中文摘要：

在绕一角点矩形域上贝齐尔曲面的光滑拼接中,切平面连续拼接已经实现。由于曲率连续拼接条件比较复杂,所以至今没有被解决,因而寻求一种拼接光滑程度好于切平面连续拼接而条件弱于曲率拼接的方法是很有意义的。利用切平面连续拼接的条件和高斯曲率定义,结合微分几何知识找到了2张贝齐尔曲面高斯曲率连续拼接的条件,这需要满足3个方程组。根据贝齐尔曲面的高斯曲率拼接的条件,方程组应具有相容性。根据相容性得到了方程组解的存在条件和绕一角点的矩形域上贝齐尔曲面的高斯曲率连续拼接方法。高斯曲率连续拼接的光滑程度优于切平面连续拼接,而且该方法容易在实际应用中实现。

英文摘要：

For the connection of Bézier surfaces on the rectangular areas with a common vertex,connection with tangent plane continuity has been realized,but the connection with curvature continuity is still unsolved,therefore,it is important to seek the method of connection which the spliced smoothness is better than that of tangent plane continuity,and the conditions are weaker than those of curvature continuity.Based on the conditions of tangent plane continuity,the definition of Gaussian curvature and geometric knowledge,the conditions of Gaussian curvature connection between two adjacent Bézier surfaces are obtained,and three systems of equations should be satisfied.The equations should have consistence according to the conditions of Gaussian curvature connection.The conditions of existence of solutions and the method of connection of Bézier surfaces around a common vertex with Gaussian curvature continuity are presented.The spliced smoothness is better than that of tangent plane continuity,and this method can be used easily in practical application.