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

TL;DR

This paper introduces a new method to optimize B-spline surfaces for developability, enabling better paneling of freeform architectural surfaces with manufacturable developable panels like cylinders, cones, and planes.

Contribution

It presents a novel algorithm that increases developability by approximating the Gauss image with circles, facilitating architectural paneling with preferred developable shapes.

Findings

Enhanced developability of B-spline surfaces achieved

Effective paneling with cylindrical, conical, and planar developable panels

Applicable to architectural freeform surface design

Abstract

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.