Optimizing shapes and structures for freeform architecture

Digital design and fabrication of complex geometries in architecture stimulated a significant amount of research most of which involves optimization. We present the main optimization methods with a focus on our preferred techniques. There, we discuss initialization, the formulation of constraints and their simplification through geometric considerations, and key concepts for regularization. This is illustrated at hand of a very recent type of discrete surfaces which are expressed via the pair of diagonal meshes in a quad mesh.