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。

将扰动约束技应用于Bézier曲线的隆阶给出了理想的结果。讨论了将这类方法应用于B样曲线降价时结果不理想的原因，提出了采用最佳平方带近技术对B样条曲线做隆价运逄的方法；并用实例对该方法和基于扰动约束的隆价方法进了比较。

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。

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.

The current cubic spline curve interpolation scheme is derived based on the implicit assumption that the magnitude of the first derivative of the curve is close to a constant. However, the assumption is not realized by the interpolation scheme. A knot choosing technique for parametric cubic spline interpolating curve construction that accommodates this assumption is presented. A comparison of the new method with several existing methods is performed and test results 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.

讨论了构造C2连续的四次样条插值曲面问题。把四次样条函数降为C2连续可提供额外的自由度，用于提高曲面的插值精度和控制曲面的形状。给出了一个确定自由度的方法和C2连续的四次样条曲线需满足的连续性方程，提出了构造C2连续的四次样条插值曲面的新方法。新方法的特点是曲面需满足的连续性方程是三对角占优势的，曲面的不连续点在给定的数据点处。所构造的曲面具有四次多项式插值精度。最后以实例对新方法和现有三、四次样条函数方法的插值精度做了比较。

The construction of a GC1 cubicinterpolatiing curve that lies on the same side of a given straight line as the data points is studied. The main task is to choose appropriate approaches to modify tangent vectors at the data points for the desired curve. Three types of approches for changing the magnitudes of the tangent vectors are presented.The first-type approach modifies the tanggent vectors by applying a constraint to the curve segment. The second one does thework by optimization techniques. The thired one is a modification of the existing method. Three critera are prsented to compare the three types of approaches with the existing method. the experiments that test the effectiveess of the approaches are included.