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Item Table of Contents CGF 22-3(Blackwell Publishers, Inc and the Eurographics Association, 2003) Fellner, Dieter W.; Brunet, Pere-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 EG Editorial(The Eurographics Association and Blackwell Publishing Ltd., 2005) Brunet, Pere; Willis, Phil; Seidel, Hans-PeterItem 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.Item Sensor-aware Normal Estimation for Point Clouds from 3D Range Scans(The Eurographics Association and John Wiley & Sons Ltd., 2018) Comino Trinidad, Marc; Andujar, Carlos; Chica, Antonio; Brunet, Pere; Ju, Tao and Vaxman, AmirNormal vectors are essential for many point cloud operations, including segmentation, reconstruction and rendering. The robust estimation of normal vectors from 3D range scans is a challenging task due to undersampling and noise, specially when combining points sampled from multiple sensor locations. Our error model assumes a Gaussian distribution of the range error with spatially-varying variances that depend on sensor distance and reflected intensity, mimicking the features of Lidar equipment. In this paper we study the impact of measurement errors on the covariance matrices of point neighborhoods. We show that covariance matrices of the true surface points can be estimated from those of the acquired points plus sensordependent directional terms. We derive a lower bound on the neighbourhood size to guarantee that estimated matrix coefficients will be within a predefined error with a prescribed probability. This bound is key for achieving an optimal trade-off between smoothness and fine detail preservation. We also propose and compare different strategies for handling neighborhoods with samples coming from multiple materials and sensors. We show analytically that our method provides better normal estimates than competing approaches in noise conditions similar to those found in Lidar equipment.Item Approximation of a Variable Density Cloud of Points by Shrinking a Discrete Membrane(The Eurographics Association and Blackwell Publishing Ltd., 2005) Esteve, Jordi; Brunet, Pere; Vinacua, AlvarThis paper describes a method to obtain a closed surface that approximates a general 3D data point set with nonuniform density. Aside from the positions of the initial data points, no other information is used. Particularly, neither the topological relations between the points nor the normal to the surface at the data points are needed. The reconstructed surface does not exactly interpolate the initial data points, but approximates them with a bounded maximum distance. The method allows one to reconstruct closed surfaces with arbitrary genus and closed surfaces with disconnected shells.