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Visualization of Level Sets and Singular Surfaces in Differential Games

### V.L. Averbukh, S.S. Kumkov, O.A. Pykhteev, and D.A. Yurtaev

In the paper, algorithms and programs of scientific visualization carried out in the
Institute of Mathematics and Mechanics, Russian Academy of Sciences (Ekaterinburg, Russia) are
considered. The objective field of these programs is the linear differential games with fixed terminal
time, convex terminal payoff and geometrical constraints on the player controls.
The main element of
the solution of a game (and the object for visualization) is the value function of the game defined
by a collection of its level sets.
Also, it is useful to investigate (including visual approach) the singular
surfaces of the game, that is the surfaces where the value function has some peculiarities.

Screenshots of the programs and pictures of views produced by them are shown.

## Electronic version of the article

algoritm2000.pdf (1887 KB).

*Averbukh V.L., Kumkov S.S., Pykhteev O.A., Yurtaev D.A.*
**Visualization of level sets and singular surfaces in differential games**
// Proceedings of ALGORITMY 2000, Conference on Scientific Computing, pp. 196–206.

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