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.
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Communicated by Helmut Pottmann.
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Kosinka, J., Jüttler, B. C1 Hermite interpolation by Pythagorean hodograph quintics in Minkowski space. Adv Comput Math 30, 123–140 (2009). https://doi.org/10.1007/s10444-007-9059-y
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DOI: https://doi.org/10.1007/s10444-007-9059-y