Reconstruction of quasi developable surfaces from ribbon curves

Mathieu Huard (1, 2) , Nathalie Sprynski (1) , Nicolas Szafran (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 deals with the acquisition and reconstruction of physical surfaces by mean of a ribbon device equipped with micro-sensors, providing geodesic curves running on the surface. The whole process involves the reconstruction of these 3D ribbon curves together with their global treatment so as to produce a consistent network for the geodesic surface interpolation by filling methods based on triangular Coons-like approaches. However, the ribbon curves follow their own way, subdividing thus the surface into arbitrary n-sided patches. We present here a method for the reconstruction of quasi developable surfaces from such n-sided curvilinear boundary curves acquired with the ribbon device.

Mots clés: Geodesic curve; Hermite interpolation; Coons filling methods; Developable and quasi developable surfaces; Capture and reconstruction of surfaces

Domaines: Géométrie différentielle [math.DG]

Mathieu Huard, Nathalie Sprynski, Nicolas Szafran, Luc Biard. Reconstruction of quasi developable surfaces from ribbon curves. Numerical Algorithms, 2013, 63 (3), pp.483-506. ⟨10.1007/s11075-012-9633-3⟩. ⟨hal-00985177⟩