Boolean operations on multi-region solids for mesh generation

Abstract

An algorithm for Boolean operations on nonmanifold models is proposed to allow the treatment of solids with multiple regions (internal interfaces) and degenerate portions (shells and wires), in the context of 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 Boolean set operators. They are intuitive and popular ways to combine solids, based on the operations applied to point sets. 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. In practice, the regularization is performed classifying the topological elements and removing internal or lowerdimensional 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 that are represented as zerothickness surfaces or wireframes in the model. Therefore, the aim of this work is the development of a generic algorithm that allows the application of the Boolean set operations in a geometric modeling environment applied to finite and boundary element mesh generation. This environment adopts a non-manifold boundary representation that considers an undefined number of topological entities (group concept), and works with objects of different dimensions and with objects not necessarily plane or polyhedral (parametric curved surfaces). Numerical examples are presented to illustrate the proposed methodology.

Solving the Inverse Problem of Recovering the 3D Surface of a Detail According to its 2D Projections in the Modelling of Electroplating Processes

“…The faces of objects during classification receive a sign of position relative to another object [13]: inside, outside or on the border. The faces lists selected for logical operations are presented in table 1.…”

Simple and Robust Boolean Operations for Triangulated Surfaces

“…Besides these popular surface-based representations, several other methods like Nef [9], surfel-bounded [1], L-Rep [27] for representing geometric models are also developed to construct new models or convert existing ones to target models, and then Boolean operations are also implemented. In another aspect, the input models can be manifold or non-manifold [19], and most methods perform Booleans on manifold ones.…”

Simple and Robust Boolean Operations for Triangulated Surfaces

“…Various implementations of Boolean operations can be found in the literature, which can be broadly classified based on three main properties: the type of input data, the type of computation, and the type of output data [15]. Input models encompass a range of sources, including those generated by B-Rep based on NURBS surfaces [16,17], curved surfaces [18], and polygonal meshes [15,19,20], which can be manifold or non-manifold [21]. Most methods focus on performing Boolean operations on manifold surfaces.…”