Three-dimensional structures in building construction and architecture are realized with conflicting goals in mind: engineering considerations and financial constraints easily are at odds with creative aims. It would therefore be very beneficial if optimization and side conditions involving statics and geometry could play a role already in early stages of design, and could be incorporated in design tools in an unobtrusive and interactive way. We take a substantial step towards this goal. Combining the classical work of Maxwell, Michell, and Airy with differential-geometric considerations one obtains a geometric understanding of “optimality” of surface-like lightweight structures. It turns out that total absolute curvature plays an important role. This enables the modeling of structures of minimal weight which in addition have properties relevant for building construction and design, like planar panels, dominance of axial forces over bending, and geometric alignment constraints.
Martin Kilian, Davide Pellis, Johannes Wallner, and Helmut Pottmann.
Material-minimizing forms and structures.
ACM Trans. Graphics, 36(6):article 173, 2017. Proc. SIGGRAPH Asia.
Dr. Martin Kilian +
University: TU Wien, Institute of Discrete Mathematics and Geometry, 104
Address: Wiedner Hauptstr. 8-10, 1040 Vienna, AUSTRIA
Tel: +43 1 58801104469
Davide Pellis +
Prof. Dr. Helmut Pottmann +
University: TU Wien
University: King Abdullah University of Science and Technology