Geometric constraint solving: The witness configuration method

Dominique Michelucci, Sebti Foufou

Research output: Contribution to journalArticle

Abstract

Geometric constraint solving is a key issue in CAD, CAM and PLM. The systems of geometric constraints are today studied and decomposed with graph-based methods, before their numerical resolution. However, graph-based methods can detect only the simplest (called structural) dependences between constraints; they cannot detect subtle dependences due to theorems. To overcome these limitations, this paper proposes a new method: the system is studied (with linear algebra tools) at a witness configuration, which is intuitively similar to the unknown one, and easy to compute.

Original languageEnglish (US)
Pages (from-to)284-299
Number of pages16
JournalCAD Computer Aided Design
Volume38
Issue number4
DOIs
StatePublished - Apr 1 2006

Fingerprint

Linear algebra
Computer aided manufacturing
Computer aided design
Computer systems

Keywords

  • Constraints dependences
  • Decomposition and solving
  • Geometric constraints
  • Rigidity theory
  • The numerical probabilistic method

ASJC Scopus subject areas

  • Computer Science Applications
  • Computer Graphics and Computer-Aided Design
  • Industrial and Manufacturing Engineering

Cite this

Geometric constraint solving : The witness configuration method. / Michelucci, Dominique; Foufou, Sebti.

In: CAD Computer Aided Design, Vol. 38, No. 4, 01.04.2006, p. 284-299.

Research output: Contribution to journalArticle

@article{dd015db2fe7242de91e4c0f0c3960ca6,
title = "Geometric constraint solving: The witness configuration method",
abstract = "Geometric constraint solving is a key issue in CAD, CAM and PLM. The systems of geometric constraints are today studied and decomposed with graph-based methods, before their numerical resolution. However, graph-based methods can detect only the simplest (called structural) dependences between constraints; they cannot detect subtle dependences due to theorems. To overcome these limitations, this paper proposes a new method: the system is studied (with linear algebra tools) at a witness configuration, which is intuitively similar to the unknown one, and easy to compute.",
keywords = "Constraints dependences, Decomposition and solving, Geometric constraints, Rigidity theory, The numerical probabilistic method",
author = "Dominique Michelucci and Sebti Foufou",
year = "2006",
month = "4",
day = "1",
doi = "10.1016/j.cad.2006.01.005",
language = "English (US)",
volume = "38",
pages = "284--299",
journal = "CAD Computer Aided Design",
issn = "0010-4485",
publisher = "Elsevier Limited",
number = "4",

}

TY - JOUR

T1 - Geometric constraint solving

T2 - The witness configuration method

AU - Michelucci, Dominique

AU - Foufou, Sebti

PY - 2006/4/1

Y1 - 2006/4/1

N2 - Geometric constraint solving is a key issue in CAD, CAM and PLM. The systems of geometric constraints are today studied and decomposed with graph-based methods, before their numerical resolution. However, graph-based methods can detect only the simplest (called structural) dependences between constraints; they cannot detect subtle dependences due to theorems. To overcome these limitations, this paper proposes a new method: the system is studied (with linear algebra tools) at a witness configuration, which is intuitively similar to the unknown one, and easy to compute.

AB - Geometric constraint solving is a key issue in CAD, CAM and PLM. The systems of geometric constraints are today studied and decomposed with graph-based methods, before their numerical resolution. However, graph-based methods can detect only the simplest (called structural) dependences between constraints; they cannot detect subtle dependences due to theorems. To overcome these limitations, this paper proposes a new method: the system is studied (with linear algebra tools) at a witness configuration, which is intuitively similar to the unknown one, and easy to compute.

KW - Constraints dependences

KW - Decomposition and solving

KW - Geometric constraints

KW - Rigidity theory

KW - The numerical probabilistic method

UR - http://www.scopus.com/inward/record.url?scp=33645868296&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33645868296&partnerID=8YFLogxK

U2 - 10.1016/j.cad.2006.01.005

DO - 10.1016/j.cad.2006.01.005

M3 - Article

VL - 38

SP - 284

EP - 299

JO - CAD Computer Aided Design

JF - CAD Computer Aided Design

SN - 0010-4485

IS - 4

ER -