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Approximating free surfaces with affine arithmetic

Grant number: 14/09650-0
Support type:Scholarships abroad - Research Internship - Master's degree
Effective date (Start): September 10, 2014
Effective date (End): February 28, 2015
Field of knowledge:Physical Sciences and Mathematics - Computer Science
Principal researcher:Afonso Paiva Neto
Grantee:Filipe de Carvalho Nascimento
Supervisor abroad: Christopher Batty
Home Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
Research place: University of Waterloo, Canada  
Associated to the scholarship:13/12883-4 - Robust Polygonal Approximation of Implicit Curves and Surfaces, BP.MS


Geometric modeling involving implicit objects is a topic of intense research in Computer Graphics. Obtaining efficient techniques for representing these objects receives even more attention in applications that demand huge computation, such as generating a free surface during a fluid flow simulation. Implicit surfaces are a subset of implicit objects, usually approximated by triangular meshes, being extracted from algebraic functions and discrete elements (e.g. points, tetrahedra, grids, etc). On the country scholarship project, we are developing a new method of adaptive robust approximation of implicit surfaces extracted from algebraic functions, using the self-validated numerical tool called Affine Arithmetic. In this project, we propose an important extension of our method to extract implicit surfaces from point sets applied to fluid flow animation. (AU)

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