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- Tor Dokken, Morten Daehlen, Tom Lyche, Knut Mørken
- Computer Aided Geometric Design
- 1990

- Tom Lyche, Knut Mørken
- Computer Aided Geometric Design
- 1987

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)

- Knut Mørken, Karl Scherer
- Math. Comput.
- 1997

In this paper we establish a general framework for so-called parametric, polynomial, interpolation methods for parametric curves. In contrast to traditional methods, which typically approximate the components of the curve separately, parametric methods utilize geometric information (which depends on all the components) about the curve to generate the… (More)

- Knut Mørken
- Computer Aided Geometric Design
- 2005

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)

- Eivind Lyche Melvær, Knut Mørken, Eigil Samset
- International Journal of Computer Assisted…
- 2011

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)

- Tom Lyche, Elaine Cohen, Knut Mørken
- Computer Aided Geometric Design
- 1985

- Tom Lyche, Knut Mørken, E. Quak
- 2001

We investigate mutually orthogonal spline wavelet spaces on non-uniform partitions of a bounded interval, addressing the existence, uniqueness and construction of bases of minimally supported spline wavelets. The relevant algorithms for decomposition and reconstruction are considered as well as some stability-related questions. In addition, we briefly… (More)

- Knut Mørken, Martin Reimers, Christian Schulz
- Computer Aided Geometric Design
- 2009

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 Lüth, Siri Øyen Larsen, Knut Mørken, Eigil Samset
- International Journal of Computer Assisted…
- 2007

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

- Knut Mørken
- 1999

In this paper we study the sensitivity of a spline function, represented in terms of Bsplines, to perturbations of the knots. We do this by bounding the difference between a primary spline, and a secondary spline with the same B-spline coefficients, but different knots. We give a number of bounds for this difference, both local bounds and global bounds in… (More)