|
Interval Bézier curves, surfaces of research in recent years , a lot , of a brief review of the history of the development of the Bézier curves and surfaces , the degree elevation of Bézier curves and surfaces , discrete nature , combined with interval arithmetic , and to study the nature of interval Bézier curves and surfaces . N-th interval Bézier curve up an order interval control points will increase by one, composed of elements of the curves will increase , curve and some n 1 and n times the original curves are not equivalent , and that is not the original Bézier curve section curves contained in the n-th gain direct bands obtained , so that from the perspective of the curve , l region after the bands and the original region is not equal to However, if as a set of points , they are equivalent same , discrete time interval curve control points also increased, and the strip-shaped region in the part of the curve is not continuous . However , the area represented by the curves as a set of points in the discrete before and after no change ! Therefore , the degree elevation and the discrete nature of the curves . Chapter II Bézier curves, surfaces, degree elevation formula extended to the interval Bézier curves, surfaces , and proposed section control polygon concept . Proved in the continuous process of degree elevation interval control polygon converges to the original interval Bézier curves, surfaces . Degree elevation formula can be used to convert low sub- interval Bézier curve, surface high form and degree elevation can increase the number of control points to facilitate more flexible shape of the curves , surfaces control . A simple and efficient convergence can be obtained by the liter -order formulas and degree elevation interval Bézier curves , and geometric surface mapping . Chapter discrete nature of the study interval Bézier curves , surfaces , discrete continuous , interval control polygon converges to the original interval Bézier curves, surfaces . Another simple and effective can be obtained by the discrete formulas and discrete convergence interval Bézier curves, surfaces, geometric constructions . Chapter IV degree elevation and the discrete nature of promotion to the rational interval Bézier curves and surfaces . Finally, we pointed out that the interval Bézier curve convexity preserving nature , the variation diminishing nature and the nature of the derivative .
|