三次均匀B样条曲线和双三次均匀B样条曲面的边界控制

Boundary Control of Cubic Uniform B Spline Curve and Bi-cubic Uniform B Spline Surface

阐述了用三次均匀Ｂ样条曲线和双三次均匀Ｂ样条曲面进行计算机辅助几何设计的原理和方法。为解决三次均匀Ｂ样条曲线通过已知点列的首、末两点以双三次均匀Ｂ样条曲线面通过已知网格的最外层顶点问题，提出了三次均匀Ｂ样条曲线和双三次均匀Ｂ样条曲面边界控制的６种方法，并建立了相应的数学模型。

The principle and method of computer-aided geometric design using the cubic B spline curve and bi-cubic B spline surface are expounded.In order to solve the problems that cubic uniform B spline curve passes through the first and end points of known arrange,and bi-cubic uniform B spline surface passes through the outmost points of known grid,six kind methods of cubic uniform B spline curve and bi-cubic uniform B spline surface boundary control are presented.The mathematic models of curve(surface)are established.