Geometric constraints solving

Michelucci, Dominique; Foufou, Sebti; Lamarque, Loïc; Schreck, Pascal

doi:10.1145/1128888.1128915

Cited by 12 publications

(6 citation statements)

References 36 publications

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“…The witness (U W , X W ) is not the solution but shares the same combinatorial features with the target (U T , X T ) , even if the witness configuration and the target configuration lie on two distinct connected components of the solution set. Therefore, analyzing a witness configuration enables to detect numerical over-constraints of a system [42,43]. These numerical over-constraints can be not only structural overconstraints but also geometric redundancies.…”

Section: R E V I S Ementioning

confidence: 99%

Geometric Over-Constraints Detection: A Survey

Hu¹,

Zhang²,

Huang³

et al. 2021

Arch Computat Methods Eng

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Currently, geometric over-constraints detection is of major interest in several different fields. In terms of product development process (PDP), many approaches exist to compare and detect geometric over-constraints, to decompose geometric systems, to solve geometric constraints systems. However, most approaches do not take into account the key characteristics of a geometric system, such as types of geometries, different levels at which a system can be decomposed e.g numerical or structural. For these reasons, geometric over-constraints detection still faces challenges to fully satisfy real needs of engineers. The aim of this paper is to review the state-of-the-art of works involving with geometric over-constraints detection and to identify possible research directions. Firstly, the paper highlights the user requirements for over-constraints detection when modeling geometric constraints systems in PDP and proposes a set of criteria to analyze the available methods classified into four categories: level of detecting over-constraints, system decomposition, system modeling and results generation. Secondly, it introduces and analyzes the available methods by grouping them based on the introduced criteria. Finally, it discusses possible directions and future challenges.

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Section: R E V I S Ementioning

confidence: 99%

Geometric Over-Constraints Detection: A Survey

Hu¹,

Zhang²,

Huang³

et al. 2021

Arch Computat Methods Eng

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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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“…In other words, two coplanar lines always meet. This simple framework remains powerful enough to study the formalization and proof of complex problems such as those suggested in [26]. In addition, there is no loss of generality since it is possible to switch from projective geometry to affine geometry by adding a chosen line at infinity.…”

Section: Introductionmentioning

confidence: 99%

Two cryptomorphic formalizations of projective incidence geometry

Braun

Magaud

Schreck

2018

Ann Math Artif Intell

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Incidence geometry is a well-established theory which captures the very basic properties of all geometries in terms of points belonging to lines, planes, etc. Moreover, projective incidence geometry leads to a simple framework where many properties can be studied. In this article, we consider two very different but complementary mathematical approaches formalizing this theory within the Coq proof assistant. The first one consists of the usual and synthetic geometric axiom system often encountered in the literature. The second one is more original and relies on combinatorial aspects through the notion of rank which is based on the matroid structure of incidence geometry. This paper mainly contributes to the field by proving the equivalence between these two approaches in both 2D and 3D. This result allows us to study the further automation of many proofs of projective geometry theorems. We give an overview of techniques that will be heavily used in the equivalence proof and are generic enough to be reused later in yet-to-bewritten proofs. Finally, we discuss the possibilities of future automation that can be envisaged using the rank notion.

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Geometric constraints solving

Cited by 12 publications

References 36 publications

Geometric Over-Constraints Detection: A Survey

Geometric Over-Constraints Detection: A Survey

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

Two cryptomorphic formalizations of projective incidence geometry

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