Plotting Planar Implicit Curves and Its Applications

We present a new method to plot planar implicit curve in a given box B is an element of R-2. Based on analyzing the geometry of the level sets of the given function, following the points with local maximal (or minimal) curvatures on the level sets, we compute points on each components of the given function in box B and trace each component to plot the curve. We also used this method to find real zeros of bivariate function systems in a given box. The experiments shows that our implementation works well. It works for polynomials with degrees more than 10,000. It also works for non-polynomial case.