[Abstract]: In this work we present a new method for determining relative positions between one moving object, modelled by a bounding spheroid, and surrounding static objects, modelled by circular hyperboloids of one sheet. The proposed strategy is based on the real-time calculation of the coefficients of degree three polynomial. We propose several algorithms for two real applications of this geometric problem: the first one, oriented to the design of video games, and the second one, devoted to surveillance tasks of a quadcopter in industrial or commercial environments.

©2019. This manuscript version is made available under the CC-BY-NC-ND 4.0 license https:// creativecommons.org/licenses/by-nc-nd/4.0/. This version of the article: Castro, P. M., Dapena, A., Souto- Salorio, M. J., & Tarrío-Tobar, A. D. (2019). 'Algorithms for determining relative position between spheroids and hyperboloids with one sheet', has been accepted for publication in Mathematics and Computers in Simulation, 160, 168–179.The Version of Record is available online at https://doi.org/10.1016/j.matcom.2018.12.006.

This work has been funded by the Xunta de Galicia, Spain (ED431C 2016-045, ED341D R2016/012, ED431G/01), the Agencia Estatal de Investigación of Spain (TEC2013-47141-C4-1-R, TEC2015-69648-REDC, TEC2016-75067-C4-1-R) and ERDF funds of the EU (AEI/FEDER, UE). The authors wish to thank José Sanmartín for his helpful work in the graphic design of the pictures included in this paper.

Xunta de Galicia; ED341D R2016/012

Xunta de Galicia; ED431C 2016-045

Xunta de Galicia; ED431G/01