Conference material: "Proceedings of the International Conference on Computer Graphics and Vision “Graphicon” (19-21 September 2023, Moscow)"
Authors:Voloshinov D.V.
Constructive Geometry of Conics Principal Conjugations
Abstract:
Curves of the second order or conics are the most important geometric images on which many provisions of projective geometry are built. Despite the development of this scientific discipline, there are still many issues that require closer study and research. The constructive geometric method makes it possible to discover new previously unknown properties that appear in conics both in independent images and in complexes of geometric images that can be represented by these curves. This approach allows us to give a new projective interpretation to many problems to which it has not been applied before. An example of such a problem, in particular, is the problem of constructing a line equidistant with respect to two circles (or spheres of higher-dimensional spaces). The constructive geometric method allows us to find the most general ways to solve geometric problems, and their extension to the region of imaginary geometric values makes it possible to get rid of annoying exceptions. The development of the theory of curves of the second order contributes to the improvement of information technologies based on automation tools for solving constructive geometric problems.
