Construction of rational surface patches bounded by lines of curvature

Luc Biard (1) , Rida Farouki (2) , Nicolas Szafran (1)

1 MGMI - Modélisation Géométrique & Multirésolution pour l'Image
2 MAE - Department of Mechanical and Aeronautical Engineering

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 RRFM 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 Bézier/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.

Mots clés: Darboux frame; angular velocity; rotation-minimizing frame; lines of curvature; Pythagorean-hodograph curve; rational surface patch

Domaines: Géométrie différentielle [math.DG]; Modélisation et simulation

Luc Biard, Rida Farouki, Nicolas Szafran. Construction of rational surface patches bounded by lines of curvature. Computer Aided Geometric Design, 2010, 27 (5), pp.359-371. ⟨10.1016/j.cagd.2010.03.002⟩. ⟨hal-00463845⟩