Implicit Modeling in high dimensions

• Grant number: 25/03039-2
• Support Opportunities: Scholarships in Brazil - Master
• Start date: May 01, 2025
• End date: March 31, 2027
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Antonio Castelo Filho
• Grantee: Juliana Souza Paz
• 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

Geometric modeling is an essential area of Computer Graphics, enabling the representation and manipulation of objects in three dimensions. Implicit modeling, in particular, stands out for its ability to represent complex surfaces through mathematical equations, eliminating the need for explicit descriptions via meshes. This project aims to develop a modeler for high-dimensional manifolds, allowing the representation and visualization of objects in hyperdimensional spaces. The aim is to contribute to the advancement of geometric modeling and computational visualization, with possible applications in image processing and numerical simulation. (AU)