Two moving coordinate frames for sweeping along a 3D trajectory
Computer Aided Geometric Design
Computing frames along a trajectory
Computer Aided Geometric Design
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
Hermite interpolation by Pythagorean hodograph quintics
Mathematics of Computation
Real-time CNC interpolators for Pythagorean-hodograph curves
Computer Aided Geometric Design
The elastic bending energy of Pythagorean-hodograph curves
Computer Aided Geometric Design
Circle and sphere as rational splines
Neural, Parallel & Scientific Computations - computer aided geometric design
The circle as a smoothly joined BR-curve on [0,1]
Computer Aided Geometric Design
Construction and shape analysis of PH Hermite interpolants
Computer Aided Geometric Design
Performance analysis of CNC interpolators for time-dependent feedrates along PH curves
Computer Aided Geometric Design
Hermite interpolation by pythagorean hodograph curves of degree seven
Mathematics of Computation
A Menagerie of Rational B-Spline Circles
IEEE Computer Graphics and Applications
Structural invariance of spatial Pythagorean hodographs
Computer Aided Geometric Design
The shape of spherical quartics
Computer Aided Geometric Design
C1 Hermite interpolation using MPH quartic
Computer Aided Geometric Design
A control polygon scheme for design of planar C2 PH quintic spline curves
Computer Aided Geometric Design
A characterization of quintic helices
Journal of Computational and Applied Mathematics
C1 Hermite interpolation with simple planar PH curves by speed reparametrization
Computer Aided Geometric Design
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
Pythagorean-hodograph preserving mappings
Journal of Computational and Applied Mathematics
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
On rational Minkowski Pythagorean hodograph curves
Computer Aided Geometric Design
Advances in Computational Mathematics
Computer Aided Geometric Design
Geometric Hermite interpolation by monotone helical quintics
Computer Aided Geometric Design
Rational Pythagorean-hodograph space curves
Computer Aided Geometric Design
Cubic helical splines with Frenet-frame continuity
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
Rotation-minimizing osculating frames
Computer Aided Geometric Design
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Helical space curves are characterized by the property that their unit tangents maintain a constant inclination with respect to a fixed line, the axis of the helix. Equivalently, a helix exhibits a circular tangent indicatrix, and constant curvature/torsion ratio. If a polynomial space curve is helical, it must be a Pythagorean-hodograph (PH) curve. The quaternion representation of spatial PH curves is used to characterize and construct helical curves. Whereas all spatial PH cubics are helical, the helical PH quintics form a proper subset of all PH quintics. Two types of PH quintic helix are identified: (i) the "monotone-helical" PH quintics, in which a scalar quadratic factors out of the hodograph, and the tangent exhibits a consistent sense of rotation about the axis; and (ii) general helical PH quintics, which possess irreducible hodographs, and may suffer reversals in the sense of tangent rotation. First-order Hermite interpolation is considered for both helical PH quintic types. The helicity property offers a means of fixing the residual degrees of freedom in the general PH quintic Hermite interpolation problem, and yields interpolants with desirable shape features.