用有理双三次Bézier曲面片混合二次曲面

Blending Quadric Surfaces with Rational Bicubic Bézier Patches

提出一种二次曲面混合方法,混合曲面由2张有理双三次Bézier曲面片构成,它们之间保持G2连续,混合曲面与二次曲面间保持G1连续.给出了混合曲面片控制顶点的显式表示,通过修改2类混合参数可以直观地调节混合方向及混合曲面的形状.另外,混合5个圆锥曲面的例子表明,该方法为多个二次曲面的混合问题提供了有效途径.

A method of blending two quadric surfaces is presented. The blending surface consists of two rational bicubic Bezier patches. G^2 continuous contact is achieved between two patches and G^1 between the blending surface and each quadric. Explicit representations of control points of two patches are given. The blending direction and the shape of the blending surface can be intuitively adjusted through adapting two types of blending parameters. In addition, an example of blending five cones illustrates that this method provides an effective way for the n-way blending problem of quadrics.