IBM Journal of Research and Development
Applications of Laguerre geometry in CAGD
Computer Aided Geometric Design
Minkowski pythagorean hodographs
Computer Aided Geometric Design
C1 Hermite interpolation using MPH quartic
Computer Aided Geometric Design
Clifford algebra, Lorentzian geometry, and rational parametrization of canal surfaces
Computer Aided Geometric Design
Exploiting curvatures to compute the medial axis for domains with smooth boundary
Computer Aided Geometric Design
MOS surfaces: medial surface transforms with rational domain boundaries
Proceedings of the 12th IMA international conference on Mathematics of surfaces XII
On rational Minkowski Pythagorean hodograph curves
Computer Aided Geometric Design
Computer Aided Geometric Design
A unified Pythagorean hodograph approach to the medial axis transform and offset approximation
Journal of Computational and Applied Mathematics
Reparameterization of curves and surfaces with respect to their convolution
MMCS'08 Proceedings of the 7th international conference on Mathematical Methods for Curves and Surfaces
Low degree euclidean and minkowski pythagorean hodograph curves
MMCS'08 Proceedings of the 7th international conference on Mathematical Methods for Curves and Surfaces
G2 hermite interpolation with curves represented by multi-valued trigonometric support functions
Proceedings of the 7th international conference on Curves and Surfaces
Algebraic curves of low convolution degree
Proceedings of the 7th international conference on Curves and Surfaces
Exploring hypersurfaces with offset-like convolutions
Computer Aided Geometric Design
Parameterizing rational offset canal surfaces via rational contour curves
Computer-Aided Design
Planar C1 Hermite interpolation with uniform and non-uniform TC-biarcs
Computer Aided Geometric Design
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As observed by [Choi, H.I., Han, Ch.Y., Moon, H.P., Roh, K.H., Wee, N.S., 1999. Medial axis transform and offset curves by Minkowski Pythagorean hodograph curves. Computer-Aided Design 31, 59-72], curves in Minkowski space R^2^,^1 are very well suited to describe the medial axis transform (MAT) of a planar domain, and Minkowski Pythagorean hodograph (MPH) curves correspond to domains, where both the boundaries and their offsets are rational curves [Moon, H.P., 1999. Minkowski Pythagorean hodographs. Computer Aided Geometric Design 16, 739-753]. Based on these earlier results, we give a thorough discussion of G^1 Hermite interpolation by MPH cubics, focusing on solvability and approximation order. Among other results, it is shown that any analytic space-like curve without isolated inflections can be approximately converted into a G^1 spline curve composed of MPH cubics with the approximation order being equal to four. The theoretical results are illustrated by several examples. In addition, we show how the curvature of a curve in Minkowski space is related to the boundaries of the associated planar domain.