Constrained Manipulation of Polyhedral Systems


Modeling or manipulating polyhedral geometry in the context of 3D Graphic Statics and reciprocal polyhedral diagrams, either as the form or force diagram, is not a trivial task. This research presents a method for the manipulation of groups of polyhedral cells that allows geometric transformation while preserving the planarity constraints of the cells and maintaining the equilibrium direction of the edges for the reciprocity of the diagrams. The work expands on previously investigated single-cell manipulations and considers the effects of these transformations in adjacent cells and the whole system. All the transformations addressed in the research maintain the topological relations of the input complex. The result of this research can be applied to both form and force diagrams to investigate various geometric transformations resulting in convex, concave or complex (self-intersecting) polyhedra as a group. The product of this research allows intuitive user interaction in working with form and force diagrams in the early stages of geometric structural design in 3D.