Geometric Constraint Solving Based on Connectivity of Graph

Zhang, Guifang; Gao, Xiao-Shan

doi:10.1080/16864360.2004.10738289

Cited by 4 publications

(4 citation statements)

References 28 publications

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“…In this paper, we extend the results in [13] to 3D case. The method works as follows, we first decompose a wellconstrained constraint graph into k-connected subgraphs for the smallest possible k. If one of the subgraphs is also wellconstrained, then we can solve the original problem by first solving the subgraphs and then merging these subgraphs.…”

Section: Introductionsupporting

confidence: 56%

“…The method proposed in [4] and the c-tree method [2] can be used to find a decomposition with the smallest controlling problem in certain sense. In [13], a method based on connectivity analysis from graph theory is proposed for solving 2D geometric constraint problems. This method is a natural generalization of the methods in [5,11] which are based on tri-connectivity analysis of the constrained graph, and can solve problems that can be reduced to triangular form.…”

Section: Introductionmentioning

confidence: 99%

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Spatial geometric constraint solving based on k-connected graph decomposition

Zhang

Gao

2006

Proceedings of the 2006 ACM Symposium on Applied Computing

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We propose a geometric constraint solving method based on connectivity analysis in graph theory, which can be used to decompose a well-constrained problem into some smaller ones if possible. We also show how to merge two rigid bodies if they share two or three geometric primitives in a biconnected or tri-connected graph respectively. Based on this analysis, problems similar to the "double banana problem" could be easily detected.

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Section: Introductionsupporting

confidence: 56%

Section: Introductionmentioning

confidence: 99%

Spatial geometric constraint solving based on k-connected graph decomposition

Zhang

Gao

2006

Proceedings of the 2006 ACM Symposium on Applied Computing

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“…So the separating pair or triplet in Gs can not be selected randomly. The reason is shown as Theorem 3.4 and Theorem 3.5 proved in [15]. The maximal number of equations to be solved simultaneously in a constraint problem is called control number.…”

Section: Proof For a Graph G = (V E) It Is Known That κ(G) ≤ 2|e|mentioning

confidence: 96%

Well-constrained completion for under-constrained geometric constraint problem based on connectivity analysis of graph

Zhang

2011

Proceedings of the 2011 ACM Symposium on Applied Computing

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This paper presents a method based on connectivity analysis of graph to solve structurally under-constrained constraint problems frequently occurred during design process in parametric CAD. We give a partial solution to the optimal wellconstrained completion problem, that is, adding automatically new constraints to the graph corresponding to an underconstrained geometric constraint problem G in such a way that G is well-constrained and the set of equations needed to be solved simultaneously in order to solve G has the smallest size. With this method, a connected, bi-connected, or tri-connected structurally under-constrained problem in 2D can be transformed into a structurally well-constrained one by adding new constraints automatically during the process of decomposing it into a decomposition tree.

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“…Fudos and Hoffmann (Fudos & Hoffmann, 1997) presented a similar decomposition method that combined bottom-up techniques to handle over-and under-constrained problems. Zhang and Gao (Zhang & Gao, 2004) proposed a method to decompose a GCS into a d-tree in a top- Generally, the top-down decomposition can better decompose the under-constrained GCS, because the under-constrained GCS only has more articulation pairs. However, the top-down decomposition can hardly handle over-constrained GCSs.…”

Section: Top-down Decompositionmentioning

confidence: 99%

A review on geometric constraint solving

Tang¹,

Qiang²,

Feng³

et al. 2022

Preprint

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This paper presents a comprehensive review of geometric constraint solving in parametric computer-aided design (CAD), with the major focus on its advances in the last 15 years. Geometric constraint solving can date back to the very first CAD prototype, Sketchpad, in the 1960s, but serious research studies were carried out only after parametric CAD was introduced in the late 1980s. In the following 30-year history of GCS research, two development stages may be identified: (1) the first 15 years (late 1980s -mid 2000s) were primarily devoted to geometric constraint decomposition for well-constrained systems or those with only structural constraint dependencies; and (2) the second 15 years (late 2000s -now) have seen research efforts shifted towards classification criteria and decomposition algorithms for general constraint systems (with and without non-structural constraint dependencies). Most existing reviews focused on the first 15 years. The problem researched in the second 15 years is, however, equally important, considering that a manually specified constraint system usually contains under-and over-constrained parts, and that such parts must be correctly detected and resolved before numerical solving can work. In this regard, this review paper covers both stages and will discusses what has already been made possible for handling general constraint systems, what developments can be expected in the near future, and which areas remain problematic.

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Geometric Constraint Solving Based on Connectivity of Graph

Cited by 4 publications

References 28 publications

Spatial geometric constraint solving based on k-connected graph decomposition

Spatial geometric constraint solving based on k-connected graph decomposition

Well-constrained completion for under-constrained geometric constraint problem based on connectivity analysis of graph

A review on geometric constraint solving

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