A geometric Newton-Raphson strategy

In the standard Newton-Raphson algorithm for solving nonlinear equations, a new guess is computed by solving a linear approximation of the problem at the current guess. A similar, very effective strategy is proposed here for solving geometric problems (e.g., finding intersections) on general plane curves. To compute a new guess, solve an elementary geometric approximation of the problem at the current guess. (C) 2001 Published by Elsevier Science B.V.