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
Characterization and construction of helical polynomial space curves
Journal of Computational and Applied Mathematics
Stability and Finiteness Properties of Medial Axis and Skeleton
Journal of Dynamical and Control Systems
Exploiting curvatures to compute the medial axis for domains with smooth boundary
Computer Aided Geometric Design
G1 Hermite interpolation by Minkowski Pythagorean hodograph cubics
Computer Aided Geometric Design
Spatial pythagorean hodograph quintics and the approximation of pipe surfaces
IMA'05 Proceedings of the 11th IMA international conference on Mathematics of Surfaces
On rational Minkowski Pythagorean hodograph curves
Computer Aided Geometric Design
A unified Pythagorean hodograph approach to the medial axis transform and offset approximation
Journal of Computational and Applied Mathematics
G2 hermite interpolation with curves represented by multi-valued trigonometric support functions
Proceedings of the 7th international conference on Curves and Surfaces
Parameterizing rational offset canal surfaces via rational contour curves
Computer-Aided Design
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We describe and fully analyze an algorithm for C^2 Hermite interpolation by Pythagorean hodograph curves of degree 9 in Minkowski space R^2^,^1. We show that for any data there exists a four-parameter system of interpolants and we identify the one which preserves symmetry and planarity of the input data and which has the optimal approximation degree. The new algorithm is applied to an efficient approximation of segments of the medial axis transform of a planar domain leading to rational parameterizations of the offsets of the domain boundaries with a high order of approximation.