  We present a discrete theory for modeling developable surfaces as
quadrilateral meshes satisfying simple angle constraints. The basis of our
model is a lesser known characterization of developable surfaces as manifolds
that can be parameterized through orthogonal geodesics. Our model is simple,
local, and, unlike previous works, it does not directly encode the surface
rulings. This allows us to model continuous deformations of discrete
developable surfaces independently of their decomposition into torsal and
planar patches or the surface topology. We prove and experimentally demonstrate
strong ties to smooth developable surfaces, including a theorem stating that
every sampling of the smooth counterpart satisfies our constraints up to second
order. We further present an extension of our model that enables a local
definition of discrete isometry. We demonstrate the effectiveness of our
discrete model in a developable surface editing system, as well as computation
of an isometric interpolation between isometric discrete developable shapes.
