IBM Journal of Research and Development
The NURBS book
Rational curves and surfaces with rational offsets
Computer Aided Geometric Design
Hermite interpolation by Pythagorean hodograph quintics
Mathematics of Computation
Offset-rational parametric plane curves
Computer Aided Geometric Design
Geometric Hermite interpolation with Tschirnhausen cubics
Journal of Computational and Applied Mathematics
Cycles upon cycles: an anecdotal history of higher curves in science and engineering
Proceedings of the international conference on Mathematical methods for curves and surfaces II Lillehammer, 1997
Hermite interpolation by pythagorean hodograph curves of degree seven
Mathematics of Computation
Comparing Offset Curve Approximation Methods
IEEE Computer Graphics and Applications
Error analysis of reparametrization based approaches for curve offsetting
Computer-Aided Design
Rational hypersurfaces with rational convolutions
Computer Aided Geometric Design
Curves and surfaces represented by polynomial support functions
Theoretical Computer Science
C1 Hermite interpolation with simple planar PH curves by speed reparametrization
Computer Aided Geometric Design
On rationally supported surfaces
Computer Aided Geometric Design
Pythagorean-Hodograph Curves: Algebra and Geometry Inseparable
Pythagorean-Hodograph Curves: Algebra and Geometry Inseparable
Approximating curves and their offsets using biarcs and Pythagorean hodograph quintics
Computer-Aided Design
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
G1 Hermite interpolation by PH cubics revisited
Computer Aided Geometric Design
Rational Pythagorean-hodograph space curves
Computer Aided Geometric Design
A unified Pythagorean hodograph approach to the medial axis transform and offset approximation
Journal of Computational and Applied Mathematics
Computer Aided Geometric Design
Support function of pythagorean hodograph cubics and G1 hermite interpolation
GMP'10 Proceedings of the 6th international conference on Advances in Geometric Modeling and Processing
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
Planar C1 Hermite interpolation with uniform and non-uniform TC-biarcs
Computer Aided Geometric Design
Geometric constraints on quadratic Bézier curves using minimal length and energy
Journal of Computational and Applied Mathematics
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We show that all rational hypocycloids and epicycloids are curves with Pythagorean normals and thus have rational offsets. Then, exploiting the convolution properties and (implicit) support function representation of these curves, we design an efficient algorithm for G^1 Hermite interpolation with their arcs. We show that for all regular data, there is a unique interpolating hypocycloidal or epicycloidal arc of the given canonical type.