Cayley–Bacharach theorem of piecewise algebraic curves

The piecewise algebraic curve, determined by a bivariate spline function, is a generalization of the classical algebraic curve. In this paper, by using Bezout's theorem and No¨ther-type theorem of piecewise algebraic curves, the Cayley–Bacharach theorem and Hilbert function of <f>C0</f> piecewise algebraic curves are presented. [Copyright &y& Elsevier]