Using Cayley Menger Determinants

Michelucci, D.; Foufou, S.

Using Cayley Menger Determinants

Files

285-290_michelucci.pdf (106.1 KB)

Date

2004

Authors

Michelucci, D.
Foufou, S.

Publisher

The Eurographics Association

Abstract

We use Cayley-Menger Determinants (CMDs) to obtain an intrinsic formulation of geometric constraints. First, we show that classical CMDs are very convenient to solve the Stewart platform problem. Second, issues like distances between points, distances between spheres, cocyclicity and cosphericity of points are also addressed. Third, we extend CMDs to deal with asymmetric problems. In 2D, the following configurations are considered: 3 points and a line; 2 points and 2 lines; 3 lines. In 3D, we consider: 4 points and a plane; 2 points and 3 planes; 4 planes.

        @inproceedings{10.2312:sm.20041403
,
booktitle = {Solid Modeling
},
editor = {Gershon Elber and Nicholas Patrikalakis and Pere Brunet
},
title = {{Using Cayley Menger Determinants
}},
author = {Michelucci, D. and 
Foufou, S.
},
year = {2004
},
publisher = {The Eurographics Association
},
ISSN = {1811-7783
},
ISBN = {3-905673-55-X
},
DOI = {10.2312/sm.20041403
}
}