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
SURFACES FOR COMPUTER-AIDED DESIGN OF SPACE FORMS
SURFACES FOR COMPUTER-AIDED DESIGN OF SPACE FORMS
Rational approximation schemes for rotation-minimizing frames on Pythagorean-hodograph curves
Computer Aided Geometric Design
An Operator Calculus for Surface and Volume Modeling
IEEE Computer Graphics and Applications
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
Quintic space curves with rational rotation-minimizing frames
Computer Aided Geometric Design
Existence conditions for Coons patches interpolating geodesic boundary curves
Computer Aided Geometric Design
Pythagorean-Hodograph Curves: Algebra and Geometry Inseparable
Pythagorean-Hodograph Curves: Algebra and Geometry Inseparable
Construction of Bézier surface patches with Bézier curves as geodesic boundaries
Computer-Aided Design
Advances in Computational Mathematics
CrossShade: shading concept sketches using cross-section curves
ACM Transactions on Graphics (TOG) - SIGGRAPH 2012 Conference Proceedings
Generalized dupin cyclides with rational lines of curvature
Proceedings of the 7th international conference on Curves and Surfaces
Constructing PDE-based surfaces bounded by geodesics or lines of curvature
Computers & Mathematics with Applications
Rotation-minimizing osculating frames
Computer Aided Geometric Design
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The fact that the Darboux frame is rotation-minimizing along lines of curvature of a smooth surface is invoked to construct rational surface patches whose boundary curves are lines of curvature. For given patch corner points and associated frames defining the surface normals and principal directions, the patch boundaries are constructed as quintic RRMF curves, i.e., spatial Pythagorean-hodograph (PH) curves that possess rational rotation-minimizing frames. The interior of the patch is then defined as a Coons interpolant, matching the boundary curves and their associated rotation-minimizing frames as surface Darboux frames. The surface patches are compatible with the standard rational Bezier/B-spline representations, and G^1 continuity between adjacent patches is easily achieved. Such patches are advantageous in surface design with more precise control over the surface curvature properties.