From: Dave Rusin Subject: Re: bezier curve intersection Date: Fri, 2 Mar 2001 10:20:41 -0600 (CST) To: bertl@sbox.tu-graz.ac.at Summary: Computing intersection of two Bezier curves Are you asking about something more sophisticated than simply solving the simultaneous pair of cubic equations x1(t)=x2(u), y1(t)=y2(u) ? One could, for example, search globally for solutions by using elimination (Grobner bases, say) to reduce to a polynomial in one variable; or if what is desired is a numerical determination of an intersection, one has recourse to Newton's method. [deletia --djr] (The generic case solves for t in terms of u, say, as a ratio of two cubic polynomials in u, each coefficient being a sum of a few products of four coefficients in x1, x2, y1, y2. Then u is determined as the root of a polynomial of degree 9. It's pretty ghastly to write down but of course once it is computed, its roots may be easily determined by well-known techniques. I don't guarantee this is the most efficient method!) dave (sci.math.research moderator)