ZHAO Ting
责任导师 : Dongming WANG
助理责任导师 : 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.
答辩 : 2012-5-3
评委会 :
Thomas STURM [Rapporteur]
Bican XIA [Rapporteur]
She ZHIKUN
Philippe AUBRY
Annick VALIBOUZE
Dongming WANG
Liu TIEGANG
Lihong ZHI
2011-2012 刊物
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2012
- T. Zhao : “Résolution de systèmes polynomiaux paramétriques par radicaux et ses applicationsgéométriques”, 博士论文, 答辩 2012-5-3, 责任导师 Wang, Dongming, 助理责任导师 : 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”, 27th Annual ACM Symposium on Applied Computing (SAC 2012), Trento, Italy, pp. 94-101 (2012)
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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)