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Item Multiresolution for Algebraic Curves and Surfaces using Wavelets(Blackwell Publishers Ltd and the Eurographics Association., 2001) Esteve, Jordi; Brunet, Pere; Vinacua, AlvarThis paper describes a multiresolution method for implicit curves and surfaces. The method is based on wavelets, and is able to simplify the topology. The implicit curves and surfaces are defined as the zero-valued piece-wise algebraic isosurface of a tensor-product uniform cubic B-spline. A wavelet multiresolution method that deals with uniform cubic B-splines on bounded domains is proposed. In order to handle arbitrary domains the proposed algorithm dynamically adds appropriate control points and deletes them in the synthesis phase.Item Hoops: 3D Curves as Conservative Occluders for Cell-Visibility(Blackwell Publishers Ltd and the Eurographics Association, 2001) Brunet, Pere; Navazo, Isabel; Rossignac, Jarek; Saona-Vazquez, CarlosMost visibility culling algorithms require convexity of occluders. Occluder synthesis algorithms attempt to construct large convex occluders inside bulky non-convex sets. Occluder fusion algorithms generate convex occluders that are contained in the umbra cast by a group of objects given an area light. In this paper we prove that convexity requirements can be shifted from the occluders to their umbra with no loss of efficiency, and use this property to show how some special non-planar, non-convex closed polylines that we call "hoops" can be used to compute occlusion efficiently for objects that have no large interior convex sets and were thus rejected by previous approaches.