### Visualization of CAE-solutions of ice navigation partial problems.
Joint maneuvering of vessels

Vasiliy A. Lobanov, Yulia R. Guro-Frolova

Accepted: 2022-01-06

__Abstract__

The article notes that ensuring efficiency and safety of ice transport operations on the water transport is distinguished by a wide range of necessary actions, maneuvers, modes and dynamic working methods of the vessels. The assessment of vessel ice performance in special operating conditions is of current interest.

Using CAE technologies the range of actual tasks of vessel movement and joint maneuvering in different ice and navigational conditions is considered: the prediction of forming speed and qualitative condition of the ice channel in thick and limit compact ices due to different tactical working methods of several icebreakers; the efficiency and safety of the slow-moving transport vessel icebreaking assistance in compact ices.

Due to the result analysis of multiple CAE modeling recommendations for the operation of the studied icebreaker and cargo fleet of different ice categories are given. These recommendations concern the choice of safe maneuvering distances, vessel control laws, performance of standard operations.

### Graph visualization in the development of the knowledge testing program on graph theory

T.M. Kuzmina, O.A. Vetrova

Accepted: 2021-12-17

__Abstract__

The article considers an interdisciplinary task that combines pedagogical aspects and visualization issues. Since graph models have become widespread, the study of graph theory in universities has become a constant practice. The article deals with the development of an application program that, on the one hand, helps to comprehend graph theory, in particular, algorithms on graphs, and on the other hand, allows you to objectively evaluate the knowledge gained. If they talk about testing knowledge using computers, then as a rule, we are talking about testing. But to test the knowledge of algorithms on graphs, the possibilities of tests are very limited. For example, when working with the algorithm "search in depth" (or "search in width"), we are dealing with tasks that have more than a hundred (!) positive responses. In other tasks, the number of correct answers is measured in units (for example, when searching for the shortest path), but there is a high probability of guessing, finding the answer by methods unrelated to the algorithms being studied. Of course, it is possible to divide the initial tasks into many smaller ones that are already suitable for testing, but knowledge of the details and features does not always indicate knowledge of the algorithm as a whole. The article describes an application program that allows the user to perform actions according to the selected algorithm. The developed visualization program reproduces the result of these actions on the screen and at the same time checks the correctness of these actions.

### Software package for three-dimensional visualization of the behavior of neutron fields and archived parameters during the operation of the RBMK-1000 reactor

À.Î. Bukalin, A.M. Zagrebaev, V.V. Pilyugin

Accepted: 2021-12-05

__Abstract__

This paper describes the calculation algorithm, software package and visualization of the three-dimensional neutron field deformation according to the archive of the RBMK (high-power pressure-tube reactor) reactor operational parameters. The determination of the field deformation is based on finding "natural" functions for approximating the readings of in-reactor control discretely located sensors. This paper considers the use of generally accepted harmonic functions and "natural" functions for describing the spatial deformation of the neutron field. It is shown that to describe the deformation of the neutron field, it is sufficient to use only a few "natural" functions, in contrast to the use of all harmonic functions from a given set. This, in turn, opens up new possibilities, in particular, for solving the problems of predictive diagnostics of in-reactor control sensors.

### Irregular curves in engineering geometry and computer graphics

V.A. Korotkiy

Accepted: 2021-11-16

__Abstract__

Graphically defined irregular curves are encountered in various engineering problems. To use such a curve in the design process, it is replaced (approximated) with some analytical function.

The article discusses the traditional approach, when a graphically defined curve is approximated by cubic Bezier segments (with unit weight coefficients) connected to each other with the order of smoothness G2 (with continuous change in curvature). It is shown that for the plane case the well-known algebraic condition for a G2-smooth connection of Bezier segments is reduced to solving an ordinary quadratic equation. An algorithm is obtained that allows you to control the shape of a plane composite Bezier curve without violating the specified order of smoothness. The algorithm differs in that it allows you to vary both the directions of the tangents at the butt points and the radii of curvature at the end points of the compound curve. In particular, the algorithm allows you to find the equation of the plane cubic Bezier segment, given by tangents and radii of curvature at their endpoints. The calculation of the coordinates of the control points of such a segment is reduced to solving a system of two quadratic equations or plotting the intersection points of two parabolas.

The problem of G2 -smooth conjugation of two straight lines, a straight line and a circle, two circles (with predetermined conjugation points) is considered. An example of constructing a G2-smooth closed contour tangent to given straight lines and having a given curvature at the closing point is presented. An experiment was carried out to approximate a physical spline by a composite cubic Bezier curve. The approximation error was less than 2%.