Related papers: Constructing isothermal curvature line coordinates…
We investigate the relationship among characteristic curves on developable surfaces. In case parameter curves coincide with these curves, we show that the base curve of a developable surface could be either a plane curve, a circular helix,…
Surface parametrization is a crucial part in various fields, having applications in computer graphic, medical imaging, scientific computing and computational engineering. The majority of surface parametrization approaches are performed on…
We study cubic rational maps that take lines to plane curves. A complete description of such cubic rational maps concludes the classification of all planarizations, i.e., maps taking lines to plane curves.
In this paper we describe the $\epsilon$-isothermic surfaces in the pseudo-Euclidean 3-space and we obtain the pseudo-Calapso equation. In sequence, we classify the Dupin surfaces in pseudo-Euclidean 3-space having distinct principal…
Conformal mapping, a classical topic in complex analysis and differential geometry, has become a subject of great interest in the area of surface parameterization in recent decades with various applications in science and engineering.…
The contribution of this paper is twofold. First, we generalize the definition of discrete isothermic surfaces. Compared with the previous ones, it covers more discrete surfaces, e.g., the associated families of discrete isothermic minimal…
A canal surface is the envelope of a moving sphere with varying radius, defined by the trajectory C(t) (spine curve) of its center and a radius function r(t). In this paper, we investigate when parameter curves of the canal surface are also…
We show how pairs of isothermic surfaces are given by curved flats in a pseudo Riemannian symmetric space and vice versa. Calapso's fourth order partial differential equation is derived and, using a solution of this equation, a M\"obius…
We define a class of Euclidean distances on weighted graphs, enabling to perform thermodynamic soft graph clustering. The class can be constructed form the "raw coordinates" encountered in spectral clustering, and can be extended by means…
We use some fundamental ideas from complex analysis to create symmetric images and animations. Using a domain coloring algorithm, we generate mappings to the entire complex plane or the hyperbolic upper half-plane. The resulting designs can…
Curves are essential concepts that enable compounded aesthetic curves, e.g., to assemble complex silhouettes, match a specific curvature profile in industrial design, and construct smooth, comfortable, and safe trajectories in vehicle-robot…
The geometrical approach to phase transitions is illustrated by simulating the high-temperature representation of the Ising model on a square lattice.
We give an account of the classical and integrable geometry of isothermic surfaces in arbitrary co-dimension. We show that the classical transformation theory of Darboux, Bianchi and Calapso goes through unchanged in arbitrary co-dimension…
A procedure for interpolating between specified points of a curve or surface is described. The method guarantees slope continuity at all junctions. A surface panel divided into p x q contiguous patches is completely specified by the…
This paper provides a tutorial and survey for a specific kind of illustrative visualization technique: feature lines. We examine different feature line methods. For this, we provide the differential geometry behind these concepts and adapt…
The classical isoperimetric inequality can be extended to a general normed plane. In the Euclidean plane, the defect in the isoperimetric inequality can be calculated in terms of the signed areas of some singular sets. In this paper we…
In this paper we study maps (curved flats) into symmetric spaces which are tangent at each point to a flat of the symmetric space. Important examples of such maps arise from isometric immersions of space forms into space forms via their…
This survey article concerns inducing schemes in the context of interval maps. We explain how the study of these induced systems allows for the fine description of, not only, the thermodynamic formalism for certain multimodal maps, but also…
The purpose of this paper is, first, to give an algorithm that enables to obtain the lines of curvature on parametric hypersurfaces in Euclidean 4-space, and then, to obtain the curvatures of such lines by using the extended Darboux frame…
We introduce a conceptually simple and efficient algorithm for seamless parametrization, a key element in constructing quad layouts and texture charts on surfaces. More specifically, we consider the construction of parametrizations with…