Comparison of interval methods for plotting algebraic curves

Abstract

This paper compares the performance and efficiency of different function range interval methods for plotting f( x, y)=0 on a rectangular region based on a subdivision scheme, where f( x, y) is a polynomial. The solution of this problem has many applications in CAGD. The methods considered are interval arithmetic methods (using the power basis, Bernstein basis, Horner form and centred form), an affine arithmetic method, a Bernstein coefficient method, Taubin's method, Rivlin's method, Gopalsamy's method, and related methods which also take into account derivative information. Our experimental results show that the affine arithmetic method, interval arithmetic using the centred form, the Bernstein coefficient method, Taubin's method, Rivlin's method, and their related derivative methods have similar performance, and generally they are more accurate and efficient than Gopalsamy's method and interval arithmetic using the power basis, the Bernstein basis, and Horner form methods.