构造参数样条曲线的关键是选取节点。本文讨论了GC2三次参数样条曲线需满足的连续性方程，提出了构造GC2三次参数样条曲线的新方法。在讨论了平面有序五点确定一组三次多项式函数曲线、平面有序六点唯一确定一条三次多项式函数曲线的基础上，提出了计算相邻两区间上的节点的算法。构造的插值曲线具有三次多项式函数精度。本文还以实例对新方法与其它方法构造的插值曲线的精度进行了比较。

提出了构造三角曲面片的一个新方法。新方法通过基本逼近算子加上附加插值算子构造满足给定边界曲线和跨界切矢的三角曲面片。基本逼近算子由逼近插值条件的5次多项式构成，附加插值算子用边点法产生。基本逼近算子和附加插值算子在构成三角曲面片中具有不同的作用，前者使三角曲面片以五次多项式精度逼近插值条件，而后者则使三角曲面片满足给定的插值条件。所构造的三角曲面片可以重构五次多项式曲面。给出了新方法和其他两种方法进行比较的结果。

A new method for constructing triangular patches is presented. A triangular patch that interpolates given boundary curves and cross-boundary slopes is formed by blending three traditional side-vertex interpolation operators (Nielson, 1979) with a new, interior interpolation operator. The new operator is the solution of an interpolation process that interpolates both the interior and the boundary of the triangular domain. The interior interpolation operator has better approximation precision on the interior of the triangle than the side-vertex operators. The constructed triangular patch reproduces polynomial surfaces of degree four. Comparison results of the new method with the side-vertex method (Nielson, 1979) are included.

New algorithms for the classical problem of fairing cubic spline curves ans bicubic spline surfaces are presented. To fair a cubic spline curve or a bicubic spline surface with abonormal portions, the algorithms (automatically or interactively) identify the 'bad' data points and replace them with new pointsproduced by minimizing the strain energy of the new cureve or suface. The proposed algorithms are more general than the existing algorithms in that the new algorithms can adjust more than one'bad' data point in each modification step and they include the existing algorithms in that the new algorithms can adjust more than one 'bad' data point in each modification step and they include the existing algorithms [Computer-Aided Design 15 (5) (1983) 288-293; 28 (1996) 59-66] as special cases. Test results ofthe new algorithms are included.

A new method to scale a trimmed NURBS surface while holding the shape and size of specific features (trimming curves) unchanged is presented. The new method is fix-and-stretch based: the new surface is formed by fixing selected regions of the given trimmed NURBS surface that contain the trimming curves and stretching the remaining part of the surface to reach certain boundary conditions. The stretching process is performed using an optimization process to ensure that the resulting surface reflects the shape and curvature distribution of the scaled version of the given surface. The resulting surface maintains a NURBS representation and, hence, is compatible with most of the current data-exchange standards. The new approach is more robust than a previous, attach-and-deform based approach (Zhang P, Zhang C, Cheng F. Constrained shape scaling of trimmed NURBS surfaces. In: Proceedings of the 1999 ASME Design Theory and Methodology Conference. Las Vegas, Nevada, 1999) in that it can tolerate scaling factors of bigger values (up to 2 in some cases). The new approach also guarantees that the features remain exactly the same after scaling. Test results on several car parts with trimming curves and comparison with the previous approach are included. The quality of the resulting surfaces is examined using the highlight line model. The presented technique is important for integrating standard parts into a sculptured product.