Knut Mørken

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This paper is the third in a sequence of papers in which a knot removal strategy for splines, based on certain discrete norms, is developed. In the first paper, approximation methods defined as best approximations in these norms were discussed, while in the second paper a knot removal strategy for spline functions was developed. In this paper the knot(More)
By exploiting the freedom in the choice of parametrization of a parametric surface, we show that there exist quadratic parametric surfaces that approximate a given parametric surface with the same approximation order as cubics, namely four, in the neighbourhood of a point where the Gaussian curvature of the surface is nonzero. This provides a first(More)
Ultrasound-guided 3D interventions require calibration to relate real-time 2D images with the position and orientation of the ultrasound probe. Capturing several images of a single fixed point from different viewpoints is a simple and commonly used approach, but it is cumbersome and tedious. A new phantom for calibration was designed, built and tested to(More)
We present a new method for computing intersections of two parametric B-Spline curves. We use an intersection of the control polygons as an approximation for an intersection of the curves in combination with knot insertion. The resulting algorithm is asymptotically Newton-like, but without the need of a starting value. Like Newton’s method, it converges(More)
Sebastian Stopp, Herbert Deppe, Tim Lueth MIMED, Lehrstuhl Mikrotechnik und Medizingerätetechni, Technische Universität München, Munich, Germany Klinik und Poliklinik für Mund-, Kieferund Gesichtschirurgie (MKG), Technischen Universität München, Fachgebiet Zahnärztliche Chirurgie und Implantologie, Munich, Germany