Geometric constraint graphs decomposition based on computing graph circuits

Geometric constraint solving is a growing field which plays a paramount role in industrial applications and that is deeply rooted in automated deduction in geometry. In this work we report on an algorithm to solve geometric constraint-based problems by decomposing biconnected graphs. The algorithm is based on recursively splitting the graph through sets with three vertices located on fundamental circuits of the graph. Preliminary practical experiments suggest that the algorithm runtime is at worst quadratic with the total number of vertices in the graph.

[1]  H. Whitney.  Non-Separable and Planar Graphs. , 1931, Proceedings of the National Academy of Sciences of the United States of America.

[2]  Christoph M. Hoffmann,et al.  A graph-constructive approach to solving systems of geometric constraints , 1997, TOGS.

[3]  J. C. Owen,et al.  Algebraic solution for geometry from dimensional constraints , 1991, SMA '91.

[4]  Robert Joan Arinyo,et al.  Decomposition of geometric constraint graphs based on computing fundamental circuits , 2007 .

[5]  Sebastià Vila-Marta,et al.  Constraint-Based Techniques to Support Collaborative Design , 2006, J. Comput. Inf. Sci. Eng..

[6]  Sebastià Vila-Marta,et al.  Revisiting decomposition analysis of geometric constraint graphs , 2002, SMA '02.

[7]  Sebastià Vila-Marta,et al.  Resolución de Restricciones Geométricas , 2003, Inteligencia Artif..

[8]  Xiao-Shan Gao,et al.  A C-tree decomposition algorithm for 2D and 3D geometric constraint solving , 2006, Comput. Aided Des..

[9]  Shimon Even,et al.  Graph Algorithms , 1979 .

[10]  C. Hoffmann,et al.  A Brief on Constraint Solving , 2005 .

[11]  Christoph M. Hoffmann,et al.  Decomposition Plans for Geometric Constraint Problems, Part II: New Algorithms , 2001, J. Symb. Comput..

[12]  C. Hoffmann,et al.  Symbolic and numerical techniques for constraint solving , 1998 .

[13]  Christoph M. Hoffmann,et al.  Decomposition Plans for Geometric Constraint Systems, Part I: Performance Measures for CAD , 2001, J. Symb. Comput..

[14]  Sebastià Vila-Marta,et al.  Revisiting decomposition analysis of geometric constraint graphs , 2004, Comput. Aided Des..

[15]  M. N. Shanmukha Swamy,et al.  Graphs: Theory and Algorithms , 1992 .