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。

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.

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.

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.