Piecewise algebraic curve (Q1612372)

In the paper context, a piecewise algebraic curve is a bivariate spline function. The subject is the detection of the number of real intersection points of two piecewise algebraic curves whose common points are finite. A lower bound of this number is given in terms of the method of rotation degree of a vector field. In order to prove the correctness of the conclusions, the B-net form of the bivariate spline function, the discriminant sequences of polynomial and the number of sign changes are used.