EXPLICIT SOLUTION FOR THE MINIMUM DISTANCE BETWEEN TWO SOLID SEMI-INFINITE CIRCULAR CONES

Baruch E. Karlin

2010

Abstract

Multi-body kinematics and object rendering often involve minimum distance calculations. Explicit solutions exist for the distance between spheres, cylinders and other simple objects. Deriving the minimum distance between cones requires numerical minimization or geometrical approximations combined with analytical solutions for the simpler objects. This paper describes an explicit solution for the minimum distance between two solid semi-infinite circular cones. The method combines geometrical reasoning with analytical derivation. The solution also includes the location of the intersection points. Solution regions are identified and discussed. A numerical method based on minimizing the distance between two cone generators was used as part of the verification process. The exact solution was compared to results of approximation by regular polytopes. The explicit solution is robust, independent of coordinate system and invariant under rigid translation and rotation of the setup.

Paper Citation

in Harvard Style

E. Karlin B. (2010). EXPLICIT SOLUTION FOR THE MINIMUM DISTANCE BETWEEN TWO SOLID SEMI-INFINITE CIRCULAR CONES . In Proceedings of the International Conference on Computer Graphics Theory and Applications - Volume 1: GRAPP, (VISIGRAPP 2010) ISBN 978-989-674-026-9, pages 154-159. DOI: 10.5220/0002849901540159

in Bibtex Style

@conference{grapp10,
author={Baruch E. Karlin},
title={EXPLICIT SOLUTION FOR THE MINIMUM DISTANCE BETWEEN TWO SOLID SEMI-INFINITE CIRCULAR CONES},
booktitle={Proceedings of the International Conference on Computer Graphics Theory and Applications - Volume 1: GRAPP, (VISIGRAPP 2010)},
year={2010},
pages={154-159},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0002849901540159},
isbn={978-989-674-026-9},
}

in EndNote Style

TY - CONF
JO - Proceedings of the International Conference on Computer Graphics Theory and Applications - Volume 1: GRAPP, (VISIGRAPP 2010)
TI - EXPLICIT SOLUTION FOR THE MINIMUM DISTANCE BETWEEN TWO SOLID SEMI-INFINITE CIRCULAR CONES
SN - 978-989-674-026-9
AU - E. Karlin B.
PY - 2010
SP - 154
EP - 159
DO - 10.5220/0002849901540159