Surface Reconstruction via Geodesic Interpolation

Nathalie Sprynski (1) , Nicolas Szafran (2) , Bernard Lacolle (2) , Luc Biard (2)

1 CEA-LETI - Commissariat à l'énergie atomique et aux énergies alternatives - Laboratoire d'Electronique et de Technologie de l'Information
2 MGMI - Modélisation Géométrique & Multirésolution pour l'Image

This paper is concerned with reconstruction of numerical or real surfaces based on the knowledge of some geodesic curves on the surface. So, considering two regular 3D-curves f0(t) and f1(t), our purpose is to construct a surface which interpolates these two curves in such a way that these two curves are geodesics on this surface. This will be accomplished using Hermite interpolation. For a real surface, it will be shown that geodesics can be acquired using a ribbon of micro-sensors.

Mots clés: Geodesic curves; surface reconstruction; Hermite interpolation; Curvature minimization; Motion capture; Embedded micro-sensors

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

Nathalie Sprynski, Nicolas Szafran, Bernard Lacolle, Luc Biard. Surface Reconstruction via Geodesic Interpolation. Computer-Aided Design, 2008, 40 (4), pp.480-492. ⟨10.1016/j.cad.2008.01.005⟩. ⟨hal-00317071⟩