Vector elimination: A technique for the implicitization, inversion, and intersection of planar parametric rational polynomial curves
Let C be a planar rational polynomial curve defined parametrically. The solution of the problem: Find the polynomial equation of the curve \(F(x,y)=0\) which defines the same curve, C, as the parametric equations, is called the implicitization. The solution of the problem: Find the parametric(s), t, corresponding to the coordinates of a point \(p=(x,y)\) known to lie on the curve, is called the inversion. Using vector techniques and Bezout's resultant both problems are readily solved. In section 9 the authors obtain an intersection algorithm for planar rational polynomial curves. The presentation is elegant and the lecture of the text is attractive.
scientific article; zbMATH DE number 3911669