Geometric Modeling for Finite Elements: Advances and Contributions in Surface Intersections, Multi-Region Detection, and Topological Structures (2000–2015)
This work presents an overview of the main contributions made between 2000 and 2015 in the field of geometric modeling applied to engineering problems, with emphasis on topological data structures, surface intersections, and automatic recognition of multi-regions. During this period, the studies conducted significantly contributed to pushing the frontier of knowledge in the area, offering conceptual and computational solutions relevant to applications based on the finite element method. The increasing demand for robust numerical simulations in engineering, especially those based on the finite element method, underscores the importance of accurate and efficient geometric representation of complex domains, which is fundamental for generating quality meshes and for the accuracy of simulations. Additionally, some of the works also addressed aspects related to mesh generation and adaptivity, expanding the scope of investigated applications and challenges. The contributions deal with topics such as the robust computation of intersections between parametric surfaces, the efficient handling of Boolean operations on non-manifold solids, and the implementation of topological data structures for the automatic detection and management of multi-regions in three-dimensional models. To present this overview, the main works published by the authors between 2000 and 2015 were selected, aiming to provide a coherent panorama of the proposed approaches, techniques, and solutions. The paper seeks to describe, in an accessible and structured manner, the main concepts, strategies, and results achieved, offering readers a comprehensive perspective of the developed contributions. The main contribution of this work is to provide a consolidated record of the solutions developed over the years, highlighting how they helped to advance the frontier of knowledge in geometric modeling for engineering. This paper establishes itself as a reference for researchers and professionals interested in the evolution of these techniques and their applications in advanced numerical simulations in engineering and related areas.
