Locally optimal knots and tension parameters for exponential splines

Authors:
Karl O. Riedel
Affiliations:
Mathematical Institute, University of Cologne, Cologne, Germany and Weißensteinerstraße, Schwäbisch Gmünd, Germany
Venue:
Journal of Computational and Applied Mathematics
Year:
2006

Citing 9
Cited 0

Convexity preserving interpolation with exponential splines

Computing
Interpolatory tension splines with automatic selection of tension factors

SIAM Journal on Scientific and Statistical Computing
A method for computing the tension parameters in convexity-preserving spline-in-tension interpolation

Numerische Mathematik
A rational cubic spline with tension

Computer Aided Geometric Design
Construction of exponential tension B-splines of arbitrary order

Curves and surfaces
Curve and surface fitting with splines

Curve and surface fitting with splines
Algorithm 716: TSPACK: tension spline curve-fitting package

ACM Transactions on Mathematical Software (TOMS)
Interpolation with exponential B-splines in tension

Geometric modelling
Shape preserving least-squares approximation by polynomial parametric spline curves

Computer Aided Geometric Design

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Abstract

Tension can be applied to cubic splines in order to avoid undesired spurious oscillations. This leads to the well-known (exponential) spline in tension. It is crucial but unfortunately difficult to find suitable tension parameters of interpolating splines in tension. Instead of heuristics, we propose a simultaneous knot placing and tension setting algorithm for least-squares splines in tension which includes interpolating splines in tension as a special case. Moreover, the splines presented here are the foundation of exponential surface splines on fairly arbitrary meshes [K.O. Riedel, Two-dimensional splines on fairly arbitrary meshes, ZAMM--Z. Angew. Math. Mech. 85(3) (2005) 176-188].