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Pottmann, Helmut; Schiftner, Alexander; Bo, Pengbo; Schmiedhofer, Heinz; Wang, Wenping; Baldassini, Niccolo; Wallner, Johannes
ACM transactions on graphics, 08/2008, Volume: 27, Issue: 3Journal Article
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.
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