Freeform surfaces from single curved panels

Helmut Pottmann*, Alexander Schiftner, Pengbo Bo, Heinz Schmiedhofer, Wenping Wang, Niccolo Baldassini, Johannes Wallner

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

121 Scopus citations

Abstract

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.

Original languageEnglish (US)
Article number76
JournalACM Transactions on Graphics
Volume27
Issue number3
DOIs
StatePublished - Aug 1 2008

Keywords

  • Architectural geometry
  • Circular strip model
  • Conical strip model
  • Developable strip model
  • Developable surface
  • Discrete differential geometry
  • Focal surface
  • Freeform surface
  • Geodesic strip model
  • Panelization
  • Principal strip model
  • Semi-discrete surface

ASJC Scopus subject areas

  • Computer Graphics and Computer-Aided Design

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