# Geometric Transformations

The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

## Geometric Transformations

a one-to-one mapping of a straight line, plane, or space onto itself. Usually sets of geometric transformations are considered such that each finite sequence of transformations in the set can be replaced by one transformation of the set, and a transformation inverse to any of those considered also belongs to the given set. Such sets of geometric transformations form what is called a group of transformations. Examples of geometric transformations that form a group of transformations are the motions of a plane (or of a space), affine transformations, and projective transformations.

### REFERENCE

Modenov, P. S., and A. S. Parkhomenko. Geometricheskie preobrazovaniia. Moscow, 1961.
References in periodicals archive ?
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We have presented examples of various complexity that were all devoted to the matrix representation of geometric transformations. The greater part of the examples dealt with the basic problems of robotics.

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