144 citations · 247 across the 11 of their papers we have counts for
12 papers
Discrete Riemann Surfaces and the Ising model
Christian Mercat
We define a new theory of discrete Riemann surfaces and present its basic results. The key idea is to consider not only a cellular decomposition of a surface, but the union with it…
Conformal Structures and Period Matrices of Polyhedral Surfaces
Alexander I. Bobenko, Christian Mercat, Markus Schmies
We recall the theory of linear discrete Riemann surfaces and show how to use it in order to interpret a surface embedded in R^3 as a discrete Riemann surface and compute its basis…
Discrete Complex Structure on Surfel Surfaces
Christian Mercat
This paper defines a theory of conformal parametrization of digital surfaces made of surfels equipped with a normal vector. The main idea is to locally project each surfel to the t…
Discrete Riemann Surfaces
Christian Mercat
We detail the theory of Discrete Riemann Surfaces. It takes place on a cellular decomposition of a surface, together with its Poincaré dual, equipped with a discrete conformal stru…
Discrete Riemann surfaces, linear and non-linear
Christian Mercat
3 pages presentation of the theory of discrete conformal parameterization using circle patterns or its linearized theory. Principal results and ideas.
Exponentials form a basis of discrete holomorphic functions
Christian Mercat
We show that discrete exponentials form a basis of discrete holomorphic functions. On a convex, the discrete polynomials form a basis as well.