Using Cayley-Menger Determinants for geometric constraint solving

Dominique Michelucci; Sebti Foufou

Using Cayley-Menger Determinants for geometric constraint solving

Dominique Michelucci, Sebti Foufou

Computer Science

Research output: Contribution to journal › Conference article › peer-review

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.

Original language	English (US)
Pages (from-to)	285-290
Number of pages	6
Journal	ACM Symposium on Solid Modeling and Applications, SM
State	Published - 2004
Event	Ninth ACM Symposium on Solid Modeling and Applications, SM'04 - Genoa, Italy Duration: Jun 9 2005 → Jun 11 2005

ASJC Scopus subject areas

General Engineering

Cite this

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title = "Using Cayley-Menger Determinants for geometric constraint solving",

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.",

author = "Dominique Michelucci and Sebti Foufou",

year = "2004",

language = "English (US)",

pages = "285--290",

journal = "ACM Symposium on Solid Modeling and Applications, SM",

issn = "1811-7783",

note = "Ninth ACM Symposium on Solid Modeling and Applications, SM'04 ; Conference date: 09-06-2005 Through 11-06-2005",

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AU - Michelucci, Dominique

AU - Foufou, Sebti

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AB - 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.

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M3 - Conference article

AN - SCOPUS:21644483350

SN - 1811-7783

SP - 285

EP - 290

JO - ACM Symposium on Solid Modeling and Applications, SM

JF - ACM Symposium on Solid Modeling and Applications, SM

T2 - Ninth ACM Symposium on Solid Modeling and Applications, SM'04

Y2 - 9 June 2005 through 11 June 2005

ER -

Using Cayley-Menger Determinants for geometric constraint solving

Abstract

ASJC Scopus subject areas

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