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Quadrilateral layouts on surfaces are valuable in texture mapping, and essential in generation of quadrilateral meshes and in fitting splines. Previous work has characterized such layouts as a special metric on a surface or as a meromorphic…
When matching parts of a surface to its whole, a fundamental question arises: Which points should be included in the matching process? The issue is intensified when using isometry to measure similarity, as it requires the validation of…
Developable surfaces are commonly observed in various applications such as architecture, product design, manufacturing, mechanical materials, and data physicalization as well as in the development of tangible interaction and deformable…
Many algorithms for surface registration risk producing significant errors if surfaces are significantly nonisometric. Manifold learning has been shown to be effective at improving registration quality, using information from an entire…
The Indus script remains one of the last major undeciphered scripts of the ancient world. We focus here on Indus inscriptions on a group of miniature tablets discovered by Meadow and Kenoyer in Harappa in 1997. By drawing parallels with…
Consider a periodical (in two independent directions) tiling of the plane with polygons (faces). In this article we shall only give examples using squares, regular hexagons, equilateral triangles and parallelograms ("unions" of two…
We present a general purpose method for solving partial differential equations on a closed surface, based on a technique for discretizing the surface introduced by Wenjun Ying and Wei-Cheng Wang [J. Comput. Phys. 252 (2013), pp. 606-624]…
Finding Hemisystems is a challenging problem and just few examples arising from the Hermitian surface are known. A recent method to obtain Hemisystems is based on using maximal curves. Along this side of research, we provide new examples of…
We fully generalize a previously-developed computational geometry tool [1] to perform large-scale simulations of arbitrary two-dimensional faceted surfaces $z = h(x,y)$. Our method uses a three-component facet/edge/junction storage model,…
This article is concerned with the problem of placing seven or eight points on the unit sphere $\mathbb{S}^2$ in $\mathbb{R}^3$ so that the surface area of the convex hull of the points is maximized. In each case, the solution is given for…
We present numerical studies of wetting on various topographic substrates, including random topographies. We find good agreement with recent predictions based on an analytical interface-displacement-type theory \cite{Herminghaus2012,…
The volumes of strata of Abelian or quadratic differentials play an important role in the study of dynamics on flat surfaces, related to dynamics in polygonal billiards. This article reviews all known ways to compute volumes in the…
A very interesting problem in the classical theory of minimal surfaces consists of the classification of such surfaces under some geometrical and topological constraints. In this short paper, we give a brief summary of the known…
The camera captured images have various aspects to investigate. Generally, the emphasis of research depends on the interesting regions. Sometimes the focus could be on color segmentation, object detection or scene text analysis. The image…
In this article a new upper bounds for the multiple trigonometrical integrals are found. The method of the work based on a new method of estimation for the areas of algebraic surfaces.
We provide an algorithm for detecting the involutions leaving a surface defined by a polynomial parametrization invariant. As a consequence, the symmetry axes, symmetry planes and symmetry center of the surface, if any, can be determined…
Quadratic residue patterns modulo a prime are studied since 19th century. In the first part we extend existing results on the number of consecutive $\ell$-tuples of quadratic residues, studying corresponding algebraic curves and their…
We present results of a long-term team collaboration of mathematicians and biologists. We focus on building a mathematical framework for the shape space constituted by a collection of homologous bones or teeth from many species. The…
In characteristic $p>0$ and for $q$ a power of $p$, we compute the number of nonplanar rational curves of arbitrary degrees on a smooth Hermitian surface of degree $q+1$ under the assumption that the curves have a parametrization given by…
Bar charts are among the most frequently used visualizations, in part because their position encoding leads them to convey data values precisely. Yet reproductions of single bars or groups of bars within a graph can be biased. Curiously,…