Computational form-finding of single-layer spatial structures: Constructing force diagrams with Vector-based Graphic Statics and guiding trails

This article extends the Vector-based Graphic Statics (VGS) computational framework to design single-layer spatial (SLS) structures. It introduces a novel computational workflow that produces ordered and controllable vector-based force diagrams for real-time interactive design. Key advancements include an algorithm for identifying guiding trails within the form diagram's underlying graph to control its planarization, an augmented half-edge (AHE) data structure for seamless force diagram assembly, and an interface for generating force diagrams using the Combinatorial Equilibrium Modelling (CEM) method. These advancements are demonstrated through practical design cases using the enhanced VGS framework, aiming to improve collaboration between structural engineers and architects by providing a direct and visual link between form and forces.