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The COVID-19 pandemic has severely impacted global healthcare and financial systems, Highlighting the need for an automatic computer-aided diagnosis system using image recognition for chest X-rays(CXR). This study aims to classify COVID-19, normal, and pneumonia patients from CXR images via a modified ResNet-50 pre-trained CNN model. Our experiments are based on Dataset-1, which contains CXR images of COVID-19 and normal, while Dataset-2 also includes pneumonia. Dataset-1 and Dataset-2 were collected from King Abdul-Aziz Medical City in National Guard, Jeddah, Saudi Arabia. Moreover, a sample from the Kaggle repository was added to Dataset-1 and 2 to make two more Datasets. Our results for diagnosis of raspatory diseases have shown reliability and high accuracy of 95.28% (97.66% Sensitivity and 93.12% Specificity), which will be beneficial in aiding physicians and healthcare centres in the global fight against harmful spreading viruses through employing AI and ML techniques in X-ray medical diagnosis. [ABSTRACT FROM AUTHOR]

The problem of covering a convex 3D polytope by the minimal number of congruent spheres is reduced to a sequence of problems of minimising sphere radius when fixing the number of the spheres. We form a mathematical model of the problem using the Voronoi polytopes. Characteristics of the model are investigated. Extrema are attained at the vertices of the Voronoi polytopes constructed for sphere centres. To search for local minima, a modification of the Zoutendijk feasible directions method in a combination with random search is developed. Some numerical results for a cube and a non-regular octahedron are obtained. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to show how to use the Gauss map to produce efficient triangulations of parametric surfaces. The central idea is to invert canonical triangulations of the sphere using the Gauss map. The main problem is that the inverse of the Gauss map is not in general well defined. We show how to overcome this problem and formulate an algorithm to generate the desired triangulation. [ABSTRACT FROM PUBLISHER]

In this note, we introduce a simple, effective numerical method, the local tangential lifting method, for solving partial differential equations for scalar- and vector-valued data defined on surfaces. Even though we follow the traditional way to approximate the regular surfaces under consideration by triangular meshes, the key idea of our algorithm is to develop an intrinsic and unified way to compute directly the partial derivatives of functions defined on triangular meshes. We present examples in computer graphics and image processing applications. [ABSTRACT FROM PUBLISHER]

Most of graph drawing algorithms draw graphs on unbounded planes. However, there are applications that require graphs to be drawn on the plane inside a given polygon. In this paper, a new algorithm for planar orthogonal drawing of complete binary trees inside rectilinear polygons is presented. Uniform distribution of nodes of graphs on drawing regions is one of the aesthetics criteria in graph drawing. The goal of this paper is to produce planar orthogonal drawings with a relatively uniform node distribution and few edge bends. The proposed algorithm can be considered as a generalization of the H-tree layout method for rectilinear polygons. A new linear time algorithm is also given for bisecting rectilinear polygons into two equi-area rectilinear sub-polygons. [ABSTRACT FROM AUTHOR]

In this paper, we develop a new method for G1 continuous interpolation of an arbitrary sequence of points on an implicit or parametric surface with a specified tangent direction at every point. Based on the normal projection method, we design a G1 continuous curve in three-dimensional space and then project orthogonally the curves onto the given surface. With the techniques in classical differential geometry, we derive a system of differential equations characterizing the projection curve. The resulting interpolation curve is obtained by numerically solving the initial-value problems for a system of first-order ordinary differential equations in the parametric domain associated to the surface representation for a parametric case or in three-dimensional space for an implicit case. Several shape parameters are introduced into the resulting curve, which can be used in subsequent interactive modification such that the shape of the resulting curve meets our demand. The presented method is independent of the geometry and parameterization of the base surface, and numerical experiments demonstrate that it is effective and potentially useful in surface trim, robot, patterns design on surface and other industrial and research fields. [ABSTRACT FROM AUTHOR]

This paper concerns the solutions of very large symmetric semipositive definite (singular) linear systems involved in the problem of optimal surface parameterizations using inverse curvature mapping. Two approaches are presented that transform the singular linear systems into two kinds of symmetric positive definite linear systems, so that the famous Conjugate Gradient (CG) method can be used for solving them. Numerical experiments are run on two practical large problems to illustrate that the CG algorithm works very efficiently. [ABSTRACT FROM AUTHOR]

Splines play an important role in approximation theory as well as in computer-aided design and geometric modelling. Specifically, designing of objects is a fundamental problem that is mainly being attempted to be resolved using splines. Many authors have worked in the area and various techniques exist in the current literature. B-splines and non-uniform B-splines (NURBS) are quite popular in literature. However, there also exist some other splines to compete. The paper is devoted towards a new spline method that is a generalization of the Ball's cubic spline method on one hand, and also serves as an effective alternate to the NURBS of degree three on the other hand. Together with a class of shape parameters in its description, it introduces a class of cubic polynomial blending functions. These blending functions play a role of basis functions that ultimately describe the newly proposed spline method. Piecewise polynomial curves with a family of shape parameters are constructed from these blending functions. The generated curves have a second-order geometric continuity similar to those of weighted Nu-splines. The proposed method also provides a strong alternate to the NURBS of degree three as far as shape control is concerned. If the values of the shape parameters are changed, the approaching degree of the curves to their control polygon is adjusted accordingly and the curves are manipulated to approximate the cubic B-spline curve from its both sides. In comparison with the existing techniques, the degree of the spline method is ideally three and the domain of the shape parameters is broader than those in NURBS. The scheme has been implemented practically to demonstrate its effectiveness.This curve design method, in addition to enjoying the good features of Ball's cubic splines, possesses interesting shape design features too. The proposed spline method possesses two families of shape parameters. One family of parameters is associated with intervals and the other with points to have variety of shape control. [ABSTRACT FROM AUTHOR]

Fillets, also known as blend arcs, are used in CNC machining to round corners. Fillets are normally circular arcs, which have G1 contact with the straight line segments to which they are joined. Recent advances in machining technology allow NURBS, including Pythagorean-hodograph (PH) curve segments, to be incorporated in CNC tool paths. This article examines the use of cubic and PH quintic Bezier curve segments that have a single curvature extremum, and which have G2 contact with the straight line segments to which they are joined, as fillets. It is shown how the extreme circle of curvature can be determined. The point of curvature extremum and the corresponding value of the curvature can be changed by adjusting the joining points of the blending curve with the neighbouring straight lines. These blending curves can also be incorporated in computer-aided design packages for curve or surface design. [ABSTRACT FROM AUTHOR]

In this paper, we present a novel simple method, based on an implementation of space mapping technique, for improvement of the quality of tetrahedral and hexahedral meshes. The same approach is used for surface meshes where geometry of the initial surface mesh is preserved by a local mesh improvement such that new positions of the interior nodes of the mesh remain on the original discrete surface. The proposed method can be used in the pre-processing stage for subsequent studies (finite element analysis, computer graphics, etc.) by providing better input parameters for these processes. Experimental results are included to demonstrate the functionality of our method. [ABSTRACT FROM AUTHOR]

This paper presents a numerical determination of the optimal shape of body located in the incompressible viscous flow. The optimal shape is defined by the shape which has the minimum fluid force acting on the body. The shape optimization problem is based on an optimal control theory and can be formulated to find out geometrical coordinates of the body to minimize the performance function defined by the force subjected to the body. The performance function should be minimized satisfying the state equation. This problem can be transformed into the minimization problem without constraint condition by the Lagrange multiplier method. As a minimization technique, the gradient-based method is applied. The approximate solution to the flow problem is obtained by the finite element method based on the mixed interpolation with bubble function. In this research, the determination of the minimum fluid force shape in the incompressible Navier-Stokes flow is carried out. [ABSTRACT FROM AUTHOR]

Dupin cyclides, their applications in geometric modelling and their parametrization using bi-quadratic patches bounded by lines of curvature, have been investigated in recent years by a number of authors such as Martin, de Pont and Sharrock in 1986, Boehm in 1990, Pratt in 1990, and Degen in 1994. However, no completely reliable and general algorithm for the determination of bi-quadratic cyclide patches has appeared in the literature. This paper presents a new approach that produces any required bi-quadratic patch, bounded by lines of curvature, without non-intrinsic geometric constraints or restrictions. Specifically, if a bi-quadratic parametrization exists for the specified region of the cyclide, then it is correctly determined. Explicit formulae are given for the Bernstein weights and vectors of the parametrizations. The method is neither cyclide specific nor specific to the construction of bi-quadratic rational parametrizations - it may therefore be applied to other surfaces and to higher degree rational constructions. [ABSTRACT FROM AUTHOR]