Geometric constraint solving: The witness configuration method

Michelucci, Dominique; Foufou, Sebti

doi:10.1016/j.cad.2006.01.005

Cited by 29 publications

(21 citation statements)

References 32 publications

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“…In the geometric constraint solving area, the early attempt may be made by [19][20][21]. They are graph-based and cannot handle models having constraint dependencies (except for the simplest structural dependencies) [16], making them inapplicable to this work. Due to this limitation, recent studies have shifted to the witness configuration method [14,15].…”

Section: Related Workmentioning

confidence: 99%

A decision-support method for information inconsistency resolution in direct modeling of CAD models

Zou

Feng

2020

Advanced Engineering Informatics

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Direct modeling is a very recent CAD paradigm that can provide unprecedented modeling flexibility. It, however, lacks the parametric capability, which is indispensable to modern CAD systems. For direct modeling to have this capability, an additional associativity information layer in the form of geometric constraint systems needs to be incorporated into direct modeling. This is no trivial matter due to the possible inconsistencies between the associativity information and geometry information in a model after direct edits. The major issue of resolving such inconsistencies is that there often exist many resolution options. The challenge lies in avoiding invalid resolution options and prioritizing valid ones. This paper presents an effective method to support the user in making decisions among the resolution options. In particular, the method can provide automatic information inconsistency reasoning, avoid invalid resolution options completely, and guide the choice among valid resolution options. Case studies and comparisons have been conducted to demonstrate the effectiveness of the method.

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Section: Related Workmentioning

confidence: 99%

A decision-support method for information inconsistency resolution in direct modeling of CAD models

Zou

Feng

2020

Advanced Engineering Informatics

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“…A solution straightforwardly follows: compute a "witness configuration" and study it with the NPM; a witness configuration [Foufou et al 2005;Michelucci and Foufou 2006] does not satisfy the metric constraints (i.e. it has typically lengths or angles different of the searched configuration), but it fulfils the specified projective constraints (see Fig.…”

Section: The Witness Configuration Principlementioning

confidence: 99%

Geometric constraints solving

Michelucci

Foufou

Lamarque

et al. 2006

Proceedings of the 2006 ACM Symposium on Solid and Physical Modeling

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This paper presents some important issues and potential research tracks for Geometric Constraint Solving: the use of the simplicial Bernstein base to reduce the wrapping effect in interval methods, the computation of the dimension of the solution set with methods used to measure the dimension of fractals, the pitfalls of graph based decomposition methods, the alternative provided by linear algebra, the witness configuration method, the use of randomized provers to detect dependences between constraints, the study of incidence constraints, the search for intrinsic (coordinate-free) formulations and the need for formal specifications.

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“…Here, we only focus on the overconstrained problem and propose using the witness method of Michelucci et al [12,13,14] to perform the problem analysis. The first part of this section will briefly introduce Michelucci's witness method.…”

Section: The Problem Analysismentioning

confidence: 99%

Defining tools to address over-constrained geometric problems in Computer Aided Design

Moinet¹,

Mandil²,

Serré³

2014

Computer-Aided Design

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To cite this version:Moinet Mireille, Guillaume Mandil, Philippe Serré. Defining tools to address over-constrained geometric problems. Computer-Aided Design, Elsevier, 2014, 48, pp. AbstractThis paper proposes a new tool for decision support to address geometric over-constrained problems in Computer Aided Design (CAD). It concerns the declarative modelling of geometrical problems. The core of the coordinate free solver used to solve the Geometric Constraint Satisfaction Problem (GCSP) was developed previously by the authors. This research proposes a methodology based on Michelucci's witness method to determine whether the structure of the problem is over-constrained. In this case, the authors propose a tool for assisting the designer in solving the over-constrained problem by ensuring the consistency of the specifications. An application of the methodology and tool is presented in an academic example.

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Geometric constraint solving: The witness configuration method

Cited by 29 publications

References 32 publications

A decision-support method for information inconsistency resolution in direct modeling of CAD models

A decision-support method for information inconsistency resolution in direct modeling of CAD models

Geometric constraints solving

Defining tools to address over-constrained geometric problems in Computer Aided Design

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