Georg Umlauf

Iso-geometric Finite Element Analysis Based on Catmull-Clark : ubdivision Solids

We present a volumetric iso‐geometric finite element analysis based on Catmull‐Clark solids. This concept allows one to use the same representation for the modeling, the physical simulation, and the visualization, which optimizes the design process and narrows the gap between CAD and CAE. In our method the boundary of the solid model is a Catmull‐Clark surface with optional corners and creases to support the modeling phase. The crucial point in the simulation phase is the need to perform efficient integration for the elements. We propose a method similar to the standard subdivision surface evaluation technique, such that numerical quadrature can be used.

A G2-Subdivision Algorithm

In this paper we present a method to optimize the smoothness order of subdivision algorithms generating surfaces of arbitrary topology. In particular we construct a subdivision algorithm with some negative weights producing G 2-surfaces. These surfaces are piecewise bicubic and are flat at their extraordinary points. The underlying ideas can also be used to improve the smoothness order of subdivision algorithms for surfaces of higher degree or triangular nets.

Improved triangular subdivision schemes

The authors improve the butterfly and Loops (1987) algorithm. As a result they obtain subdivision algorithms for triangular nets which can be used to generate G/sup 1/- and G/sup 2/-surfaces, respectively.

Gaussian and Mean Curvature of Subdivision Surfaces

By explicitly deriving the curvature of subdivision surfaces in the extraordinary points, we give an alternative, more direct account of the criteria necessary and sufficient for achieving curvature continuity than earlier approaches that locally parametrize the surface by eigenfunctions.

Loop subdivision with curvature control

In this paper the problem of curvature behavior around extraordinary points of a Loop subdivision surface is addressed. A variant of Loops algorithm with small stencils is used that generates surfaces with bounded curvature and prescribed elliptic or hyperbolic behavior. We present two different techniques that avoid the occurrence of hybrid configurations, so that an elliptic or hyperbolic shape can be guaranteed. The first technique uses a symmetric modification of the initial control-net to avoid hybrid shapes in the vicinity of an extraordinary point. To keep the difference between the original and the modified mesh as small as possible the changes are formulated as correction stencils and spread to a finite number of subdivision steps. The second technique is based on local optimization in the frequency domain. It provides more degrees of freedom and so more control over the global shape.

Image compression using data-dependent triangulations

We present a method to speed up the computation of a high-quality data-dependent triangulation approximating an image using simulated annealing by probability distributions guided by local approximation error and its variance. The triangulation encodes the image, yielding compression rates comparable to or even superior to JPEG and JPEG2000 compression. The specific contributions of our paper are a speed-up of the simulated annealing optimization and a comparison of our approach to other image approximation and compression methods. Furthermore, we propose an adaptive vertex insertion/removal strategy and termination criteria for the simulated annealing to achieve specified approximation error bounds.

A G 1 and a G 2 subdivision Scheme for triangular Nets.

In this article we improve the butterfly and Loops algorithm. As a result we obtain subdivision algorithms for triangular nets which can be used to generate G1- and G2-surfaces, respectively.

Natural neighbor extrapolation using ghost points

Among locally supported scattered data schemes, natural neighbor interpolation has some unique features that makes it interesting for a range of applications. However, its restriction to the convex hull of the data sites is a limitation that has not yet been satisfyingly overcome. We use this setting to discuss some aspects of scattered data extrapolation in general, compare existing methods, and propose a framework for the extrapolation of natural neighbor interpolants on the basis of dynamic ghost points.

Computing curvature bounds for bounded curvature subdivision

For a stationary, affine invariant, symmetric, linear and local subdivision scheme that is C^2 apart from the extraordinary point the curvature is bounded if the square of the subdominant eigenvalue equals the subsubdominant eigenvalue. This paper gives a technique for quickly establishing an interval to which the curvature is confined at the extraordinary point. The approach factors the work into precomputed intervals that depend only on the scheme and a mesh-specific component. When the intervals are tight enough they can be used as a test of shape-faithfulness of the given subdivision scheme; i.e., if the limit surface in the neighborhood of the extraordinary point of the subdivision scheme is consistent with the geometry implied by the input mesh.

Online Triangulation of Laser-Scan Data

Hand-held laser scanners are used massively in industry for reverse engineering and quality measurements. In this process, it is difficult for the human operator to scan the target object completely and uniformly. Therefore, an interactive triangulation of the scanned points can assist the operator in this task.