signed. Instead of having six beams meeting in a node, like it is the case with triangular meshes, in a quadrilateral mesh there are only four beams meeting in each node. PQ (planar quadrilateral) meshes have, in comparison to triangular meshes, fewer panels, less cutting waste and less total joint length. (a)
Developable strip panelizations Developable strip panelizations (Figure 3.15 - c) are one-directional refinements of a planar quad pan(b)
elization. A fairly coarse PQ mesh is subdivided with strip subdivision in only one direction. This process results in densely subdivided mesh strips which are developable if all of its subdivided quad faces are
(c)
planar. There are numerous benefits from the design approach with DStrips. Developable strips can be manufactured from planar sheets without the necessity
Figure 3.15: Freeform surface rationalization. (a) for any moulding or advanced bending machines. A freeform surface rationalized with triangular panels. (b) A freeform surface rationalized with planar This leads to a significant reduction of cost. The fact quadrilateral panels. (c) A freeform surface rationalized with developable strips that they are produced by bending material in one
direction makes them a semi-discrete representation of a freeform surface, thus they are perfectly smooth in one direction as opposed to panelizations with PQ panels. Another benefit of developable surfaces is that offsets of a developable surface are developable again, which means that multilayered structures with developable strips are easy to achieve. The entire substructure of a DStrip model can be made of developable materials [Schiftner et al. 2012]. 26