Freeform surfaces from single curved panels

Motivated by applications in architecture and manufacturing, we discuss the problem of covering a freeform surface by single curved panels. This leads to the new concept of semi-discrete surface representation, which constitutes a link between smooth and discrete surfaces. The basic entity we are working with is the developable strip model. It is the semi-discrete equivalent of a quad mesh with planar faces, or a conjugate parametrization of a smooth surface. We present a B-spline based optimization framework for efficient computing with D-strip models. In particular we study conical and circular models, which semi-discretize the network of principal curvature lines, and which enjoy elegant geometric properties. Together with geodesic models and cylindrical models they offer a rich source of solutions for surface panelization problems. CR Categories: I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling--Geometric algorithms, languages, and systems; I.3.5 [Computer Gra...

• Type: Journal
• Year: 2008
• Where: TOG
• Authors: Helmut Pottmann, Alexander Schiftner, Pengbo Bo, Heinz Schmiedhofer, Wenping Wang, Niccolo Baldassini, Johannes Wallner
• Keywords: Computational Geometry, Semi-discrete Surface Representation, Single Curved Panels, TOG 2008