A B-Rep data structure and object GUI programming to implement 2D boundary elements

Abstract

One of the main advantages of the Boundary Elements Methods (BEM) is the inherent feature of a Boundary Representation scheme (B-Rep),since it represents the geometry and physical properties of a model using just its boundary. This characteristic makes the representation andmanipulation of the model geometry an easy task, also allowing the boundary element mesh generation in a straightforward and simple way.Even though a simple pre-processor program may suffice for generating most two-dimensional boundary element models, in some specialcases the modeling procedure represents a cumbersome task, requiring pre-processor programs with enhanced characteristics. The specialcases considered in this work are non-trivial models, such as geometries with infinite or semi-infinite domains, multiple regions, disconnectedregions, cracks and holes. To handle with the modeling task of these special models, the present development proposes a scheme based onthe well-known Half-Edge data structure (HED). It also considers the use of Object-Oriented Programming (OOP) to implement a graphicaluser interface (GUI) with the proposed data structure. The results of step-by-step generation of some special two-dimensional models in theimplemented GUI illustrate the main characteristics of the proposed scheme.Keywords: Geometric Modeling, HED Data Structure, BEM, OOP, GUIs.