Transfer functions have a crucial role in the understanding and visualization of 3D data. While research has
scrutinized the possible uses of one and multi-dimensional transfer functions in the spatial domain, to our
knowledge, no attempt has been done to explore transfer functions in the frequency domain. In this work we
propose transfer functions for the purpose of frequency analysis and visualization of 3D data. Frequency-based
transfer functions offer the possibility to discriminate signals, composed from different frequencies, to analyze
problems related to signal processing, and to help understanding the link between the modulation of specific
frequencies and their impact on the spatial domain. We demonstrate the strength of frequency-based transfer
functions by applying them to medical CT, ultrasound and MRI data, physics data as well as synthetic seismic
data. The interactive design of complex filters for feature enhancement can be a useful addition to conventional
classification techniques.
There is a wide range of visualization techniques for dynamical systems. These methods are used to visualize certain properties as, e.g., stability of fixed points, characteristic changes of velocity, and bifurcations. This paper gives a short introduction to dynamical system and describes several visualization techniques. Some of those are applied to three different dynamical system. The application of different visualization methods to dynamical systems shows how scientific visualization can be used for analyzing the behavior of dynamical systems, and how visualization can make analysis of a dynamical system fast and efficient.
'Shadow profiling' measures shadow durations on an arbitrary scene during several hours of a specific day or even several weeks or months. The result is to be displayed visually. We shortly discuss already known techniques like simplified radiosity or discontinuity meshing with regard to their suitability for this problem. Due to various drawbacks of these techniques, we present our won approach. Especially a pixel-oriented version works very efficiently in connection with fast polygon-oriented shadow algorithms. It can be applied to architectural design, and it can also be used in computer graphics for the computation-inexpensive simulation of complex light sources.
Nonlinear deterministic dynamical systems often exhibit complex and chaotic behavior which is difficult to comprehend. Visualizing the characteristics of such systems is therefore essential for an understanding of the underlying dynamics. In this paper concepts for the interactive graphical exploration of analytically defined dynamical systems are discussed. Emphasis is put on interactivity which shall facilitate the investigation and exploration of such systems. The following topics on dynamical systems are treated in more detail: interactive specification, simple and fast graphical representation, and interactive modification. The paper concentrates on 2D and 3D orthographic projections of higher-dimensional phase spaces and on the display of bifurcation diagrams. A prototype software system which incorporates the previously presented ideas is shortly discussed. The software system is intended to offer a quick insight into the dynamics of a dynamical system and to enable fast investigation of variations of a dynamical system.
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