The correspondence between multivariate spline ideals and piecewise algebraic varieties

[摘要] As a piecewise polynomial with a certain smoothness, the spline plays an important role in computational geometry. The algebraic variety is the most important subject in classical algebraic geometry. As the zero set of multivariate splines, the piecewise algebraic variety is a generalization of the algebraic variety. In this paper, the correspondence between piecewise algebraic varieties and spline ideals is discussed. Furthermore, Hilbert's Nullstellensatz for the piecewise algebraic variety is also studied. (C) 2011 Elsevier B.V. All rights reserved.

[发布日期] 2011-10-01

[效力级别]  Proceedings Paper

[关键词] Piecewise algebraic varieties;Algebraic varieties;Multivariate splines;Ideals