IBM Journal of Research and Development
An algebraic approach to curves and surfaces on the sphere and on other quadrics
Selected papers of the international symposium on Free-form curves and free-form surfaces
The conformal map z→z2 of the hodograph plane
Computer Aided Geometric Design
Characterizations of the set of rational parametric curves with rational offsets
Proceedings of the international conference on Curves and surfaces in geometric design
Rational curves and surfaces with rational offsets
Computer Aided Geometric Design
Hermite interpolation by Pythagorean hodograph quintics
Mathematics of Computation
Curves with rational Frenet-Serret motion
Computer Aided Geometric Design
Minkowski pythagorean hodographs
Computer Aided Geometric Design
Hermite interpolation by pythagorean hodograph curves of degree seven
Mathematics of Computation
Polynomial and Rational Pythagorean-Hodograph Curves Reconciled
Proceedings of the 6th IMA Conference on the Mathematics of Surfaces
Structural invariance of spatial Pythagorean hodographs
Computer Aided Geometric Design
Rational approximation schemes for rotation-minimizing frames on Pythagorean-hodograph curves
Computer Aided Geometric Design
Characterization and construction of helical polynomial space curves
Journal of Computational and Applied Mathematics
A characterization of quintic helices
Journal of Computational and Applied Mathematics
Identification of spatial PH quintic Hermite interpolants with near-optimal shape measures
Computer Aided Geometric Design
Nonexistence of rational rotation-minimizing frames on cubic curves
Computer Aided Geometric Design
Branching blend of natural quadrics based on surfaces with rational offsets
Computer Aided Geometric Design
Journal of Symbolic Computation
Helical polynomial curves and double Pythagorean hodographs II. Enumeration of low-degree curves
Journal of Symbolic Computation
Quintic space curves with rational rotation-minimizing frames
Computer Aided Geometric Design
Pythagorean-Hodograph Curves: Algebra and Geometry Inseparable
Pythagorean-Hodograph Curves: Algebra and Geometry Inseparable
The elastic bending energy of pythagorean-hodograph curves
Computer Aided Geometric Design
Hermite interpolation by hypocycloids and epicycloids with rational offsets
Computer Aided Geometric Design
Rational rotation-minimizing frames on polynomial space curves of arbitrary degree
Journal of Symbolic Computation
On rational Minkowski Pythagorean hodograph curves
Computer Aided Geometric Design
Advances in Computational Mathematics
Spatial pythagorean hodograph quintics and the approximation of pipe surfaces
IMA'05 Proceedings of the 11th IMA international conference on Mathematics of Surfaces
Planar C1 Hermite interpolation with uniform and non-uniform TC-biarcs
Computer Aided Geometric Design
Reducibility of offsets to algebraic curves
Computer Aided Geometric Design
An interpolation scheme for designing rational rotation-minimizing camera motions
Advances in Computational Mathematics
Dual representation of spatial rational Pythagorean-hodograph curves
Computer Aided Geometric Design
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A method for constructing rational Pythagorean-hodograph (PH) curves in R^3 is proposed, based on prescribing a field of rational unit tangent vectors. This tangent field, together with its first derivative, defines the orientation of the curve osculating planes. Augmenting this orientation information with a rational support function, that specifies the distance of each osculating plane from the origin, then completely defines a one-parameter family of osculating planes, whose envelope is a developable ruled surface. The rational PH space curve is identified as the edge of regression (or cuspidal edge) of this developable surface. Such curves have rational parametric speed, and also rational adapted frames that satisfy the same conditions as polynomial PH curves in order to be rotation-minimizing with respect to the tangent. The key properties of such rational PH space curves are derived and illustrated by examples, and simple algorithms for their practical construction by geometric Hermite interpolation are also proposed.