A comparison of analytical solutions of nonlinear complex generalized Zakharov dynamical system for various definitions of the differential operator

<abstract><p>This paper considers deriving new exact solutions of a nonlinear complex generalized Zakharov dynamical system for two different definitions of derivative operators called conformable and $ M- $ truncated. The system models the spread of the Langmuir waves in ionized plasma. The extended rational $ sine-cosine $ and $ sinh-cosh $ methods are used to solve the considered system. The paper also includes a comparison between the solutions of the models containing separately conformable and $ M- $ truncated derivatives. The solutions are compared in the $ 2D $ and $ 3D $ graphics. All computations and representations of the solutions are fulfilled with the help of Mathematica 12. The methods are efficient and easily computable, so they can be applied to get exact solutions of non-linear PDEs (or PDE systems) with the different types of derivatives.</p></abstract>

On Soliton Solutions of Perturbed Boussinesq and KdV-Caudery-Dodd-Gibbon Equations

Nonlinear science is a fundamental science frontier that includes research in the common properties of nonlinear phenomena. This article is devoted for the study of new extended hyperbolic function method (EHFM) to attain the exact soliton solutions of the perturbed Boussinesq equation (PBE) and KdV–Caudery–Dodd–Gibbon (KdV-CDG) equation. We can claim that these solutions are new and are not previously presented in the literature. In addition, 2d and 3d graphics are drawn to exhibit the physical behavior of obtained new exact solutions.

Evaluating Extensible 3D (X3D) Graphics For Use in Software Visualisation

<p>3D web software visualisation has always been expensive, special purpose, and hard to program. Most of the technologies used require large amounts of scripting, are not reliable on all platforms, are binary formats, or no longer maintained. We can make end-user web software visualisation of object-oriented programs cheap, portable, and easy by using Extensible (X3D) 3D Graphics, which is a new open standard. In this thesis we outline our experience with X3D and discuss the suitability of X3D as an output format for software visualisation.</p>

Evaluating Extensible 3D (X3D) Graphics For Use in Software Visualisation

<p>3D web software visualisation has always been expensive, special purpose, and hard to program. Most of the technologies used require large amounts of scripting, are not reliable on all platforms, are binary formats, or no longer maintained. We can make end-user web software visualisation of object-oriented programs cheap, portable, and easy by using Extensible (X3D) 3D Graphics, which is a new open standard. In this thesis we outline our experience with X3D and discuss the suitability of X3D as an output format for software visualisation.</p>

PROCEDURAL GENERATION OF MASSIVE 3D GEOMETRY USING IMPROVED MARCHING CUBES ALGORITHM

Процедурная генерация, или создание контента во время работы программы, это сложное направление, которое требует не только понимания 3D-графики, но и навыков программирования графики, что часто сводится к изучению работы графических процессоров. Из-за такой сложности разработчики часто используют уже готовые инструменты для создания контента. Такие инструменты обобщают и упрощают работу, предоставляя большой заготовленный набор функции, который можно использовать не зная программирования вовсе. К сожалению, обобщение часто приводит к уменьшению гибкости и вводит новые ограничения. Статистика показывает, что использование процедурной генерации, для создания массивной 3D-геометрии, невозможно при использовании готовых инструментов с уже заготовленными функциями. Такие инструменты не позволяют воплотить огромные масштабы массивной геометрии в жизнь из-за различных ограничений. Кроме того, существующие алгоритмы создания 3D-геометрии часто не учитывают применение этих алгоритмов для создания массивной 3D-геометрии, например, планет. Рассматриваемый в этой работе алгоритм Marching Cubes также не учитывает применение алгоритма для создания массивной геометрии, из-за чего применение этого алгоритма в таких целях будет иметь много ограничений и много недостатков. Но данный алгоритм выбран не случайно, он обладает большой популярностью и мы поговорим почему. Данная работа фокусируется на представлении новой модификации на уже существующий алгоритм Marching Cubes в целях применения его в рамках массивной геометрии. Данный алгоритм найдет применение в компьютерных играх с космической тематикой, наш алгоритм позволяет создавать массивную 3D-геометрию планетарных масштабов даже на слабых компьютерах без особых затрат по ресурсам. Кроме того, наш алгоритм позволяет изменять сгенерированную геометрию в реальном времени, без задержек по времени, что так важно компьютерным играм. Procedural generation, or the creation of content while a program is running, is a complex area that requires not only an understanding of 3D graphics, but also graphics programming skills, which often boils down to learning how GPUs work. Because of this complexity, developers often use off-the-shelf content creation tools. Such tools generalize and simplify work by providing a large pre-built set of functions that can be used without knowing programming at all. Unfortunately, generalization often reduces flexibility and introduces new constraints. Statistics show that using procedural generation to create massive 3D geometry is impossible when using ready-made tools with already prepared functions. Such tools do not allow the huge scales of massive geometry to be brought to life due to various constraints. In addition, existing 3D geometry creation algorithms often do not account for the application of these algorithms to create massive 3D geometry such as planets. The Marching Cubes algorithm considered in this work also does not take into account the use of the algorithm for creating massive geometry, which is why the use of this algorithm for such purposes will have many limitations and many disadvantages. But this algorithm was not chosen by chance, it is very popular and we will talk why. This work focuses on modifying the existing Marching Cubes algorithm to apply it to massive geometry. This algorithm will find application in computer games with a space theme, our algorithm allows to create massive 3D geometry of planetary scales even on a low-end computers without special resource costs. In addition, our algorithm allows to change the generated geometry in real time, without time delays, which is so important for computer games.

Teaching the Notion Conic Section with Computer

The article discusses the problem of introducing and constructing mathematical concepts using a computer. The Wolfram Mathematica 12 symbolic calculation system is used at each stage of the complex spiral process to form the notion of conic section and the related concepts of focus, directrix and eccentricity. The nature of these notions implies the use of appropriate animations, 3D graphics and symbolic calculations. Our vision of the process of formation of mathematical concepts is presented. The notions ellipse, parabola and hyperbola are defined as the intersection of a conical surface with a plane not containing the vertex of the conical surface. The conical section is represented as a geometric location of points on the plane for which the ratio of the distance to the focus to the distance to the directrix is a constant value. The lines of hyperbola and ellipse are determined by their foci. The equivalence of different definitions for conical sections is commented.

Design and Development of Gesture Based Gaming Console

Game controllers have been planned and improved throughout the years to be as easy to understand as could reasonably be expected. A game controller is a gadget utilized with games or theatre setups to give contribution to a computer game, commonly to control an item or character in the game. Information gadgets that have been named game controllers incorporate consoles, mice, gamepads, joysticks, and so on. A few controllers are intended to be purposely best for one sort of game, for example, guiding wheels for driving games, move cushions for moving games, and light firearms for firing games. The aim here is to create a virtual environment, where the user is appealed by various gesture controls in a gaming application. A Gesture is an action that has to be seen or felt by someone else (here a PC) and has to convey some piece of information. Now obviously, to create a virtual gaming environment, we need to create a real-time gaming application first. We’ll be designing our 2D and 3D gaming applications through Unity 3D video game engine. The data used in this project is primarily from the Ego Hands dataset. After an input has been taken, and the consequent action has been performed, we’ll use this activity for future development of the model by using Tensor-Flow. The input will be taken through the webcam of the PC which will be accessed and combined to the gaming application and hands dataset by WebGL. WebGL is a JavaScript API for rendering interactive 2D and 3D graphics within any compatible web browser without the use of plug-ins.