http://dl.gi.de/handle/20.500.12116/4388 2026-07-21T14:18:04Z http://dl.gi.de/handle/20.500.12116/4629 Deriving global material properties of a microscopically heterogeneous medium - computational homogenisation and opportunities in visualisation Hirschberger, C. B.; Ricker, S.; Steinmann, P.; Sukumar, N. Hagen, Hans; Hering-Bertram, Martin; Garth, Christoph In order to derive the overall mechanical response of a microscopically material body, both the theoretical and the numerical framework of multi scale consideration coined as computational homogenisation is presented. Instead of resolving the actual heterogeneous microstructure in all detail for its simulation, representative micro elements are considered which provide the material properties for the coarse or rather scale. This procedure allows for a smaller and less inexpensive computation. However both the chance and challenge of visualising the decisive features arise on two scales. 2008-01-01T00:00:00Z http://dl.gi.de/handle/20.500.12116/4620 A Survey of Implicit Surface Rendering Methods, and a Proposal for a Common Sampling Framework Knoll, Alois Hagen, Hans; Hering-Bertram, Martin; Garth, Christoph We consider several applications of implicit surfaces in visualization, and methods for rendering them. In particular we focus on geometry processing techniques for mesh extraction; and ray casting methods for direct rendering of implicits. Given that both methods rely on sampling the implicit function in question, we design a soft- ware framework that could accomodate both algorithms. We conclude by evaluating the time complexity and performance of existing systems, and discuss the long-term potential of both methods for rendering and computational goals. 2008-01-01T00:00:00Z http://dl.gi.de/handle/20.500.12116/4619 Why interval arithmetic is so useful Hijazi, Y.; Hagen, H.; Hansen, C. D.; Joy, K. I. Hagen, Hans; Hering-Bertram, Martin; Garth, Christoph Interval arithmetic was introduced by Ramon Moore [Moo66] in the 1960s as an approach to bound rounding errors in mathematical computation. The theory of interval analysis emerged considering the computation of both the exact solution and the error term as a single entity, i.e. the interval. Though a simple idea, it is a very powerful technique with numerous applications in mathematics, computer science, and engineering. In this survey we discuss the basic concepts of interval arithmetic and some of its extensions, and review successful applications of this theory in particular in computer science. 2008-01-01T00:00:00Z http://dl.gi.de/handle/20.500.12116/4625 Natural neighbor concepts in scattered data interpolation and discrete function approx- imation Bobach, T.; Umlauf, G. Hagen, Hans; Hering-Bertram, Martin; Garth, Christoph The concept of natural neighbors employs the notion of distance to define local neighborhoods in discrete data. Especially when querying and accessing large scale data, it is important to limit the amount of data that has to be processed for an answer. Because of its implicit definition on distances, the natural neighbor concept is extremely well suited to provide meaningful neighborhoods in spatial data with a scattered, inhomogeneous distribution. This paper revisits some unique properties of natural neighbor based methods and summarizes important findings for their successful application to scattered data interpolation, and the computation of discrete harmonic functions. 2008-01-01T00:00:00Z