h-graphs: A new representation for tree decompositions of graphs

Hidalgo, Marta R.; Joan-Arinyo, Robert

doi:10.1016/j.cad.2015.05.003

Cited by 3 publications

(2 citation statements)

References 23 publications

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“…Hidalgo and Joan-Arinyo Joan-Arinyo, 2012, 2014) formalized the constructive method (Van der Meiden and Bronsvoort, 2005), proved its correctness in single-parameter editing problem, and presented an implementation of this method. Considering that the constructive method (Van der Meiden and Bronsvoort, 2005) relies heavily on searching the construction steps related to the variable parameter, Hidalgo and Joan-Arinyo (Hidalgo and Joan-Arinyo, 2015) further introduced h-graphs as a representation for graph tree decomposition to improve the efficiency for capturing the dependencies between the construction steps of a geometric constraint problem.…”

Section: Problem For Solvable Modelsmentioning

confidence: 99%

“…Thus, researchers are seeking a more efficient way to calculate parameter ranges. Existing methods (Joan-Arinyo and Mata, 2001;Sitharam, Wang, and Gao, 2011a,b;Sitharam and Wang, 2014; Van der Meiden and Bronsvoort, 2005;Hidalgo and Joan-Arinyo, 2012, 2015 can compute allowable ranges of individual parameters in specific geometric constraint systems. However, when applied to the multi-parameter editing, the methods could omit certain feasible parameter values, which will result in incomplete parameter ranges.…”

Section: Introductionmentioning

confidence: 99%

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Towards computing complete parameter ranges in parametric modeling

Tang¹,

Qiang²,

Gao³

2022

Preprint

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In parametric design, the geometric model is edited by changing relevant parameters in the parametric model, which is commonly done sequentially on multiple parameters. Without guidance on allowable parameter ranges that can guarantee the solvability of the geometric constraint system, the user could assign improper parameter values to the model's parameters, which would further lead to a failure in model updating. However, current commercial CAD systems provide little support for the proper parameter assignments. Although the existing methods can compute allowable ranges for individual parameters, they face difficulties in handling multi-parameter situations. In particular, these methods could miss some feasible parameter values and provide incomplete allowable parameter ranges. To solve this problem, an automatic approach is proposed in this paper to compute complete parameter ranges in multi-parameter editing. In the approach, a set of variable parameters are first selected to be sequentially edited by the user; before each editing operation, the one-dimensional ranges of the variable parameters are presented as guidance. To compute the one-dimensional ranges, each variable parameter is expressed as an equality-constrained function, and its one-dimensional allowable range is obtained by calculating the function range. To effectively obtain the function range which can hardly be calculated in a normal way, the function range problem is converted into a constrained optimization problem, and is then solved by Lagrange multiplier method and the Niching particle swarm optimization algorithm (the NichePSO). The effectiveness and efficiency of the proposed approach is verified by several experimental results.

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Section: Problem For Solvable Modelsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Towards computing complete parameter ranges in parametric modeling

Tang¹,

Qiang²,

Gao³

2022

Preprint

View full text Add to dashboard Cite

show abstract

A decision-support method for multi-parameter editing of parametric CAD models

Tang

Zou

Gao

2023

Advanced Engineering Informatics

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Variational B-rep model analysis for direct modeling using geometric perturbation

Zou

Feng

2019

Journal of Computational Design and Engineering

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The very recent CAD paradigm of direct modeling gives rise to the need of processing 3D geometric constraint systems defined on boundary representation (B-rep) models. The major issue of processing such variational B-rep models (in the STEP format) is that free motions of a well-constrained model involve more than just rigid-body motions. The fundamental difficulty lies in having a systematic description of what pattern these free motions follow. This paper proposes a geometric perturbation method to study these free motions. This method is a generalization of the witness method, allowing it to directly deal with variational B-rep models represented by the STEP format. This generalization is essentially achieved by using a direct, geometric representation of the free motions, and then expressing the free motions in terms of composites of several basis motions. To demonstrate the effectiveness of the proposed method, a series of comparisons and case studies are presented. Highlights A new method to analyze geometric constraint systems for direct modeling. A generalization of the witness configuration method. A new method to characterize the constraint states of variational B-rep models.

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h-graphs: A new representation for tree decompositions of graphs

Cited by 3 publications

References 23 publications

Towards computing complete parameter ranges in parametric modeling

Towards computing complete parameter ranges in parametric modeling

A decision-support method for multi-parameter editing of parametric CAD models

Variational B-rep model analysis for direct modeling using geometric perturbation

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