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 Bezoutʹs theorem and Nöther-type theorem of piecewise algebraic curves, the Cayley–Bacharach theorem and Hilbert function of C0 piecewise algebraic curves are presented.