High order approximation method for curves Original Research Article

In this paper, an approximation procedure for space curves is described, which significantly improves the standard approximation rate via parametric Taylorʹs approximations. The method takes advantages of the freedom in the choice of the parametrization and yields the order (m + 1) + [(m + 1)(2d - 1)] for a curve in Rd, where m is the degree of the approximating polynomial parametrization. Moreover, the optimal rate (m + 1)+[(m - 1)(d - 1)], for a curve in Rd, is also achieved for a particular set of curves. The cubic case is studied with examples which shows that our approximation method is an interesting quantity as well as quality improvement over standard methods.