Guido Brunnett

Geometric modeling for scientific visualization

1. Surface Reconstruction and Interpolation Marietta E. Cameron, Kenneth R. Sloan, and Ying Sun: Reconstruction from Unorganized Point Sets using Gamma Shapes Ingrid Hotz and Hans Hagen: Isometric embedding for a discrete metric David Levin: Mesh-Independent Surface Interpolation Robert Mencl and Heinrich Mueller: Empirical Analysis of Surface Interpolation by Spatial Environment Graphs 2. Surface Interrogation and Modeling Georges-Pierre Bonneau and Stefanie Hahmann: Smooth Polylines on Polygon Meshes Mark A. Duchaineau and Kenneth I. Joy: Progressive Precision Surface Design Helwig Hauser, Thomas Theussl, Andreas Konig, and Eduard Groller: Smart Surface Interrogation for Advanced Visualization Techniques Yootai Kim, Raghu Machiraju, and David Thompson: Modeling Rough Surfaces Georgios Stylianou: A Feature Based Method for Rigid Registration of Anatomical Surfaces 3. Wavelets and Compression on Surfaces Martin Bertram: Lifting Biorthogonal B-spline Wavelets Ioannis Ivrissimtzis, Christian Roessl, and Hans-Peter Seidel: Tree-based Data Structures for Triangle Mesh Connectivity Encoding Andrei Khodakovsky and Igor Guskov: Compression of Normal Meshes Gabriel Taubin: New Results in Signal Processing and Compression of Polygon Meshes 4. Topology, Distance Fields and Solid Modeling Jian Huang and Roger Crawfis: Adaptively Refined Complete Distance Fields of Polygonal Models Marcelo Kallmann, Hanspeter Bieri, and Daniel Thalmann: Fully Dynamic Constrained Delaunay Triangulations Jorge Rodriguez, Dolors Ayala, and Antonio Aguilera: EVM: A Complete Solid Model for Surface Rendering Xavier Tricoche and Gerik Scheuermann: Topology Simplification of Symmetric, Second-Order 2D Tensor

The geometry of optimal degree reduction of Be´zier curves

Optimal degree reductions, i.e. best approximations of \(n\)-th degree Bezier curves by Bezier curves of degree \(n\) - 1, with respect to different norms are studied. It is shown that for any \(L_p\)-norm the euclidean degree reduction where the norm is applied to the euclidean distance function of two curves is identical to componentwise degree reduction. The Bezier points of the degree reductions are found to lie on parallel lines through the Bezier points of any Taylor expansion of degree \(n\) - 1 of the original curve. This geometric situation is shown to hold also in the case of constrained degree reduction. The Bezier points of the degree reduction are explicitly given in the unconstrained case for \(p\) = 1 and \(p\) = 2 and in the constrained case for \(p\) = 2.

Real-Time Interaction with a Humanoid Avatar in an Immersive Table Tennis Simulation

In this paper, we report on the realization of an immersive table tennis simulation. After describing the hardware necessities of our system, we give insight into different aspects of the simulation. In particular, the developed methods for collision detection and physical simulation are presented. The design of the virtual opponent is of crucial importance to realize an enjoyable game. Therefore, we report on the implemented game strategy and the animation of the opponent. Since table tennis is one of the fastest sports, the synchronization of the human players movements and the visual output on the projection wall is a very challenging problem to solve. To overcome the latencies in our system, we designed a prediction method that allows high speed interaction with our application

Direct segmentation of algebraic models for reverse engineering

In Reverse Engineering a physical object is digitally reconstructed from a set of boundary points. In the segmentation phase these points are grouped into subsets to facilitate consecutive steps as surface fitting. In this paper we present a segmentation method with subsequent classification of simple algebraic surfaces. Our method is direct in the sense that it operates directly on the point set in contrast to other approaches that are based on a triangulation of the data set. The segmentation process involves a fast algorithm for k-nearest neighbors search and an estimation of first and second order surface properties. The first order segmentation, that is based on normal vectors, provides an initial subdivision of the surface and detects sharp edges as well as flat or highly curved areas. One of the main features of our method is to proceed by alternating the steps of segmentation and normal vector estimation. The second order segmentation subdivides the surface according to principal curvatures and provides a sufficient foundation for the classification of simple algebraic surfaces. If the boundary of the original object contains such surfaces the segmentation is optimized based on the result of a surface fitting procedure.

Interpolation with minimal-energy splines

Abstract The problem of interpolating a sequence of points in the plane with a nonlinear spline curve of minimal energy and prescribed tangents in the endpoints is addressed. The method presented is based on the idea of representing the interpolant as a curve of a piecewise polynomial curvature function. The algorithm to determine the interpolant involves a table lookup to speed up the computation of the relevant parameters, and an optimization to minimize curvature discontinuities in the curve.

V-Pong: an immersive table tennis simulation

Most applications for immersive virtual environments (VEs) allow slow-or medium-speed user interaction. Examples of this kind of interaction include changing an objects position, triggering an action, or setting a control parameter. To broaden the application range for VR systems, we need to integrate technologies that allow for faster VE-user movements. This raises the question, What response times can we achieve with VR systems built from standard recent hardware components? To answer this question, we created a table tennis simulation as this game involves fast user movements and has moderate space requirements. In this article we report on the realization of our immersive table tennis simulation, V-Pong

Real time tracking of high speed movements in the context of a table tennis application

In this paper we summarize the experiences we made with the implementation of a table tennis application. After describing the hardware necessities of our system we give insight into different aspects of the simulation. These include collision detection, physical simulation and some aspects of the design of the virtual opponent.Since table tennis is one of the fastest sports the synchronization of the players movements and the visual output on the projection wall is the most challenging problem to solve. Therefore we analysed the latencies of all subcomponents of our system and designed a prediction method that allows high speed interaction with our application.

An extended concept of voxel neighborhoods for correct thinning in mesh segmentation

We present a method for mesh segmentation based on volume representation and the so called skeleton graph. In this method, the triangle mesh is first trans-formed into a voxel representation. A thinning algorithm based on our definition of a local neighborhood is employed to extract a voxel skeleton which is then transformed into a graph representation. The branching points of this graph are used to define the segmentation of the mesh.This article focuses on the data structure used to manage the voxel set and the extension of the neighborhood concept that allows to distinguish be-tween local and global neighborhoods. Our rasteriza-tion is not based on equilateral cells, leading to an efficient data structure in terms of memory usage.

Compressing dynamic meshes with geometric laplacians

This paper addresses the problem of representing dynamic 3D meshes in a compact way, so that they can be stored and transmitted efficiently. We focus on sequences of triangle meshes with shared connectivity, avoiding the necessity of having a skinning structure. Our method first computes an average mesh of the whole sequence in edge shape space. A discrete geometric Laplacian of this average surface is then used to encode the coefficients that describe the trajectories of the mesh vertices. Optionally, a novel spatio‐temporal predictor may be applied to the trajectories to further improve the compression rate. We demonstrate that our approach outperforms the current state of the art in terms of low data rate at a given perceived distortion, as measured by the STED and KG error metrics.

Surface Reconstruction from Unorganized Point Data with Quadrics

We present a reverse engineering method for constructing a surface approximation scheme whose input is a set of unorganized noisy points in space and whose output is a set of quadric patches. The local surface properties, necessary for the subsequent segmentation, are estimated directly from the data using a simple and efficient data structure—the neighborhood graph. Our segmentation scheme, based on principal curvatures, constructs initial point subsets, which may be enlarged or further subdivided based on associated approximation error estimates obtained through approximation of the initial segments by quadric surfaces. Our method is highly efficient and produces a high‐quality piecewise quadric surface approximation of engineering objects, which we demonstrate for several simple and complex example data sets.