Robust Polygonal Approximation of Implicit Curves and Surfaces

• Grant number: 13/12883-4
• Support Opportunities: Scholarships in Brazil - Master
• Start date: November 01, 2013
• End date: August 21, 2015
• Field of knowledge: Physical Sciences and Mathematics - Computer Science
• Principal Investigator: Afonso Paiva Neto
• Grantee: Filipe de Carvalho Nascimento
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Associated scholarship(s): 14/09650-0 - Approximating free surfaces with affine arithmetic, BE.EP.MS

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 curvesand 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 two new methods of robust polygonization of implicit curves and surfaces using the self-validated numerical tool called Affine Arithmetic. The first method consists in the adaptive polygonization of implicit curves in three-dimensional triangular meshes. The second method consists in an adaptive poligonal approximation of implicit surfaces.

Academic Publications

(References retrieved automatically from State of São Paulo Research Institutions)

NASCIMENTO, Filipe de Carvalho. Robust polygonal approximation of implicit curves. 2016. Master's Dissertation - Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB) São Carlos.