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