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Author: Baruch E. Karlin

Affiliation: Rafael, Israel

ISBN: 978-989-674-026-9

Keyword(s): Minimum Distance, Semi-infinite Cone, Geometric Reasoning, Explicit Solution.

Related Ontology Subjects/Areas/Topics: Computer Vision, Visualization and Computer Graphics ; Fundamental Methods and Algorithms ; Geometric Computing ; Geometry and Modeling ; Modeling and Algorithms ; Scene and Object Modeling

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.

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Paper citation in several formats:
E. Karlin B. and (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

@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},
}

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

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