Properties of Dimension of Piecewise Algebraic Varieties

摘要

An important subject in computational geometry is the interpolation of scattered data by multivariate splines. It is necessary to study the piecewise algebraic variety in order to solve the multivariate spline interpolation. The piecewise algebraic variety, as a set of the common zeros of multivariate splines, is a kind of generalization of the classical algebraic variety. In this paper, we discuss several elementary properties of dimension of piecewise algebraic varieties. Meanwhile, we study the relationship between the dimension of a piecewise algebraic variety and the number of its defining multivariate splines.