Optimizing B-spline surfaces for developability and paneling architectural freeform surfaces

• Published in: Computer aided design Vol. 111; pp. 29 - 43
• Main Authors: Gavriil, Konstantinos, Schiftner, Alexander, Pottmann, Helmut
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Ltd 01.06.2019; Elsevier BV
• Subjects: Algorithms; Architectural geometry; Architecture; Computational differential geometry; Constrained optimization; Developable surface; Panels; Production costs; Spline surface; Developable surface; Computational differential geometry; Spline surface; Architectural geometry; Constrained optimization
• ISSN: 0010-4485; 1879-2685
• DOI: 10.1016/j.cad.2019.01.006

Motivated by applications in architecture and design, we present a novel method for increasing the developability of a B-spline surface. We use the property that the Gauss image of a developable surface is 1-dimensional and can be locally well approximated by circles. This is cast into an algorithm for thinning the Gauss image by increasing the planarity of the Gauss images of appropriate neighborhoods. A variation of the main method allows us to tackle the problem of paneling a freeform architectural surface with developable panels, in particular enforcing rotational cylindrical, rotational conical and planar panels, which are the main preferred types of developable panels in architecture due to the reduced cost of manufacturing. •Geometric study of local approximants of developable surfaces.•Optimization algorithm for increasing the developability of a B-spline surface.•Optimization algorithm for paneling a freeform surface with special developables.