Computing the Minimum Distance between Two Planar Algebraic Curves

Through geometric observation, it is found that the nearest point on a curve is a tangent point between the curve and an offset curve of the other curve. Based on this observation, an offset method is presented for computing the minimum distance between two planar algebraic curves. The new method is geometrically instructive, and can be used for computing the minimum distance between an algebraic curve and a parametric one on the same plane. For planar quadratic curves, the degree of the resulting univariate polynomial equation by our method is much lower than that of the equations in previous comparable methods, which may lead to lower computation complexity or higher robustness of the solutions.