Constructing a G2-Smooth Compound Curve Based on Cubic Bezier Segments

The article describes the model of group pursuit of a single target by the chase method. All objects participating in the pursuit model move with a constant modulo speed. One of the participants in the process moves along a certain trajectory and releases objects at specified intervals, the task of which is to achieve the goal by the chase method. All objects have restrictions on the curvature of the motion path. A single target, in turn, is tasked with achieving the target that releases objects using the parallel approach method. For each pursuing object, a detection area is formed in the form of two beams. The object's velocity vector is directed along the bisector of the angle formed by such rays. If the target enters the detection area, then the object starts pursuit and the velocity vector is directed to the target. If the target leaves the detection area, then the object makes a uniform and rectilinear movement. The task is to implement a dynamic model of multiple group pursuit, where each object has its own tasks, implemented by the chase method. As an example, where the model developed in the article could be in demand, the following example can be given. Consider the movement of a low-maneuverable object that is overtaking a faster target. As a means of protection, instead of releasing passive heat traps, it is proposed to drop a variety of autonomously controlled weapons. An analysis of existing studies has shown that such means of protecting aircraft do not exist. The results of the research can be in demand in the design of unmanned aerial vehicles with elements of autonomous control and artificial intelligence.

Geometric Model of Group Pursuit of a Single Target by the Chase Method

Dubanov

2022

All-Russian Scientific and Methodological Conference «Problems of Engineering Geometry» and the Seminar «Geometry and Graphics» 2021

Vyshnyepolskiy

Kadykova

Vereschagina

2022

The article is devoted to the annual All-Russian scientific and methodological conference "Problems of Engineering Geometry" and the annual All-Russian scientific and methodological seminar "Geometry and Graphics" in 2021. Statistical information about the conference and seminar is provided: the number of participants, universities, the number of cities and countries in which universities are located -participants. Using the expression proposed earlier, the activity of participation of the departments of graphic disciplines in the conference "Problems of Engineering Geometry" and the seminar "Geometry and Graphics", held in 2021, was determined. The comparison of the number of participants and reports of the conference and seminar in 2021 with the number of participants and reports is given and analyzed International Internet conferences "Quality of graphic training" at the Perm National Research Polytechnic University. The results of the All-Russian Seminars "Geometry and Graphics" and the All-Russian Conferences "Problems of Engineering Geometry" of the last two years are compared with each other. In order to compare conferences and seminars quantitatively, not qualitatively, a relationship has been proposed. The content of the reports of the participants of the conference and the seminar is briefly considered. Conclusions are drawn: 1) in 2021, in terms of the success of the seminar "Geometry and Graphics" and the conference "Problems of Engineering Geometry", we managed to move forward - the success rate increased; 2) judging by the number of reports, scientific work on the profile of the department is carried out in a small number of departments. This is due to shortcomings in the staffing of departments of graphic disciplines by teachers. One of them is a lack of understanding that the winners or participants of All-Russian and regional Olympiads who have undergone appropriate training should work as teachers.

Point Tools of Geometric Modeling, Invariant Relating to Parallel Projection

Konopatskiy

Бездитный

2022

The purpose of this paper is to familiarize experts in geometric and computer modeling with specific tools for point calculus; demonstrate the possibilities of point calculus as a mathematical apparatus for modeling of multidimensional space’s geometric objects. In the paper with specific examples have been described the basic constructive tools for point calculus, having invariant properties relating to parallel projection. These tools are used to model geometric objects, including: affine ratio of three points of a straight line, intersection of two straight lines, intersection of a straight line with a plane, parallel translation and tangent to a curve. The theoretical foundations of point tools for geometric modeling, invariant relating to parallel projection, have been presented. For example, instead of traditional determination for straight lines intersection point by composing and solving a system of equations in coordinate form, zeroing of a moving triangle’s area is used. This approach allows to define geometric objects in multidimensional spaces keeping the symbolic representation of point equation, as well as to perform its coordinate-wise calculation at the last stage of modeling, which allows to significantly reduce computing resources in the process of solving the problems related to engineering geometry and computer graphics. The local results of the research presented in this paper, which served as examples for the use of point calculation constructive tools, are: definition of the cubic Bezier curve as a curve of one relation in point and coordinate form; determination of excessive parameterization of the plane and bypass arcs based on it; determination of the tangent to the spatial curve by differentiation the original curve with respect to a current parameter, followed by parallel transfer of the obtained segment to the tangency point; the general point equation for the torso surface has been obtained on account of its definition as a geometric place of tangents to its cusp edge, and examples for the construction of torso surfaces based on the cubic Bezier curve and a transcendental space curve have been presented.