In the following you will find a list of research projects carried out at NUHAG.If you are interested in a certain project, please click on the title.Click on the header line to change sorting. admin» |
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X | Analysis of non-uniform subdivision schemes | FWF | AnONSS | 2015.10.01 | 2018.09.30 |
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This project is devoted to the analysis of non-uniform subdivision schemes. These are efficient level dependent and spatially variant recursive algorithms for generation of curves and surfaces. The analysis of subdivision schemes constitutes a modern and application oriented branch of approximation theory. Indeed, subdivision schemes play a role in biological imaging, computer aided geometric design, computer animation, wavelet frame theory and isogeometric analysis. The first goal of this project is the development of a general, computationally efficient method for the analysis of the convergence and regularity of non-uniform subdivision schemes. In the stationary setting, the smoothness of subdivision limits is characterized by the joint spectral radius of a certain finite set of square matrices defined by the corresponding subdivision rules. Recent results by the applicant and her co-authors show that, surprisingly, such a link also exists in the more general non-stationary setting. It is still an open problem, whether the characterization of the regularity of general non-uniform subdivision schemes is possible via the joint spectral radius approach. This project will either give an affirmative answer to this open problem, thus, demonstrating the full strength of the joint spectral radius approach, or expose its limitations. Generation and reproduction properties of subdivision schemes are particularly relevant for applications. Polynomial generation of stationary subdivision schemes determines the efficiency of wavelet frame decomposition and reconstruction algorithms. Generation and reproduction of exponential polynomials by non-stationary subdivision schemes link subdivision and isogeometric analysis. Non-uniform schemes are appreciated for their capability to reduce unwanted wobbly artifacts and self-intersections of curves and surfaces of arbitrary topology. The generation and reproduction properties of non-uniform subdivision schemes are not completely understood. The second goal of this project is a characterization of the variety of shapes and of classes of functions that can be generated and reproduced by non-uniform schemes. |
ANB | ... | Austrian National Bank |
EC | ... | European Commission |
FWF | ... | Fonds zur Förderung der wissenschaftlichen Forschung |
UniVie | ... | University of Vienna |
WWTF | ... | Wiener Wissenschafts-, Forschungs- und Technologiefonds |