We discuss recent progress, ongoing research and open problems on the relation between shape properties and requirements for their fabrication with various technologies. These include CNC machining, curved folding and paneling architectural skins. In the area of CNC machining, we address flank milling and the detection of surface parts which can be produced efficiently with this technology. We address the difficult problem of best approximating a given surface by one that can be produced from a single flat sheet by curved folding and show that certain folding patterns have a close relation to special families of curves on the reference surface. Finally, we report on the design and approximation with surfaces that possess only a one-parameter family of curvature elements and discuss their advantages in architectural applications.
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