Shuranova E. N.

ONE METHOD OF CONSTRUCTING ALGEBRAIC CURVES

The article examines the problems of constructing algebraic curves as constituent
contours satisfying certain technical characteristics. The author proposes a method for constructing
universal circular curves by means of circular inversion, which is the simplest method
of Cremona transformations.
The relationship between the special points of the pre-image and the image obtained by
the transformation is established, which is very important for ensuring smoothness of the contour.
The influence of the location of the pre-image relatively to the apparatus of transformation on the
shape of the image curve is shown in the article. The article contains an analysis of the formation
of the order of the image in quadratic transformations, depending on the location of the pre-image
relatively to apparatus of transformation.

Keywords: Cremona transformations, curve «image», curve «pre-image», unicursal circular curves, кремоновы преобразования, кривая образ, кривая прообраз, уникурсальные циркулярные кривые