A constraint-based dynamic geometry system

Dynamic geometry systems are tools for geometric visualization. They allow the user to define geometric elements, establish relationships between them and explore the dynamic behavior of the remaining geometric elements when one of them is moved. The main problem in dynamic geometry systems is the ambiguity that arises from operations which lead to more than one possible solution. Most dynamic geometry systems deal with this problem in such a way that the solution selection method leads to a fixed dynamic behavior of the system. This is specially annoying when the behavior observed is not the one the user intended. In this work we propose a modular architecture for dynamic geometry systems built upon a set of functional units which will allow to apply some well known results from the Geometric Constraint Solving field. A functional unit called filter will provide the user with tools to unambiguously capture the expected dynamic behavior of a given geometric problem.

[1]  John Beidler,et al.  Data Structures and Algorithms , 1996, Wiley Encyclopedia of Computer Science and Engineering.

[2]  Robert Joan-Arinyo,et al.  A correct rule-based geometric constraint solver , 1997, Comput. Graph..

[3]  B. Aldefeld Variation of geometrics based on a geometric-reasoning method , 1988 .

[4]  Alfred V. Aho,et al.  Data Structures and Algorithms , 1983 .

[5]  Harald Winroth,et al.  Dynamic projective geometry , 1999 .

[6]  Caroline Essert,et al.  Sketch-based pruning of a solution space within a formal geometric constraint solver , 2000, Artif. Intell..

[7]  Gilles Trombettoni,et al.  Decomposition of Geometric Constraint Systems: a Survey , 2006, Int. J. Comput. Geom. Appl..

[8]  Sebastià Vila-Marta,et al.  On the domain of constructive geometric constraint solving techniques , 2001, Proceedings Spring Conference on Computer Graphics.

[9]  Christoph M. Hoffmann,et al.  Symbolic Constraints in Constructive Geometric Constraint Solving , 1997, J. Symb. Comput..

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

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

[12]  M. Victoria Luzón,et al.  Genetic algorithms for root multiselection in constructive geometric constraint solving , 2003, Comput. Graph..

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

[14]  Denis Bouhineau Vers une approche déclarative pour les logiciels de dessins géométriques , 1995 .

[15]  Christoph M. Hoffmann,et al.  Correctness proof of a geometric constraint solver , 1996, Int. J. Comput. Geom. Appl..

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

[17]  Laurent Trilling,et al.  Constraint Based Automatic Construction and Manipulation of Geometric Figures , 1993, IJCAI.

[18]  Robert Joan-Arinyo,et al.  Combining constructive and equational geometric constraint-solving techniques , 1999, TOGS.

[19]  Nicholas Jackiw,et al.  The Geometer’s Sketchpad , 2008 .

[20]  Christoph M. Hoffmann,et al.  Geometric constraint solver , 1995, Comput. Aided Des..

[21]  Greg Nelson,et al.  Juno, a constraint-based graphics system , 1985, SIGGRAPH.

[22]  Denis Bouhineau,et al.  La programmation loique par contraintes pour l'aide à l'enseignant , 1996, Intelligent Tutoring Systems.

[23]  Ulrich Kortenkamp Foundations of dynamic geometry , 2000 .