Boolean Operations on Non-manifold and B-rep Solids for Mesh Generation

In a solid modeler, one of the most powerful tools to create three-dimensional objects with any level of geometric complexity is the application of Boolean set operations. They constitute intuitive and popular ways of combining solids, based on operations applied to sets. The main types of Boolean operations commonly applied to solids are: union, intersection and difference. In order to assure that the resulting objects have the same dimension as the original objects, without loose or dangling parts, a regularization process is usually applied after a Boolean operation. To regularize means to restrict the result in a way that only filling volumes are allowed. In practice, regularization is performed by classifying the topological elements and removing internal or lower dimensional structures. However, in many engineering applications, the adopted geometric model may contain idealized internal parts, as in the case of multi-region models, or lower dimensional parts, as in the case of solids that contain dangling slabs, which are represented as zero-thickness surfaces in the model. The objective of this work is the development of a generic algorithm that allows the application of Boolean set operations in a geometric modeling environment applied to finite element mesh generation. This environment adopts a non-manifold B-Rep representation that considers an undefined number of topological entities (group concept), works with objects of different dimensions, and works with objects not necessarily plane or polyhedral (parametric curved surfaces). The present paper discusses the implementation of this algorithm in a preexisting geometric modeler named MG, using the concept of object oriented programming and keeping the user interface simple and efficient.