Speaker: Xiao-Ran Shi
Beijing Computational Science Research Center

Abstract: The μ-bases of rational curves/surfaces are newly developed tools which play an important role in connecting parametric forms and implicit forms of rational curves/surfaces. They provide efficient algorithms to implicitize rational curves/surfaces as well as algorithms to compute singularities of rational planar curves/ruled surfaces.

 In this talk, I will show more applications of μ-bases in rational space curves and surfaces of revolution. For rational curves, we apply μ-bases to compute the singularities of rational spaces curves, and based on a new constructing bihomogeneous resultant matrix to analyze the multiplicities of all singular points. For rational surfaces, we construct a μ-basis for surface of revolution, and a Sylvester-type matrix whose determinant gives the implicit equation of surface of revolution. And we extend the result to more general surfaces which has a pair of orthogonal directrices.

Date&Time: August 3, 2012  14:30 - 15:30
Location: 606 Conference Room