  Folding can transform mundane objects such as napkins into stunning works of
art. However, finding new folding transformations for sheet materials is a
challenging problem that requires expertise and real-world experimentation. In
this paper, we present Modal Folding -- an automated approach for discovering
energetically optimal folding transformations, i.e., large deformations that
require little mechanical work. For small deformations, minimizing internal
energy for fixed displacement magnitudes leads to the well-known elastic
eigenmodes. While linear modes provide promising directions for bending, they
cannot capture the rotational motion required for folding. To overcome this
limitation, we introduce strain-space modes -- nonlinear analogues of elastic
eigenmodes that operate on per-element curvatures instead of vertices. Using
strain-space modes to determine target curvatures for bending elements, we can
generate complex nonlinear folding motions by simply minimizing the sheet's
internal energy. Our modal folding approach offers a systematic and automated
way to create complex designs. We demonstrate the effectiveness of our method
with simulation results for a range of shapes and materials, and validate our
designs with physical prototypes.
