WireWarping++: Robust and flexible surface flattening with length control

Surface flattening has numerous applications in sheet manufacturing industries, such as garment industry, shoe industry, toy industry, furniture industry, and ship industry. Motivated by the requirements of those industries, WireWarping approach presented by Wang, 2008 is exploited to generate 2-D patterns with invariant length of feature and boundary curves. However, strict length constraints on all feature curves sometimes cause large distortions on 2-D patterns, especially for those 3-D surfaces which are highly non-developable. In this paper, we present a flexible and robust extension of WireWarping by introducing a new type of feature curves named elastic feature, which brings flexibility to shape control of the resultant 2-D patterns. On these new feature curves, instead of strictly preserving the exact lengths, only the ranges of their lengths are controlled. To achieve this function, a multiloop shape control optimization framework is proposed to find the optimized 2-D shape among all possible flattening results with different length variations on those elastic feature curves, while the lengths of other feature curves are kept unchanged. Besides, we also present a topology processing algorithm on the network of feature curves to eliminate cases that lead to numerical singularity. Experimental results show that the WireWarping++ can successfully flatten surface patches into 2-D patterns with more flexible shape control and more robust numerical performance.