Supervision : Dongming WANG

Co-supervision : AUBRY Philippe

Dynamic Geometry and geometric Constrain Solving

This thesis focuses on the design and implementation of efficient algorithms and software tools for solving parametric geometric constraints involving both equalities and inequalities, with application to automated generation of dynamic diagrams. It introduces a real convention for cubic and quartic polynomial equations that leads to a main advance on Lagrange's formula, under the form of real solution formulas for generic cubic and quartic polynomial equations with constraints. These results are applied to improve an existing approach in terms of stability of numeric computation and quality of generated diagrams. Finally a software package developed with Java, Maple and QEPCAD for automated generation of dynamic diagrams with inequality constraints is presented.

2011-2012 Publications

• 2012
  • T. Zhao : “Résolution de systèmes polynomiaux paramétriques par radicaux et ses applicationsgéométriques”, thesis, phd defence 05/03/2012, supervision Wang, Dongming, co-supervision : Aubry, Philippe (2012)
  • X. Chen, D. Wang, T. Zhao : “GeoText: An Intelligent Dynamic Geometry Textbook (Extended Abstract)”, ACM Communications in Computer Algebra, vol. 46 (4), pp. 171-175, (Association for Computing Machinery (ACM)) (2012)
  • T. Zhao, D. Wang, H. Hong, Ph. Aubry : “Real Solution Formulas of Cubic and Quartic Equations Applied to Generate Dynamic Diagrams with Inequality Constraints”, 27^th Annual ACM Symposium on Applied Computing (SAC 2012), Trento, Italy, pp. 94-101 (2012)
• 2011
  • T. Zhao, D. Wang, H. Hong : “Solution Formulas for Cubic Equations Without or With Constraints”, Journal of Symbolic Computation, vol. 46 (8), pp. 904-918, (Elsevier) (2011)