Vector quantization is a classical signal-processing technique with significant applications in data compression, pattern recognition, clustering, and data stream mining. It is well known that for critical points of the quantization energy, the tessellation of the domain is a centroidal Voronoi tessellation. However, for dimensions greater than one, rigorously verifying a given centroidal Voron...

To facilitate printing, coatings are typically applied to paperboard used for packaging provide a good surface application. optimise the performance of coating, it is important understand relationship between microstructure material and its mass transport properties. In this work, three samples coating imaged using combined focused ion beam scanning electron microscope (FIB-SEM) tomography data...

Traditional polygon-arc-node topology is standard in vector GIS, but it has its limitations. This is particularly evident at the digitizing stage, which often appears excessively complex and tedious, Other methods, however, are capable of maintaining some forms of topology “automatically”, and this paper is an overview of three approaches based on the Voronoi diagram (or the equivalent Delaunay...

Abstract. Global warming and changes in Earth’s weather patterns are the main consequences of climate change, bioclimate discomfort has significant public health problems, especially for elderly. Normally, thermal characteristics urban areas poor due to a phenomenon known as heat island. Mobile fixed temperature measurements were performed on 19 March 2021 city Bologna, Italy. took place with c...

We analyze the problem of tessellating an n-sided patch with ideal, maximally-regular internal quadrangulation, featuring a single irregular vertex (or none, for n=4). derive, in closed-form, necessary and sufficient conditions that boundary must meet it to admit quadrangulation this kind, and, if so, provide full description resulting tessellation(s), as functions number edges subdividing side...

A robust statistics approach to curvature estimation on discretely sampled surfaces, namely polygon meshes and point clouds, is presented. The method exhibits accuracy, stability and consistency even for noisy, non-uniformly sampled surfaces with irregular configurations. Within an M-estimation framework, the algorithm is able to reject noise and structured outliers by sampling normal variation...

Leapfrog transformations starting with the genus 3 Klein and Dyck tessellations consisting of 24 heptagons and 12 octagons, respectively, can generate possible highly symmetrical structures for allotropes of carbon and the isosteric boron nitride, (BN)x. The Klein tessellation, alternatively described as a platonic 3,7 tessellation, corresponds to the Riemann surface for the multi-valued functi...

In this paper we present a fractional parametric splitting scheme for Reyes-style adaptive tessellation. Our parallel algorithm generates crack-free tessellation from a parametric surface, which is also free of sudden temporal changes under animation. Continuous level of detail is not addressed by existing Reyes-style methods, since these aim to produce subpixel-sized micropolygons, where topol...

A tessellation which is capable of producing rough boundaries is proposed. Some properties of the proposed tessellation are also described.