### On the development of aeroballistic experiment techniques for flow visualization

S.I. Gerasimov, V.I. Erofeev, V.A. Kikeev, K.V. Totyshev, E. G. Kosyak, P. G. Kuznetsov, R.V. Gerasimova

Accepted: 2020-12-01

__Abstract__

The schemes of shadow rendering, supplementing the methodology of aeroballistic experiment, consisting in the ejection model, mounted in a special separable pallet, ballistic installation; the separation and capture of the pallet by the clipper; the span of the model with given initial conditions of motion speed and angle of attack on the measuring site aeroballistic tracks; contactless external trajectory registration model of the synchronous photographing models of digital cameras stereophotos, operating in standby mode on the background of reference marks of the coordinate reference system. Photographing takes place at the moment when pulsed light sources are triggered synchronously with the model's movement. Under these conditions, shadow visualization schemes are functional, which represent an upgraded method of a luminous point using a protective lens, a combined method that includes registration in passing light using a camera with an electron-optical shutter, and a shadow background method. Typical registration patterns are given.

### Testing and Visualization of the Singularities of the Mutual Intersection of a Tetrahedron and a Quadric (Chasles' Theorem)

A. L. Kheyfets

Accepted: 2020-10-09

__Abstract__

The article presents the results of experimental research and testing of M. Chasles’ historical theorem. The theorem shows the singularities of the intersection of an arbitrary tetrahedron and an arbitrary quadric (second-order surface). The need for testing is preconditioned by the absence of proof of the theorem and the complexity of its perception in the author’s version.

The experiments included construction, visualization, and study of computer 3d models obtained in the AutoCAD and SolidWorks suites. All variants of quadrics are considered in their different relative positions to the tetrahedron. The experimental procedure is considered in detail. The accuracy of the experimental study is estimated. The author tested all the intersection variants given in the theorem: the edges intersect a quadric, the vertices belong to a quadric, the edges are tangent to a quadric, the faces are tangent to a quadric, etc. The experiments confirmed the scientific novelty of the theorem, which consists in the fact that four intersecting straight lines drawn according to the algorithm of this theorem belong to the surface a single one-sheeted hyperboloid.

The author investigated in detail the variant of the theorem, when the planes drawn through the edges of a tetrahedron are tangent and enclose the quadric. It is shown that there are 4,096 combinations of plane positions. Only 64 combinations out of them lead to the realization of the theorem. This conclusion supplements the theorem. It is obtained using AutoLisp language programming.

The obtained results differ from the theorem in two variants. The author obtained and presented a proof of one of the theorem variants.

The author concludes that it is necessary to develop a universal proof of the theorem. It is proposed to apply the obtained models and algorithms when teaching students in the computer geometric simulation course.