Declarative modelling and transformation of a constrained geometric object

Moinet, Mireille; Serré, Philippe

doi:10.1504/ijpd.2011.042028

Cited by 2 publications

(6 citation statements)

References 14 publications

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“…The first two types of equations were already discussed in a previous paper of Moinet and Serré (2011). Thus, Section 4.1 and 4.2 recall the significant results.…”

Section: Establishing the Equations Of The Problemmentioning

confidence: 86%

“…In this section, we are not going to attempt to describe in detail the method used to solve the equations. Previously, this study was carried out by Moinet and Serré (2011) for a different set of equations but well adapted to the new problem presented in this paper.…”

Section: Geometric Problem Solvingmentioning

confidence: 99%

“…This research uses the variational model already presented by Serré (2000) and Moinet and Serré (2011). This model allows describing 2D geometric objects using the point and the straight line as basic geometric entities.…”

Section: Introductionmentioning

confidence: 99%

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Geometric transformation of a constrained object using a non-Cartesian method

Moinet¹,

Serré²

2014

IJPD

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This paper presents a new approach to transform a constrained geometric object. The geometric model is based on the vectorisation of the object's shape. Thus, elementary geometric entities and constraints are represented by a set of vectors or bivectors in order to establish the object specifications. The metric tensor is the mathematical tool used to define the vector space generated by the set of vectors and bivectors. The transformation of the initial object is realised thanks to a transformation matrix associated with a connection matrix. Based on the point of displacements of the initial object, this new method gives the final object satisfying the geometric specifications required by the designer.

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“…The first two types of equations were already discussed in a previous paper of Moinet and Serré (2011). Thus, Section 4.1 and 4.2 recall the significant results.…”

Section: Establishing the Equations Of The Problemmentioning

confidence: 86%

Section: Geometric Problem Solvingmentioning

confidence: 99%

See 1 more Smart Citation

Geometric transformation of a constrained object using a non-Cartesian method

Moinet¹,

Serré²

2014

IJPD

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“…Here we itemize only two types of specifications (useful as examples) but many other specifications have been developed by the authors. The reader may refer to [5] and [11] for more details.…”

Section: The Specificationsmentioning

confidence: 99%

“…In this section, we do not attempt to describe in detail the method used to solve the equations for the isoconstrained problem. This study was carried out by Moinet in [11] for a different set of equations but it remains well-adapted to the problem presented in this paper. The geometrical solver developed with Matlab R computes the X perturbation matrix of equation (14) in order to obtain an object that conforms to the specifications given by the designers.…”

Section: Geometric Problem Solvingmentioning

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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Declarative modelling and transformation of a constrained geometric object

Cited by 2 publications

References 14 publications

Geometric transformation of a constrained object using a non-Cartesian method

Geometric transformation of a constrained object using a non-Cartesian method

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

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