2010
DOI: 10.1016/j.cad.2009.03.003
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A non-rigid cluster rewriting approach to solve systems of 3D geometric constraints

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Cited by 12 publications
(6 citation statements)
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References 24 publications
(32 reference statements)
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“…These techniques are a subset of graph-based synthetic methods [12], [34], [37] in which the constraint graph is decomposed and recombined to extract construction steps that are then solved by algebraic methods [3], [13], [39]. Notable improvements include Sitharam's frontier algorithm [21], [22], which generalizes the graph decomposition, treatment for over-and under-constrained problems [23], [29], [32], [40], [42], and parameter ranges for dimensional constraints [26], [30], [31], [38], [41]. Despite the success of these methods for CAD applications, these constructive approaches generally do not translate to complex geometric configurations in theorem proving.…”
Section: B Geometric Constraint Problemmentioning
confidence: 99%
“…These techniques are a subset of graph-based synthetic methods [12], [34], [37] in which the constraint graph is decomposed and recombined to extract construction steps that are then solved by algebraic methods [3], [13], [39]. Notable improvements include Sitharam's frontier algorithm [21], [22], which generalizes the graph decomposition, treatment for over-and under-constrained problems [23], [29], [32], [40], [42], and parameter ranges for dimensional constraints [26], [30], [31], [38], [41]. Despite the success of these methods for CAD applications, these constructive approaches generally do not translate to complex geometric configurations in theorem proving.…”
Section: B Geometric Constraint Problemmentioning
confidence: 99%
“…3.1. We randomly project the node positions into 2D, and then use the geometric constraint solver proposed by van der Meiden and Bronsvoort [51] (Fig. 4.3) to resolve any geometric constraints.…”
Section: Geometric Reasoning and Constraint Satisfactionmentioning
confidence: 99%
“…(2) Traverse the graph, adding candidate angle constraints between a node and two of its neighbors (for all permutations of neighbors). (3) Evaluate candidates using either a solver [51] or the loop mobility criterion (Sec. 4.4) [2] to determine if the added constraint will determine the system.…”
Section: Geometric Reasoning and Constraint Satisfactionmentioning
confidence: 99%
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