Related papers: Parametrization of translational surfaces
The notion of geometric construction is introduced. This notion allows to compare incidence configurations in the algebraic and tropical plane. We provide an algorithm such that, given a tropical instance of a geometric construction, it…
This paper introduces a new method to stylize 3D geometry. The key observation is that the surface normal is an effective instrument to capture different geometric styles. Centered around this observation, we cast stylization as a shape…
We propose a general framework for constructing and describing infinite type flat surfaces of finite area. Using this method, we characterize the range of dynamical behaviors possible for the vertical translation flows on such flat…
Field-guided parametrization methods have proven effective for quad meshing of surfaces; these methods compute smooth cross fields to guide the meshing process and then integrate the fields to construct a discrete mesh. A key challenge in…
For a Del Pezzo surface of degree 8 given over the rationals we decide whether there is a rational parametrization of the surface and construct one in the affirmative case. We define and use the Lie algebra of the surface to reach the aim.…
Effectively parsing the facade is essential to 3D building reconstruction, which is an important computer vision problem with a large amount of applications in high precision map for navigation, computer aided design, and city generation…
We introduce the notion of a standard weighted graph and show that every weighted graph has an essentially unique standard model. Moreover we classify birational transformations between such models. Our central result shows that these are…
In this short note, we give a new sufficient condition for a linear map from a product of copies of a field to endomorphisms of a finite dimensional vector space over the same field to be an algebra homomorphism. We expect that this result…
We show that all hyperbolic surfaces admit an ideal triangulation with bounded shear parameters. This upper bound depends logarithmically on the topology of the surface.
We discuss an alternative approach to the uniformisation problem on surfaces with boundary by representing conformal structures on surfaces $M$ of general type by hyperbolic metrics with boundary curves of constant positive geodesic…
In this paper we generalise a celebrated result of Milnor that characterises whether a rotationally symmetric surface is parabolic or hyperbolic to the case of biharmonic functions.
In the present paper we study the $\SOL$ geometry that is one of the eight homogeneous Thurston 3-geomet\-ri\-es. We determine the equation of the translation-like bisector surface of any two points. We prove, that the isosceles property of…
Optical surfaces represented by second-degree polynomials (quadratic or conics) are ubiquitous in optics. We revisit the equations of the conic shapes in the context of grazing incidence optics, gathering together the curves commonly used…
It is a long-standing conjecture from the 1970s that every translation generalized quadrangle is linear, that is, has an endomorphism ring which is a division ring (or, in geometric terms, that has a projective representation). We show that…
Let T be a tile in the Cartesian plane made up of finitely many rectangles whose corners have rational coordinates and whose sides are parallel to the coordinate axes. This paper gives necessary and sufficient conditions for a square to be…
We study geometrical properties of translation surfaces: the finite blocking property, bounded blocking property, and illumination properties. These are elementary properties which can be fruitfully studied using the dynamical behavior of…
We give cohomological criteria for logarithmic good reduction of elliptic surfaces up to modification. Along the way, we prove several more general results about such surfaces in positive characteristic, as well as about log smooth…
The revised version has two additional references and a shorter proof of Proposition 5.7. This version also makes numerous small changes and has an appendix containing a proof of the degree formula for a parametrized surface.
This communication describes a representation of images as a set of edges characterized by their position and orientation. This representation allows the comparison of two images and the computation of their similarity. The first step in…
The non-linear transformations incurred by the rays in an optical system can be suitably described by matrices to any desired order of approximation. In systems composed of uniform refractive index elements, each individual ray refraction…