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We describe a method for modeling the geometry of porous materials. The approach enables the independent selection of crucial parameters, including porosity, pore size distribution, pore shape, and connectivity. Consequently, it can…
Graph colouring is a combinatorial optimisation problem with applications in several important domains, including sports scheduling, cartography, street map navigation, and timetabling. It is also of significant theoretical interest and a…
Volumetric parameterization problem refers to parameterization of both the interior and boundary of a 3D model. It is a much harder problem compared to surface parameterization where a parametric representation is worked out only for the…
We study surfaces with parallel normalized mean curvature vector field in Euclidean or Minkowski 4-space. On any such surface we introduce special isothermal parameters (canonical parameters) and describe these surfaces in terms of three…
We propose a new formulation for integrating over smooth curves and surfaces that are described by their closest point mappings. Our method is designed for curves and surfaces that are not defined by any explicit parameterization and is…
We investigate straight-line drawings of topological graphs that consist of a planar graph plus one edge, also called almost-planar graphs. We present a characterization of such graphs that admit a straight-line drawing. The…
We study the classical problem of computing geometric thickness, i.e., finding a straight-line drawing of an input graph and a partition of its edges into as few parts as possible so that each part is crossing-free. Since the problem is…
We classify all ruled surfaces in Euclidean space that are critical points of the Dirichlet energy, obtaining explicit parametrizations of these surfaces.
The developable surface is an important surface in computer aided design, geometric modeling and industrial manufactory. It is often given in the stan- dard parametric form, but it can also be in the implicit form which is commonly used in…
We develop a transitional geometry, that is, a family of geometries of constant curvatures which makes a continuous connec-tion between the hyperbolic, Euclidean and spherical geometries. In this transitional setting, several geometric…
An $(n_k)$-configuration is a set of $n$ points and $n$ lines in the projective plane such that their point-line incidence graph is $k$-regular. The configuration is geometric, topological, or combinatorial depending on whether lines are…
Spherometer is an instrument widely used for measuring the radius of curvature of a spherical surface. Cylindrometer is a modified spherometer, which can measure the radii of both spherical and cylindrical surfaces. Both of these…
A mesh-based parametrization is a parametrization of a geometric object that is defined solely from a mesh of the object, e.g., without an analytical expression or computer-aided design (CAD) representation of the object. In this work, we…
The metric known to be relevant for standard quantization procedures receives a natural interpretation and its explicit use simultaneously gives both physical and mathematical meaning to a (coherent-state) phase-space path integral, and at…
In this article we describe an algorithm that can be applied for the generation of various classes of maps on orientable surfaces. It uses existing generators for abstract graphs and combines them with an efficient embedding and isomorphism…
This paper introduces a set of numerical methods for Riemannian shape analysis of 3D surfaces within the setting of invariant (elastic) second-order Sobolev metrics. More specifically, we address the computation of geodesics and geodesic…
The Coherence Length Diagram and the related maps have been shown to represent a useful tool for image analysis. Setting threshold parameters is one of the most important issues when dealing with such applications, as they affect both the…
In this work we are interested in the characterization of curves that belong to a given surface. To the best of our knowledge, there is no known general solution to this problem. Indeed, a solution is only available for a few examples:…
We investigate geometric properties of surfaces given by certain formulae. In particular, we calculate the singular curvature and the limiting normal curvature of such surfaces along the set of singular points consisting of singular points…
An isometric embedding of a graph into a metric space is an embedding of the vertices such that the smallest number of edges connecting any two vertices equals to the distance in the metric space between the images. In this paper, we study…