatorial topology according to a Hasse diagram representation.

Scientific Applications:

• Computational Topology: Enables construction and manipulation of ASCs for topological analysis and algorithms.
• Mesh Generation and Geometric Modeling: Represents meshes and supports operations relevant to mesh generation and geometric modeling.
• Orientable Surface Mesh Representation: Represents orientable surface meshes used in computer graphics, 3D modeling, and scientific visualization.
• Data Reduction and Simplification: Applies the metadata-aware decimation algorithm for data reduction and simplification tasks across domains.

Methodology:

Stores combinatorial topology via a Hasse diagram; uses metatemplate programming to decouple topology and user data; implements C++11 variadic templates and C++14 automatic return type deduction; includes a metadata-aware decimation algorithm that collapses simplices of arbitrary dimension.