| With the rapid development of computer technology, the storage capacity and amount of data calculation needed in computer graphics and image processing are lager and lager. Efficient, fast and simple data processing algorithm is highly needed.In response to this situation, this paper proposes a method of cubic Hybrid clipping for solving polynomial roots. It’s a new method which has simple algorithm and easily to be programmed, especially quick and efficient in solving the double roots of polynomials. This method needs to take several steps. First, it changes a degree n (n>3) Bezier curve to a cubic Hybrid curve which is equivalent to the original curve. The cubic Hybrid curve has a moving control point and three fixed points. Find the point which is the farthest away from the coordinate axis and the one nearest to the coordinate axis among the moving control points. Using these two points, we can get two degree four Bezier curves with other fixed control points. Then the two new Bezier curves can envelop the original curve. To compute the roots of these two four-order curves, we get an interval which contains the root of the original curve. Discrete the original curve and reserve the part that contained by the interval. Repeat this process by iteration until the length of the interval is smaller than a given value. This paper even proposes a quartic Hybrid clipping bases on the methods of Hybrid clipping. By doing numerical experiments, this paper proves that we can get correct-roots with cubic Hybrid clipping and quartic Hybrid clipping.The quadratic Hybrid clipping is compared with our cubic Hybrid clipping in this paper. Compared with quadratic Hybrid clipping, we find that cubic Hybrid clipping is better in solving the double roots of polynomials. Hybrid clipping is compared with polynomial clipping in detail in this paper by doing numerical experiments. Although the experimental result shows that Hybrid Clipping is not better than polynomial clipping, it is much simpler in the logic algorithm, to implement by programming and the storage space needed is much smaller than polynomial clipping. |
