A Hierarchical Data Structure for A Non-Manifold B-Rep Modeler for Thin Components

Abstract

This paper proposes a Hierarchical Data Structure (HDS) for modeling of non-manifold thin objects, consisting of seven nodes named as Thin Object, Sheet, Feature, Face, Part Edge, Edge and Vertex. This paper modifies and validates a general topological invariant s + eL + eNL + eFF +b + j - v - gn - fP - fNP- fFF = 0 regarding the number of sheets, linear edges, non-linear edges, freeform edges, bends, joints, vertices, non-manifold genuses, planer faces, non-planer faces and free form faces respectively for non-manifold thin objects. Corresponding Euler operators are derived, providing a basis for a modeling system for thin-walled objects.