Transforming an under-constrained geometric constraint problem into a well-constrained one

Joan-Arinyo, Robert; Soto-Riera, Antoni; Vila-Marta, Sebastià; Vilaplana, Josep

doi:10.1145/781606.781616

Cited by 25 publications

(27 citation statements)

References 18 publications

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“…Latham et al presented a method to detect whether the constraint graph is structurally under-constrained and decide how to add constraints if the graph is structurally under-constrained [23]. Joan-Arinyo et al also proposed a algorithm used to get a well-constrained problem from a under-constrained problem [17]. But the type of the constraints added to G s should be based on the shape of the split graph G 1 assuming that G 1 is a rigid while G 2 is not.…”

Section: Corollary 36 a Structurally Well-constrained Bi-connected Cmentioning

confidence: 99%

Geometric Constraint Solving Based on Connectivity of Graph

Zhang¹,

Gao²

2004

Computer-Aided Design and Applications

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Section: Corollary 36 a Structurally Well-constrained Bi-connected Cmentioning

confidence: 99%

Geometric Constraint Solving Based on Connectivity of Graph

Zhang¹,

Gao²

2004

Computer-Aided Design and Applications

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“…Solving Eq. (19) with this Δv will give the intended geometry change. Also, as Δv(C) has the unit magnitude, the solved Δ# gives directly the change rate for the C-th constraint.…”

Section: General Angle Between Directionsmentioning

confidence: 99%

“…The second equality is due to Eq. (19). In the equation, Δv M denotes the vector: Δv(C) = 1 and Δv(¢ ≠ C) = 0.…”

Section: General Angle Between Directionsmentioning

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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“…In fact, a restricted OC problem was studied by [18] requiring the completion to be tree-decomposable. We now connect the OMD problem to the informal optimal recombination (OR) problem mentioned as motivation at the beginning of Section 4.…”

Section: Optimal Modification Completion and Recombination: Previousmentioning

confidence: 99%

Optimal decomposition and recombination of isostatic geometric constraint systems for designing layered materials

Baker

Sitharam

Wang

et al. 2015

Computer Aided Geometric Design

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Optimal recursive decomposition (or DR-planning) is crucial for analyzing, designing, solving or finding realizations of geometric constraint sytems. While the optimal DR-planning problem is NP-hard even for general 2D bar-joint constraint systems, we describe an O(n 3 ) algorithm for a broad class of constraint systems that are isostatic or underconstrained. The algorithm achieves optimality by using the new notion of a canonical DR-plan that also meets various desirable, previously studied criteria. In addition, we leverage recent results on Cayley configuration spaces to show that the indecomposable systems-that are solved at the nodes of the optimal DR-plan by recombining solutions to child systems-can be minimally modified to become decomposable and have a small DR-plan, leading to efficient realization algorithms. We show formal connections to well-known problems such as completion of underconstrained systems. Well suited to these methods are classes of constraint systems that can be used to efficiently model, design and analyze quasi-uniform (aperiodic) and self-similar, layered material structures. We formally illustrate by modeling silica bilayers as body-hyperpin systems and cross-linking microfibrils as pinned line-incidence systems. A software implementation of our algorithms and videos demonstrating the software are publicly available online 1 .

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Transforming an under-constrained geometric constraint problem into a well-constrained one

Cited by 25 publications

References 18 publications

Geometric Constraint Solving Based on Connectivity of Graph

Geometric Constraint Solving Based on Connectivity of Graph

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

Optimal decomposition and recombination of isostatic geometric constraint systems for designing layered materials

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