![]() ![]() We, therefore, embrace the whole field, revisiting and structuring a vast amount of literature, and covering basic topological (Section 2) and geometrical (Section 3) concepts, all kinds of approaches to hexahedral mesh generation (Section 4), operators to edit mesh connectivity and to perform refinement or coarsening (Section 5), mesh optimization and untangling (Section 6), visual exploration (Section 7), and also addressing the recent trend of methods for hex-dominant meshing (Section 4.9). We wish to create a comprehensive entry point for researchers and practitioners dealing with hexahedral meshing. The engineering community has already produced a few surveys on this topic, but they are either no longer up to date or focus just on a particular subset of the available techniques. ![]() In this survey, we wish to summarize this work, also report on previous methods developed by other scientific communities. In the last decade, the Computer Graphics community has contributed significantly to this field, proposing seminal ideas, theoretical insights, and practical algorithms. Ever since, many advancements in the field have been made, while major challenges still remain. The hex-meshing problem had been so elusive that it was even once termed the “holy grail” of mesh generation. But no known method successfully combines all these properties into a single product. Some of the known methods are extremely robust and scale well on complex geometries some others produce high-quality meshes some others are fully automatic. Despite the huge effort that various scientific and industrial communities have spent so far, the computation of a high-quality hexahedral mesh conforming to (or suitably approximating) a target geometry remains a challenge with various open aspects for which no fully satisfactory solutions have been provided yet. In academic research, the algorithmic generation and processing of hexahedral meshes have been studied for more than 30 years now. Meshes entirely or partially made of hexahedra have been used for many years as the computational domain to solve partial differential equations ( PDEs) that are relevant for the automobile, naval, aerospace, medical, and geological industries to name a few, and are at the core of prominent software tools used by such industries, such as Altair, ANSYS, CoreForm, CUBIT, Distene SAS, and Tessaels. Alongside tetrahedral, hexahedral elements are the most prominent solid elements used to represent discrete volumes in computational environments. They are primarily used in industrial and biomedical applications, where volume elements are exploited to encode various information, such as structural and material properties, permitting to simulate and precisely estimating the physical behavior of an object, subject to external or internal forces, or the dynamics involving multiple objects interacting in the same environment. ![]() ![]() Volume meshes explicitly encode both the surface and the interior of an object, thus offering a richer representation than surface meshes. Skip 1INTRODUCTION Section 1 INTRODUCTION ![]()
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