Team : APR
Departure date : 06/30/2012
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.
Defence : 05/03/2012 - 09h30 - UNiVERSITE BEIHANG (BEIJING, CHINE) Jury members : Thomas STURM [Rapporteur]
Bican XIA [Rapporteur]