From Ruled Surfaces to Elastica-ruled Surfaces: New Possibilities for Creating Architectural Forms

Ruled surfaces are widely used for architectural forms, as diverse 3D shapes can be conveniently generated by the movement of a straight ruling. There is vast potential to create a rich variety of new architectural forms by introducing curved rulings into ruled surfaces. This paper presents a new method to generate ruled surface variants by making a fundamental change to existing ruled surfaces through parametric reformulation and the use of curved rulings. A new type of ruled surface composed of curved rulings, the elastica-ruled surface, is proposed. An analytical geometric modelling method is developed based on the transformation of line-ruled surfaces, enabling convenient generation of elegant shapes and forms for architectural applications. In this paper, curved rulings are represented by elastica curves—large, elastic, bending deformations of a straight slender beam. We demonstrate that elastica curve design parameters can completely control the shape of an elastica-ruled surface and define a large set of transformation results. This study classifies elastica-ruled surfaces into five categories based on their shape characteristics. Potential applications of elastica-ruled surfaces that consider elastic bending behaviour are presented, including bending-active structures, robot-assisted manufacturing and kinetic architectural designs. By extension, this study shows that adopting higher-order elastica curves can further enhance the design diversity of novel architectural forms.