Abstract. Geometry processing applications frequently rely on octree structures, since they provide simple and efficient hierarchies for discrete data. However, octrees do not guarantee direct continuous interpolation of this data inside its nodes. This motivates the use of the octree's dual structure, which is one of the simplest continuous hierarchical structures. With the emergence of pointerless representations, with their ability to reduce memory footprint and adapt to parallel architectures, the generation of duals of pointerless octrees becomes a natural challenge. This work proposes strategies for dual generation of static or dynamic pointerless octrees. Experimentally, those methods enjoy the memory reduction of pointerless representations and speed up the execution by several factors compared to the usual recursive generation.
Chernyaev's Marching Cubes 33 is one of the first algorithms intended to preserve the topology of the trilinear interpolant. In this work, we address three issues with the Marching Cubes 33 algorithm, two of which are related to its original description and one that is related to its variant. In particular, we solve a problem with the core disambiguation procedure of Marching Cubes 33 that prevents the extraction of topologically correct isosurfaces for the ambiguous configuration 13.5. This work closes an existing gap in the topological correctness of Marching Cubes 33. Furthermore, we make our results reproducible, meaning that examples provided in this work can be easily explored and studied. Finally, as part of the philosophy of reproducibility, we provide a corrected version of the Marching Cubes 33 open-source implementation and access to datasets that can be used to verify the correctness of any available topologically correct isosurface extraction implementation that preserves the topology of the trilinear interpolant.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.