Implementing discrete mathematics: combinatorics and graph theory with Mathematica
Implementing discrete mathematics: combinatorics and graph theory with Mathematica
Algebraic solution for geometry from dimensional constraints
SMA '91 Proceedings of the first ACM symposium on Solid modeling foundations and CAD/CAM applications
Graphs: theory and algorithms
A graph-constructive approach to solving systems of geometric constraints
ACM Transactions on Graphics (TOG)
Computational geometry: algorithms and applications
Computational geometry: algorithms and applications
Algorithm 447: efficient algorithms for graph manipulation
Communications of the ACM
Decomposition plans for geometric constraint systems, part I: performance measures for CAD
Journal of Symbolic Computation
Decomposition plans for geometric constraint problems, part II: new algorithms
Journal of Symbolic Computation
Symbolic and numerical techniques for constraint solving
Symbolic and numerical techniques for constraint solving
A C-tree decomposition algorithm for 2D and 3D geometric constraint solving
Computer-Aided Design
Example-based procedural modelling by geometric constraint solving
Multimedia Tools and Applications
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The graph-based geometric constraint solving technique works in two steps. First the geometric problem is translated into a graph whose vertices represent the set of geometric elements and whose edges are the constraints. Then the constraint problem is solved by decomposing the graph into a collection of subgraphs each representing a standard problem which is solved by a dedicated equational solver. In this work we report on an algorithm to decompose biconnected tree-decomposable graphs representing either under-or wellconstrained 2D geometric constraint problems. The algorithm recursively first computes a set of fundamental circuits in the graph then splits the graph into a set of subgraphs each sharing exactly three vertices with the fundamental circuit. Practical experiments show that the reported algorithm clearly outperforms the treedecomposition approach based on identifying subgraphs by applying specific decomposition rules.