We propose a new model and algorithm to capture the high-definition statics
of thin shells via coarse meshes. This model predicts global, fine-scale wrinkling at frequencies much higher than the resolution of the coarse mesh;
moreover, it is grounded in the geometric analysis of elasticity, and does not
require manual guidance, a corpus of training examples, nor tuning of ad-hoc
parameters. We first approximate the coarse shape of the shell using tension
field theory, in which material forces do not resist compression. We then
augment this base mesh with wrinkles, parameterized by an amplitude and
phase field that we solve for over the base mesh, which together characterize the geometry of the wrinkles. We validate our approach against both physical experiments and numerical simulations, and show that our algorithm
produces wrinkles qualitatively similar to those predicted by traditional
shell solvers requiring orders of magnitude more degrees of freedom.