PIECEWISE RATIONAL APPROXIMATIONS OF REAL ALGEBRAIC CURVES

We use a combination of both algebraic and numerical techniques to construct a C1-continuous, piecewise (m, n) rational E-approtimation of a real algebraic plane curve of degree d. At singular points we use the classical Weierstrass Preparation Theorem and Newton power series factorizations, based on the tecdrique of Hensel lifting. These, together with modifled rational Pade approkimations, are used to efficiently construct locally approximate, rational parametric representations for all real branches of an algebraic plane curve. Besides singular points we obtain an adaptive selection of simple points about which the curve approalmations yield a small number of pieces yet achieve C1 continuity between pieces. The simpler cases of C-1 and Co continuity are also handled in a sbolar manner. The computation of singularity, the approkimation error bounds and details of the implemeniation of these algorithms are also provided.