Geometric Modeling Techniques Based on Simplicial Complexes

This paper proposes a geometric modeling technique based on simplicial complexes to address the limitation of traditional solid modeling techniques, which are unable to meet the requirements of CAD/E software for representing non-manifold bodies. By leveraging manifold decomposition and employing a strict hierarchy of “complex-chain-atom” object design pattern, this approach achieves a unified representation of arbitrary complex shapes. Additionally, by adopting a data structure that stores adjacency relations between topological objects in a unidirectional ordered manner and establishing a mechanism to associate topological objects with lists of geometric objects, we achieve a balance between model retrieval efficiency and model size, further reducing system development complexity and subsequent maintenance costs.