可展有理Bezier曲面

Construction Algorithm of Rational Developable Bezier Interpolation Patches

认为由于三维形体的几何表示处处用到自由曲面造型 ,因此 ,曲面造型是 CAD和计算机图形中最活跃、最关键的学科分支之一 .首先通过给定两条形状相似的有理曲线 ,将其参数相同的对应点用直线段连接 ,构成可展曲面 ,提出了一种可展有理 Bezier曲面的构造算法 .其次将二次、三次有理曲线分别作为可展有理 Bezier曲面的设计曲线和伴随曲线 ,具体讨论了有关可展有理 (2 ,3 ) Bezier曲面的构造及其分类问题 .应用此算法使所设计的曲面更易修改 。

A method of constructing rational developable interpolation patches is put forward: two rational curves with similar shape are used as design curve and adjoint curve separately, and the points on the design curve and the corresponding points of the same parameters on the adjoint curve are joined with straight lines. Since quadratic Bezier curve and cubic Bezier curve have wider application in engineering, the rational developable patches of (2,3) degree is discussed in detail, which is obtained by using quadratic Bezier curve and cubic Bezier curve as as design curve and adjoint curve respectively. The rational developable surface designed by this method in the paper is easy to be modified.