Multivariate spline and algebraic geometry

The purpose of this survey is to emphasize the special relationship between multivariate spline and algebraic geometry. We will not only point out the algebraic–geometric method of multivariate spline, but also the algebraic–geometric background and essence of multivariate spline. Especially, we have made an introduction to the so-called piecewise algebraic curve, piecewise algebraic variety, and some of their properties.