Algebra-Geometric and Differential Geometric Methods in Solid Geometric Modeling

摘要

This research seeks to address problems in geometric modeling that requiresophisticated and powerful techniques from two traditional mathematical disciplines: differential geometry and algebraic geometry. It also concerns the search for algorithms to effectively implement theoretical results in these disciplines. Geometric Modeling, Splines/Finite Elements, Rational Surfaces, Resultants, Grobner Basis, Wavelets, Generalized Characteristic Polynomial, Computational Algebraic Geometry.