English

A minimal closed-form solution to the conic based on self-polar triangle

Algebraic Geometry 2018-01-10 v1

Abstract

In this paper, we use the properties of the self-polar triangle to not only show a novel method for a basic point-line enumerative problem of conics, but also present a series of closed-form solutions to the conics from all minimal configurations of points and lines in general position. These closed-form formulae may allow us to derive easily the algebraic and geometric conditions which characterize when the obtained conic is real and non-degenerate, so we propose a criterion for a non-degenerate real conic from each of all minimal configurations. The correctness of our results is validated by some examples.

Keywords

Cite

@article{arxiv.1801.02751,
  title  = {A minimal closed-form solution to the conic based on self-polar triangle},
  author = {Yang Guo},
  journal= {arXiv preprint arXiv:1801.02751},
  year   = {2018}
}
R2 v1 2026-06-22T23:39:58.462Z