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 …

We discretize isometric mappings between surfaces as correspondences between
checkerboard patterns derived from quad meshes. This method captures the degrees of …

We propose a novel way to capture and characterize distortion between pairs of shapes by
extending the recently proposed framework of shape differences built on functional maps …

The isolines of principal symmetric surface parametrizations run symmetrically to the
principal directions. We describe two discrete versions of these special nets/quad meshes …

We obtain a unified theory of discrete minimal surfaces based on discrete holomorphic
quadratic differentials via a Weierstrass representation. Our discrete holomorphic quadratic …

Spectral mesh analysis and processing methods, namely ones that utilize eigenvalues and
eigenfunctions of linear operators on meshes, have been applied to numerous geometric …

In 1883, Darboux gave a local classification of isothermic surfaces with one family of planar
curvature lines using complex analytic methods. His choice of real reduction cannot contain …

We study circle packings with the combinatorics of a triangulated disk in the plane and
parametrize deformations of circle packings in terms of vertex rotation and cross ratios. We …

We obtain many objects of discrete differential geometry as reductions of skew
parallelogram nets, a system of lattice equations that may be formulated for any unit …

This paper studies the discrete differential geometry of the checkerboard pattern inscribed in
a quadrilateral net by connecting edge midpoints. It turns out to be a versatile tool which …