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Advances in Computational Mathematics

, Volume 30, Issue 2, pp 123–140 | Cite as

C1 Hermite interpolation by Pythagorean hodograph quintics in Minkowski space

  • Jiří Kosinka
  • Bert JüttlerEmail author
Article

Abstract

Curves in the Minkowski space \(\mathbb{R}^{2,1} \) are very well suited to describe the medial axis transform (MAT) of planar domains. Among them, Minkowski Pythagorean hodograph (MPH) curves correspond to domains where both the boundaries and their offsets admit rational parameterizations (Choi et al., Comput Aided Design 31:59–72, 1999; Moon, Comput Aided Geom Design 16:739–753; 1999). We construct MPH quintics which interpolate two points with associated first derivative vectors and analyze the properties of the system of solutions, including the approximation order of the ‘best’ interpolant.

Keywords

Hermite interpolation Minkowski space Minkowski Pythagorean hodograph curves 

Mathematics Subject Classifications (2000)

65D17 68U05 

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Copyright information

© Springer Science+Business Media, LLC. 2007

Authors and Affiliations

  1. 1.Institute of Applied GeometryJohannes Kepler UniversityLinzAustria
  2. 2.CMABlinderuNorway

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