  Given a designer created free-form surface in 3d space, our method computes a
grid composed of elastic elements which are completely planar and straight.
Only by fixing the ends of the planar elements to appropriate locations, the 2d
grid bends and approximates the given 3d surface. Our method is based purely on
the notions from differential geometry of curves and surfaces and avoids any
physical simulations. In particular, we introduce a well-defined elastic grid
energy functional that allows identifying networks of curves that minimize the
bending energy and at the same time nestle to the provided input surface well.
Further, we generalize the concept of such grids to cases where the surface
boundary does not need to be convex, which allows for the creation of
sophisticated and visually pleasing shapes. The algorithm finally ensures that
the 2d grid is perfectly planar, making the resulting gridshells inexpensive,
easy to fabricate, transport, assemble, and finally also to deploy.
Additionally, since the whole structure is pre-strained, it also comes with
load-bearing capabilities. We evaluate our method using physical simulation and
we also provide a full fabrication pipeline for desktop-size models and present
multiple examples of surfaces with elliptic and hyperbolic curvature regions.
Our method is meant as a tool for quick prototyping for designers, architects,
and engineers since it is very fast and results can be obtained in a matter of
seconds.
