Spline spaces on topological manifold
摘要：In CAGD, a standard representation of shapes is by parameterized surfaces or volumes based on tensor product B-spline functions, which with a given regularity and degree. Recently, the problem of are the basis of the space of piecewise polynomial functions on a grid representing functions on shapes has also been considered in the geometry and the physical solution of a simulation problem on this isogeometric analysis, using the same basis functions to describe both geometry. In this talk, we will consider spline functions over topological these spline spaces, in particular to analyse their dimension and to manifolds with arbitrary topology. We describe algebraic-geometric techniques which can be used advantageously to get a better insight on construct basis. Examples including splines over triangular meshes or T-meshes, in dimension 2 and 3 will be detailed. 简历：法国国家信息与自动化研究所Bernard MOURRAIN教授长期从事在几何造型、计算机辅助几何、计算符号代数等方向的研究。计算数学领域Journal of Symbolic Computation、SIAM Journal on Applied Algebra and Geometry编委成员、计算几何领Theoretical Computer Science, Computer Aided Geometric Design等受邀编辑。多个计算几何领域国际核心期刊，如Applicable Algebra in Engineering Communication and Computing, Discrete Applied Mathematics, Theoretical Computer Science, Computer Aided Geometric Design, Computer Aided Design, Math. Of Comp, Math, Review, CRAS的评审人以及ISSAC、Geometric Modeling and Processing、Symposium on Solid and Physical Modeling, Symbolic-Numeric Computation, MEGA, ACA, ADG, ACSM等计算几何与符号计算国际会议Program chair, program co-chair以及Member of program committees.