Series Of Polygons Research Articles

Spatio-temporal analysis of COVID-19 in India – a geostatistical approach

Coronavirus (Covid) is a severe acute respiratory syndrome infectious disease, spreads primarily between human beings during close contact, most often through the coughing, sneezing, and speaking small droplets. A retrospective surveillance research is conducted in India during 30th January–21st March 2020 to gain insight into Covid’s epidemiology and spatial distribution. Voronoi statistics is used to draw attention of the affected states from a series of polygons. Spatial patterns of disease clustering are analyzed using global spatial autocorrelation techniques. Local spatial autocorrelation has also been observed using statistical methods from Getis-Ord Gi*. The findings showed that disease clusters existed in the area of research. Most of the clusters are concentrated in the central and western states of India, while the north-eastern countries are still predominantly low-rate of clusters. This simulation technique helps public health professionals to identify risk areas for disease and take decisions in real time to control this viral disease.

Effect analysis of design parameter of trawl door by considering interaction with seabed

In this study, a seabed comprising numerous particles was simulated using discrete element method. To express the viscosity of the seabed, the material and cohesion properties of medium clay were used. The trawl door was defined by a series of polygons. Researchers used the CATIA software suite to obtain polygon data for the trawl door. First, the shape model of the trawl door was established. Next, mesh data were exported to a text file used to define the polygon elements in the program. To reduce analysis time, parallel computing (general-purpose computing on graphics processing units) was used. Following the L9-Taguchi experimental design method, the design parameters of the trawl door were determined using three levels of four factors including the front fillet angle, length and depth of the trawl door, and angle of attack. The average trawl door contact forces were compared to determine optimal trawl door design.

Commentary on: Rhinoplasty: Surface Aesthetics and Surgical Techniques

Contour of the nose is determined by a series of shadows and highlights that emphasize the shape of the nose.1 The desired contours are curvilinear with smooth transitions from dorsum to mid-vault to nasal tip. Control of nasal contour requires precise management of the underlying nasal structures. The structure approach to rhinoplasty employs conservative reduction of the cartilage structures and reshaping using cartilage grafting.2 Cartilage grafts such as spreader grafts and lateral crural strut grafts help to control the shape of the middle nasal vault and lower third of the nose, respectively.3,4 Such grafts have helped surgeons improve their long-term outcomes as well as link nasal aesthetics and surgical technique. In the article entitled, “Rhinoplasty: Surface Aesthetics and Surgical Technique,” Dr Cakir and his coauthors have described how the nasal contour is composed of a series of polygons as aesthetic units and linked these concepts to their own techniques. The ideal contour on frontal view is typically described as having bilateral divergent concave lines that create symmetric “brow tip aesthetic lines.”5–7 In contrast, the authors describe the frontal view as a series of polygons, with a superior polygon that is narrow at the radix and widens toward the middle nasal vault and an inferior polygon that narrows at the supratip. This series of shapes more closely represents the shape of the underlying nasal structures (nasion, nasal bones, and upper lateral cartilages) rather than the superficial nasal contour. Transitions in skin thickness—from thick in the radix region, to …

Analytical algorithm for the generation of polygonal projection data for tomographic reconstruction

Tomographic reconstruction algorithms and filters can be tested using a mathematical phantom, that is, a computer program which takes numerical data as its input and outputs derived projection data. The input data is usually in the form of pixel “densities” over a regular grid, or position and dimensions of simple, geometrical objects. The former technique allows a greater variety of objects to be simulated, but is less suitable in the case when very small (relative to the ray-spacing) features are to be simulated. The second technique is normally used to simulate biological specimens, typically a human skull, modelled as a number of ellipses. This is not suitable for simulating non-biological specimens with features such as straight edges and fine cracks. We have therefore devised an algorithm for simulating objects described as a series of polygons. These polygons, or parts of them, may be smaller than the ray-spacing and there is no limit, except that imposed by computing resources, on the complexity, number or superposition of polygons. A simple test of such a phantom, reconstructed using the filtered back-projection method, revealed reconstruction artefacts not normally seen with “biological” phantoms.

Fourier Series of Polygons

Fourier Series of Polygons

Visualization of 3-D palate shape for an enhanced electropalatography system

Electropalatography (EPG), a system for real-time measurement of tongue–palate contact during speech, uses a stylized 2-D output system which, though useful for speech therapy and research, omits the actual spatial location of the contacts. This paper presents an enhanced EPG (eEPG) system that combines standard EPG data and digitized palate shape data to display the tongue–palate contact pattern in 3D. The palate shape can be obtained using a color-encoded structured light 3-D digitization system [Monks etal., IEEE Coll. on Biomed. Apps. of Dig. Sig. Proc. Dig. No. 1989/144, London (1989)]. The 3-D palate shape is represented by a series of polygons and can be displayed on a graphics workstation as a smoothly shaded, ‘‘lit,’’ colored surface, on which colored EPG contact patterns can be superimposed. Contact patterns can then be related more easily to articulatory features, and parameters derived from the contact pattern can be expressed in terms of absolute distances, making them more useful for sound production models. Examples of cross-subject comparisons will be shown, including cases where the dimensions of the constriction for an /s/ appear identical in EPG but clearly differ with eEPG. [Work supported in part by a Croucher Foundation Scholarship and SERC Grant No. GR/G 2115.]