Formal resolution of geometrical constraint systems by assembling

Dufourd, Jean-François; Mathis, Pascal; Schreck, Pascal

doi:10.1145/267734.267804

Cited by 16 publications

(12 citation statements)

References 18 publications

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“…. y n−1 ), where h i are multi-valued functions for computing the intersection between two cercles, or between a line and a cercle, etc; dynamic geometry softwares [Bellemain 1992;Kortenkamp 1999;Dufourd et al 1997;Dufourd et al 1998] have popularized this last approach, which unfortunately does not scale well in 3D.…”

Section: Solving With a Continuum Of Solutionsmentioning

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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Section: Solving With a Continuum Of Solutionsmentioning

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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“…Then, widely used in the industry, we find the numerical approaches [16,14,18]. Finally, the family of the geometrical approaches includes methods related to rule-based systems [1,22,3,5,13] or graph analysis [19,15,9,10,25]. In this paper, we describe a new method Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page.…”

Section: Introductionmentioning

confidence: 99%

Decomposition of geometrical constraint systems with reparameterization

Mathis

Schreck

Imbach

2012

Proceedings of the 27th Annual ACM Symposium on Applied Computing

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Decomposition of constraint systems is a key component of geometric constraint solving in CAD. On the other hand, some authors have introduced the notion of reparameterization which aims at helping the solving of indecomposable systems by replacing some geometric constraints by other ones. In previous works, the minimal change of the initial system is a main criterion. We propose to marry these two ingredients, decomposition and reparameterization, in a method able to reparameterize and to decompose a constraint system according to this reparameterization. As a result, we do not aim at minimizing the number of added constraints during the reparameterization, but we want to decompose the system such that each component owns a minimal number of such added constraints.

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“…With regard to the shape of the objects, we have limited ourselves to simple linear embeddings. More complex embeddings could be treated in the same formal frame using for instance geometric construction plans as in [14,15,18]. In this way, we could build a unified framework for describing and manipulating geometric objects at the formal, graphical or interpretative level.…”

Section: Introductionmentioning

confidence: 99%

Parametrizing geometric objects using λ-calculus

Dufourd¹,

Luther²

2002

Proceedings of the 18th Spring Conference on Computer Graphics

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This paper focuses on the general parameterization in geometric modeling. We have adapted the -calculus formalism to an existing geometrical model which has an applicative representation: the generalized maps embedded in the plane. We investigated how this allows us to parameterize geometric objects by other objects, which can themselves be functional, rather than just by values such as size, shape or position. Thus, conditional, iterative, recursive and shared objects can be built and managed in an homogenous way. We have based the study on an interactive prototype implemented in Objective Caml. Its interface offers two consistent working views. The first interacts with geometric objects while the second interacts with the corresponding programs. We have examined in detail various higher-order operations where -calculus abstraction and application are used extensively to demonstrate how such objects can be built and manipulated. We will illustrate the force of our proposals using more complex constructions.

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Formal resolution of geometrical constraint systems by assembling

Cited by 16 publications

References 18 publications

Geometric constraints solving

Geometric constraints solving

Decomposition of geometrical constraint systems with reparameterization

Parametrizing geometric objects using λ-calculus

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