Approximating free surfaces with affine arithmetic

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)