Robust polygonal approximation of implicit curves

Author(s)

Filipe de Carvalho Nascimento

• Document type: Master's Dissertation
• Press: São Carlos.
• Institution: Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB)
• Defense date: 2016-05-19

Examining board members

Afonso Paiva Neto; Márcio Fuzeto Gameiro; Dimas Martinez Morera

• Advisor: Afonso Paiva Neto

Abstract

Geometric modeling involving implicit objects is a topic of intense research in Computer Graphics. Thus, obtain efficient techniques for representing these objects is of utmost importance. Two groups of relevant implicit objects for Computer Graphics are implicit curves and implicit surfaces. Traditional techniques for approximating implicit curves and surfaces involve splitting the domain and searching for parts of the curve or the surface. In this project we propose a new methods of robust polygonization of implicit curves using the self-validated numerical tool called Affine Arithmetic. The method consists in the adaptive polygonization of implicit curves in three-dimensional triangular meshes. (AU)

• FAPESP's process: 13/12883-4 - Robust Polygonal Approximation of Implicit Curves and Surfaces
• Grantee: Filipe de Carvalho Nascimento
• Support Opportunities: Scholarships in Brazil - Master