Adaptive combinatorial marching hypercubes

• Grant number: 23/12195-2
• Support Opportunities: Scholarships in Brazil - Doctorate (Direct)
• Start date: November 01, 2023
• End date: June 30, 2026
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Antonio Castelo Filho
• Grantee: Lucas Martinelli Reia
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Associated research grant: 13/07375-0 - CeMEAI - Center for Mathematical Sciences Applied to Industry, AP.CEPID

Abstract

Algorithms for representing manifolds are widely used in exact sciences.One of the best known algorithms is the Marching Cubes, which performs the extraction of a surface mesh from a 2-dimensional manifold (surface) by using a composition of triangles contained in R3. Due to the need to store a lookup table in memory, it is observed that applying the traditional algorithm to higher dimensions is not sustainable, as the size of the lookup table scales in a 2^(2^n) way, where n is the dimension of the space. An alternative version, called Generalized Combinatorial Marching Hypercubes (GCMH), is able to generate approximations of manifolds of dimension (n-k) contained in a space of dimension n, where k