# Approximation of the Distance from a Point to an Algebraic Manifold

### Alexei Uteshev, Marina Goncharova

#### Abstract

The problem of geometric distance d evaluation from a point X0 to an algebraic curve in R2 or manifold G(X) = 0 in R3 is treated in the form of comparison of exact value with two its successive approximations d(1) and d(2). The geometric distance is evaluated from the univariate distance equation possessing the zero set coinciding with that of critical values of the function d2(X0), while d(1)(X0) and d(2)(X0) are obtained via expansion of d2(X0) into the power series of the algebraic distance G(X0). We estimate the quality of approximation comparing the relative positions of the level sets of d(X), d(1)(X) and d(2)(X).

Download#### Paper Citation

#### in Harvard Style

Uteshev A. and Goncharova M. (2019). **Approximation of the Distance from a Point to an Algebraic Manifold**.In *Proceedings of the 8th International Conference on Pattern Recognition Applications and Methods - Volume 1: ICPRAM,* ISBN 978-989-758-351-3, pages 715-720. DOI: 10.5220/0007483007150720

#### in Bibtex Style

@conference{icpram19,

author={Alexei Uteshev and Marina Goncharova},

title={Approximation of the Distance from a Point to an Algebraic Manifold},

booktitle={Proceedings of the 8th International Conference on Pattern Recognition Applications and Methods - Volume 1: ICPRAM,},

year={2019},

pages={715-720},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0007483007150720},

isbn={978-989-758-351-3},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 8th International Conference on Pattern Recognition Applications and Methods - Volume 1: ICPRAM,

TI - Approximation of the Distance from a Point to an Algebraic Manifold

SN - 978-989-758-351-3

AU - Uteshev A.

AU - Goncharova M.

PY - 2019

SP - 715

EP - 720

DO - 10.5220/0007483007150720