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Robust Polygonal Approximation of Implicit Curves and Surfaces

Grant number: 13/12883-4
Support Opportunities:Scholarships in Brazil - Master
Effective date (Start): November 01, 2013
Effective date (End): 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


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.

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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.

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