A fast high-dimensional continuation hypercubes algorithm

• Published in: Computers & graphics Vol. 129; p. 104237
• Main Authors: Reia, Lucas Martinelli, Gameiro, Marcio, Ribeiro, Tomás Bueno Moraes, Castelo, Antonio
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.06.2025
• Subjects: Continuation method; High-Dimensional Marching Cubes; Isomanifold; Manifold approximation/polygonization/tracing; Triangulation; Triangulation; High-Dimensional Marching Cubes; Manifold approximation/polygonization/tracing; Continuation method; Isomanifold
• ISSN: 0097-8493
• DOI: 10.1016/j.cag.2025.104237

This paper introduces the Fast Continuation Hypercubes (FCH) algorithm, a method for generating piecewise linear approximations of implicitly defined manifolds of arbitrary dimension. By integrating and mixing key aspects of existing approaches, the FCH algorithm offers significant improvements in both speed and memory efficiency. It traverses the domain by generating and processing only the necessary cells, which reduces the computational cost associated with high-dimensional manifold approximation. Additionally, the algorithm stores only the cells at the boundary of the traversed region, further optimizing memory efficiency. Experimental results demonstrate that FCH outperforms state-of-the-art algorithms in terms of runtime and memory usage. [Display omitted] •New algorithm for approximating implicitly defined manifolds of arbitrary dimension.•Mixing key concepts from existing approaches, leveraging their strengths.•Significant performance improvements, outperforming state-of-the-art algorithms.