中文摘要：

该文首先采用代数曲线样条逼近的方法参数化混合边界,然后用三次样条曲面混合任意两个隐式代数曲面,实现样条曲面和基曲面之间光滑过渡.进一步,文中采用GB样条混合两张代数曲面,当混合边界为Lissajous曲线、二次曲线、三角函数曲线、双曲函数曲线、悬链线或螺旋线等特殊曲线时,可实现混合曲面精确插值边界曲线.而对于多个隐式代数曲面混合,又首次提出了G1连续的切分结合S曲面片补洞的方法,且每张曲面片的形状都可通过形状参数直观地进行调整.

英文摘要：

Based on the method of approximating boundary curves with spllnes, we use a spnne surface of degree 3 to blend two arbitrary implicit algebraic surfaces. Smooth transition is achieved between the spline surface and two base surfaces. Furthermore, we use GB-splines to blend two algebraic surfaces which can exactly represent Lissajous curves, conics, trigonometric function curves, hyperbolic function curves, catenary curves and helixes etc. For several implicit algebraic surfaces, we present the blending method that combines splitting and filling holes with S-patches. G1-continiuty is persisted between splitting blending patches and S-patches. All blending patches are control point patches and the shape of each patch can be adjusted by shape parameters intuitively.