Analysis of the speed and curvature of the trajectory in the problem of pursuing a set of targets

Introduction. A kinematic model of group pursuit of a set of targets on a plane is considered. Pursuers use a technique similar to parallel approach method to achieve goals. Unlike the parallel approach method, the speed vectors of pursuers and targets are directed arbitrarily. In the parallel approach method, the instantaneous directions of movement of the pursuer and the target intersect at a point belonging to the circle of Apollonius. In the group model of pursuing multiple goals, the pursuers try to adhere to a network of predictable trajectories.Materials and Methods. The model sets the task of achieving goals by pursuers at designated points in time. This problem is solved by the methods of multidimensional descriptive geometry using the Radishchev diagram. The predicted trajectory is a composite line that moves parallel to itself when the target moves. On the projection plane “Radius of curvature — speed value”, the permissible speed range of the pursuer is displayed in the form of level lines (these are straight lines parallel to one of the projection planes). Images of speed level lines are displayed on the projection plane “Radius of curvature — time to reach the goal”. The search for points of intersection of the speed line images and the appointed time level line is being conducted. Along the communication lines, the values of the intersection points are lowered to the plane “Radius of curvature — speed value”. Using the obtained points, we construct an approximating curve and look for the intersection point with the line of the assigned speed. As a result, we get values of the radius of the circle at the predicted line of the trajectory of the pursuer.Results. Based on the results of the conducted research, test programs have been created, and animated images have been made in the computer mathematics system.Discussion and Conclusions. This method of constructing trajectories of pursuers to achieve a variety of goals at a given time values can be in demand by developers of autonomous unmanned aerial vehicles.

Shadows, Highlights and Faces: the Contribution of a ‘Human in the Loop’ to Digital Art History

While automatic computational techniques appear to reveal novel insights in digital art history, a complementary approach seems to get less attention: that of human annotation. We argue and exemplify that a ‘human in the loop’ can reveal insights that may be difficult to detect automatically. Specifically, we focused on perceptual aspects within pictorial art. Using rather simple annotation tasks (e.g. delineate human heights, indicate highlights and classify gaze direction) we could both replicate earlier findings and reveal novel insights into pictorial conventions. We found that Canaletto depicted human figures in rather accurate perspective, varied viewpoint elevation between approximately 3 and 9 m and highly preferred light directions parallel to the projection plane. Furthermore, we found that taking the averaged images of leftward-looking faces reveals a woman, and for rightward-looking faces showed a male, confirming earlier accounts on lateral gender bias in pictorial art. Lastly, we confirmed and refined the well-known light-from-the-top-left bias. Together, the annotations, analyses and results exemplify how manual annotations can contribute and complement to digital art history.

The Possibility of Applying Rumen Research at the Projective Plane PG (2,17)

One of the main objectives of this research is to use a new theoretical method to find arcs and Blocking sets. This method includes the deletion of a set of points from some lines under certain conditions explained in a paragraph 2.In this paper we were able to improve the minimum constraint of the (256,16) – arc in the projection plane PG(2,17).Thus , we obtained a new {50,2}-blocking set for size Less than 3q , and according to the theorem (1.3.1),we obtained the linear 257,3,24117    code, theorem( 2.1.1 ) giving some examples on arcs of the Galois field GF(q);q=17."

The Optimal Size of {b, t} - Blocking Set When t = 3,4 by Intersection the Tangent in PG (2, q)

In this research, we have been able to construct a triple blocking set of optimal size - {4q, 3} Based on the theorem (1.4.7) (Maruta, 2017, pp. 1-47).Without improving the minimum constraint of the projection level PG (2, q) We have also been able to develop the theorem (2.3.2) to construct quadratic blocking set of optimal size {5q + 1,4} - After we have engineered a quadratic blocking set of an optimal size for the projection plane PG (2,1.3) In the example (2.3.1).In general, we were able to conclude theorems (2.3.3) and (2.3.4) for construct engineered blocking sets with an optimal size when t = 3,4.

Manufacture and prefabrication practice on a test model of a novel six-bar tetrahedral cylindrical lattice shell

A six-bar tetrahedral unit of a rhombic projection plane is a basic geometric invariable body with a simple configuration. A six-bar tetrahedral cylindrical lattice shell can be assembled by rhombic projection plane six-bar tetrahedral units with identical geometry sizes, which is conducive to standardized design, industrial production, and prefabricated construction. The popularization and application requirements of green architecture industry can also be met using such a shell. A model test of a six-bar tetrahedral cylindrical lattice shell was developed to simulate the practical application of the prefabricated structural system. A new type of joint for the prefabricated structure was proposed that is easy to assemble and is lightweight. A tridimensional fine-tuning bed jig was developed to ensure the manufacturing precision of the pre-made six-bar tetrahedral units. Stacking and transport of the units were practiced. The assembly process from units to the integral shell was conducted in an experimental hall; the result testified the advantages of easy stack, convenient transport, and highly efficient fabrication. The structural assembly errors of the shell were measured, and the measurement results verified the installation accuracy of the test model. This practical study lays the foundation for further engineering applications of six-bar tetrahedral cylindrical lattice shells.