Using Cayley-Menger Determinants for geometric constraint solving

Dominique Michelucci, Sebti Foufou

Research output: Contribution to journalConference articlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)285-290
Number of pages6
JournalACM Symposium on Solid Modeling and Applications, SM
StatePublished - 2004
EventNinth ACM Symposium on Solid Modeling and Applications, SM'04 - Genoa, Italy
Duration: Jun 9 2005Jun 11 2005

ASJC Scopus subject areas

  • General Engineering

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