Quaternion and Hopf map characterizations for the existence of rational rotation-minimizing frames on quintic space curves
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Publication:1960200
DOI10.1007/s10444-009-9138-3zbMath1202.53004OpenAlexW2132148545MaRDI QIDQ1960200
Publication date: 13 October 2010
Published in: Advances in Computational Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s10444-009-9138-3
angular velocitycomplex polynomialsquaternionsPythagorean-hodograph curvesHopf maprotation-minimizing frames
Computer science aspects of computer-aided design (68U07) Computer graphics; computational geometry (digital and algorithmic aspects) (68U05) Plane and space curves (14H50) Special algebraic curves and curves of low genus (14H45) Computational aspects of algebraic curves (14Q05) Curves in Euclidean and related spaces (53A04)
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Cites Work
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- Quintic space curves with rational rotation-minimizing frames
- Identification of spatial PH quintic Hermite interpolants with near-optimal shape measures
- Nonexistence of rational rotation-minimizing frames on cubic curves
- Pythagorean-hodograph curves. Algebra and geometry inseparable
- Helical polynomial curves and double Pythagorean hodographs II. Enumeration of low-degree curves
- A characterization of helical polynomial curves of any degree
- Two moving coordinate frames for sweeping along a 3D trajectory
- Computing frames along a trajectory
- Cubic Pythagorean hodograph spline curves and applications to sweep surface modeling.
- Characterization and construction of helical polynomial space curves.
- Clifford algebra, spin representation, and rational parameterization of curves and surfaces
- Hermite interpolation by rotation-invariant spatial Pythagorean-hodograph curves
- Euler-Rodrigues frames on spatial Pythagorean-hodograph curves.
- Helical polynomial curves and double Pythagorean hodographs. I: Quaternion and Hopf map representations
- Rational approximation schemes for rotation-minimizing frames on Pythagorean-hodograph curves
- There is More than One Way to Frame a Curve
- Exact rotation-minimizing frames for spatial Pythagorean-hodograph curves
- Mathematics of Surfaces XI
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