中文摘要：

测定单一类型（凸或马鞍）区域和计算其边界是进行自由曲面的形状分析与控制研究的基本内容之一．目前这方面的研究局限于一些特殊曲面，如可展曲面，对自由曲面则无来境的理论和方法．本文提出了一些对复杂自由曲面进行形状分析的几何结论．通过计算高斯抛物线，划分了曲面的单类型区域．设计了算法判断单类型区域、分离单类型区域，并计算其边界，对自由曲面整体的形状有了较好的把握．最后蛤出了算法对两个例子的计算结果．

英文摘要：

Determining convex or hyperbolic area of free-form surface and computing its borderlines is one of basic contents in analysis and control shape of free-form surface. At present, the research is limited in some special surface as developable surface, the research in free-form surface has no success in theory and method. Some geometric conclusions with respect to shape analysis of the complex free-form surface is put forward. Through computing Gauss parabolic lines, the convex area of a freeform surface was determined, and divided up, and its borderlines was computed. Convexness of a whole free-form surface was commanded. At last, two example＇s running results with the algorithm was provided.