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.
News published in Agência FAPESP Newsletter about the scholarship: