Elements of Draping
We consider the gravity-induced draping of a 3D object with a
naturally flat, isotropic elastic sheet. As the size of the sheet
increases, we observe the appearance of new folded structures of
increasing complexity that arise because of the competition between elasticity and gravity. We analyze some of the simpler 3D
structures by determining their shape and analyzing their response
and stability and show that these structures can easily switch
between a number of metastable configurations. For more complex draperies, we derive scaling laws for the appearance and
disappearance of new length scales. Our results are consistent with
commonplace observations of drapes and complement large-scale
computations of draping by providing benchmarks. They also yield
a qualitative guide to fashion design and virtual reality animation.