An interpolation scheme for designing rational rotation-minimizing camera motions

DOI10.1007/S10444-011-9226-ZzbMath1315.65011OpenAlexW2003407090MaRDI QIDQ1946487

Rida T. Farouki, Carlotta Giannelli, Alessandra Sestini

Publication date: 15 April 2013

Published in: Advances in Computational Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10444-011-9226-z

zbMATH Keywords

interpolationangular velocityquaternionsrotation-minimizing framescamera orientationdirected framesPythagorean curves

Mathematics Subject Classification ID

Kinematics of mechanisms and robots (70B15) Numerical interpolation (65D05)

Related Items (3)

\(C^1\) interpolation by rational biarcs with rational rotation minimizing directed frames ⋮ Spatial quintic Pythagorean-hodograph interpolants to first-order Hermite data and Frenet frames ⋮ Rational rotation-minimizing frames -- recent advances and open problems

Cites Work

• Quintic space curves with rational rotation-minimizing frames
• Rational Pythagorean-hodograph space curves
• Identification of spatial PH quintic Hermite interpolants with near-optimal shape measures
• Nonexistence of rational rotation-minimizing frames on cubic curves
• Rational rotation-minimizing frames on polynomial space curves of arbitrary degree
• Pythagorean-hodograph curves. Algebra and geometry inseparable
• Clifford algebra, spin representation, and rational parameterization of curves and surfaces
• Euler-Rodrigues frames on spatial Pythagorean-hodograph curves.
• Quaternion and Hopf map characterizations for the existence of rational rotation-minimizing frames on quintic space curves
• Construction of Rational Curves with Rational Rotation-Minimizing Frames via Möbius Transformations
• Design of rational rotation–minimizing rigid body motions by Hermite interpolation

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