Approximating free surfaces with affine arithmetic

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

Abstract

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)