VISUAL GEOMETRIC POWER FIELD MODEL WITH TWO POINT ENERGY SOURCES

Abstract

One of the problems of geometric modeling is the visual representation of the results and data obtained experimentally in the form of an understandable geometric image. The visibility of geometric models, processes and phenomena contributes to a better understanding of the essence of this process and phenomenon.

Of particular importance is the visibility of images of multidimensional processes. The increase in such visibility contributes to the reflection of a process or phenomenon by the set of lines characterizing the features of the process or phenomenon.

A geometric interpretation of any force field is a manifold whose dimension depends on the number of field parameters that are taken into account when modeling it. The visual representation of varieties as well as any surface depends on the choice of the sets of curves (or straight lines) into which the manifold can be stratified. For example, a grid of curves on a surface can both increase and decrease the visibility of its image. On surfaces that are created by the skeleton-kinematic method, generators and trajectories of the generatrix are usually selected for these lines. Such families of lines not only represent the surface, but also demonstrate the process of its formation.

Any variety can be stratified into various sets of surfaces (planes), each of which can be represented by its mesh or linear skeleton.

This article proposes a four-dimensional force field to be graphically displayed as a set of lines of equal potentials and lines of force.

The force field potential at an arbitrary point in three-dimensional space is affected by the distance from the field point to energy sources. This effect decreases with increasing distance from a point in space to energy sources. In [3], the authors proposed such a geometric apparatus that takes into account the influence of the distance of the energy source from the points of the energy field on the potentials of these points, as well as various schemes of this device depending on the type of energy of the sources and the medium in which the energy field propagates.

Representation of the physical field as the set of lines of intersection of one-parameter sets of confocal ellipsoids, two-sheeted hyperboloids and one-parameter bundles of planes allows you to geometrically simulate the field in the form of sets of isolines and lines of force, and also enhances the visibility of the geometric model.

The set of isolines and field lines with two point sources of energy form a geometric model of the field in the form of an orthogonal line structure.

Keywords: field line, force field, contour, isosurface, manifold, physical field, energy, energy source, distance, distance effect, energy potential.