An emerging field of discrete differential geometry aims at the development of discrete
equivalents of notions and methods of classical differential geometry. The latter appears as …

An introduction, at a basic level, to the conformal differential geometry of surfaces and
submanifolds is given. That is, the book discusses those aspects of the geometry of surfaces …

A survey is given of the Weierstrass representations of surfaces in three-and four-
dimensional spaces, their applications to the theory of the Willmore functional, and related …

We present a formulation of Willmore flow for triangulated surfaces that permits
extraordinarily large time steps and naturally preserves the quality of the input mesh. The …

The aim of the present paper is to clarify the relationship between immersions of surfaces
and solutions of the Dirac equation. The main idea leading to the description of a surface M2 …

We introduce a new method for computing conformal transformations of triangle meshes in
R3. Conformal maps are desirable in digital geometry processing because they do not …

Priors play an essential role in Bayesian theory, and they are frequently center stage in
scientific inference. In image processing, geometric priors became very popular in the past …

The Bonnet theorem characterizes surfaces via the coefficients eu, H, Q of their fundamental
forms. These coefficients are not independent and are subject to the Gauss-Codazzi …

Geometric operators are common objects in surface-based shape analysis and geometry
processing. While the intrinsic Laplace–Beltrami operator has been a ubiquitous choice …

Generalized Weierstrass representations for generic surfaces conformally immersed into
four-dimensional Euclidean and pseudo-Euclidean spaces of different signatures are …