Optimization of 3D models for fabrication

This thesis presents a set of novel optimization approaches for dealing with three different architecturally motivated rationalization tasks: First, a planarization technique for enabling efficient (e.g., glass) panelings of tessellated freeform geometries is presented. The formulation is based on plane intersections and yields planar panels by construction. Furthermore, the used constraints are straightforward algebraic expressions of lower polynomial degree than used in various comparable methods. The generality of the method is demonstrated by application to a variety of architecturally inspired optimization problems. Then, for a new type of support structures called point-folded structures an anti-diversification technique is developed for reducing the number of geometrically different panels. By a problem-adapted parametrization and carefully designed search strategy, the shape redundancy can be reduced by over 90% for various freeform designs, enabling significant reductions of fabrication costs in practice. Finally, for the still largely unexplored high potential area of constrained tessellation techniques, i.e., tessellation algorithms restricted to using only structural elements from a predefined set, two novel approaches based on a commercially available construction system (Zometool) are presented. The first method concerns approximation of closed surfaces of arbitrary genus, and implements an effective model-exploration strategy to efficiently find a solution. Furthermore, for guaranteeing planarity of panels when tessellating the architecturally important class of freeform surface patches, a second method based on an advancing front method guided by a novel growing strategy is developed.