Given two spatial $C^1$ PH spline curves, aim of this paper is to study the construction of a tensor–product spline surface which has the two curves as assigned boundaries and which in addition incorporates a single family of isoparametric PH spline curves. Such a construction is carried over in two steps. In the first step a bi–patch is determined in a ‘Coons–like’ way having as boundaries two quintic PH curves forming a single section of given spline curves, and two polynomial quartic curves. In the second step the bi–patches are put together to form a globally $C^1$ continuous surface. In order to determine the final shape of the resulting surface, some free parameters are set by minimizing suitable shape functionals. The method can be extended to general boundary curves by preliminary approximating them with quintic PH splines.

给定两个空间 $C^{\mathrm{1个}}$PH样条曲线，本文的目的是研究张量-乘积样条曲面的构造，该曲面具有两条曲线作为指定边界，并且还包含单个等参PH样条曲线系列。这样的构造分两个步骤进行。第一步，以“类库恩斯”（Coons-like）方式确定双修补程序，以两条五次PH曲线为边界，形成给定样条曲线的单个部分，并以两个多项式四次曲线为边界。第二步，将两修补程序放在一起以形成全局$C^{\mathrm{1个}}$连续的表面。为了确定最终表面的最终形状，通过最小化合适的形状功能来设置一些自由参数。该方法可以扩展为通用边界曲线，方法是用五阶PH样条曲线初步逼近它们。