利用三階貝茲曲線逼近四階貝茲曲線

Use Of Cubic Bezier Curve Approximation Of Fourth-order Bezier Curve

林容妃(Lin JoungFei)

指導教授 ： 吳志揚

國立中正大學/理學院/數學系應用數學研究所/碩士(2012年)

摘要

本篇論文想要探討的問題是：如何用三階的 Bezier 曲線去近似四階的 Bezier 曲線。我們將利用「升階」這個技巧，將我們的三階 Bezier 曲線升階到四階。最後我們利用「最小平方近似法」的技巧來求未知的三階 Bezier 曲線的四個控制點，所以我們就可以求得近似四階 Bezier 曲線的三階 Bezier 曲線了。後續則可以推廣至逼近更高階。

關鍵字

貝氏曲線

並列摘要

Want to explore this thesis, the question is: how to use the third-order Bezier curves to approximate the fourth-order Bezier curves. We will use the "degree elevation" skills, our third-order Bezier curves l-order to fourth order. Finally, we use the "least squares approximation "technique to seek the unknown cubic Bezier curves of the four control points, so we can obtain the approximate fourth-order Bezier curves of cubic Bezier curve. Follow-up can be extended to the approximation of higher order.

並列關鍵字

Bezier Curve

參考文獻

Guido Brunnett, Thomas Schreiber, and Jörg Braun. The geometry of optimal

degree reduction of Bézier curves. Comput. Aided Geom. Design, 13(8):773–788,

Matthias Eck. Degree reduction of Bézier curves. Comput. Aided Geom. Design,

Gerald Farin. Curves and surfaces for computer-aided geometric design. Computer

and Physics, Vol. III. Gordon and Breach Publishers, Inc., New York, 1960.