Two moving coordinate frames for sweeping along a 3D trajectory
Computer Aided Geometric Design
Computing frames along a trajectory
Computer Aided Geometric Design
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
Computation of rotation minimizing frames
ACM Transactions on Graphics (TOG)
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
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
Spatial pythagorean hodograph quintics and the approximation of pipe surfaces
IMA'05 Proceedings of the 11th IMA international conference on Mathematics of Surfaces
Construction of rational surface patches bounded by lines of curvature
Computer Aided Geometric Design
Rational Pythagorean-hodograph space curves
Computer Aided Geometric Design
Computer Aided Geometric Design
A complete classification of quintic space curves with rational rotation-minimizing frames
Journal of Symbolic Computation
Original Articles: Motion design with Euler-Rodrigues frames of quintic Pythagorean-hodograph curves
Mathematics and Computers in Simulation
Pythagorean-hodograph curves in Euclidean spaces of dimension greater than 3
Journal of Computational and Applied Mathematics
C1 rational interpolation of spherical motions with rational rotation-minimizing directed frames
Computer Aided Geometric Design
An interpolation scheme for designing rational rotation-minimizing camera motions
Advances in Computational Mathematics
Optimal tool orientation control for 5-axis CNC milling with ball-end cutters
Computer Aided Geometric Design
Constructing PDE-based surfaces bounded by geodesics or lines of curvature
Computers & Mathematics with Applications
Inverse kinematics for optimal tool orientation control in 5-axis CNC machining
Computer Aided Geometric Design
Rotation-minimizing osculating frames
Computer Aided Geometric Design
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Simple criteria for the existence of rational rotation-minimizing frames (RRMFs) on quintic space curves are determined, in terms of both the quaternion and Hopf map representations for Pythagorean-hodograph (PH) curves in 驴3. In both cases, these criteria amount to satisfaction of three scalar constraints that are quadratic in the curve coefficients, and are thus much simpler than previous criteria. In quaternion form, RRMF quintics can be characterized by just a single quadratic (vector) constraint on the three quaternion coefficients. In the Hopf map form, the characterization is in terms of one real and one complex quadratic constraint on the six complex coefficients. The identification of these constraints is based on introducing a "canonical form" for spatial PH curves and judicious transformations between the quaternion and Hopf map descriptions. The simplicity of these new characterizations for the RRMF quintics should help facilitate the development of algorithms for their construction, analysis, and practical use in applications such as animation, spatial motion planning, and swept surface constructions.