以离散曲线为测地线的离散曲面构造

Constructing discrete surface through a given discrete geodesic

为了解决已知曲面特征线的外形设计问题,提出一种以B样条为度量函数的离散曲面构造算法。即假设给定离散曲线为测地线,并计算给定离散曲线的Frenet标架以获取曲线特征,然后由测地线特征计算出曲面约束条件,从而通过离散化约束条件设计满足约束条件的B样条度量函数来构建离散曲面。实验结果表明:该算法能有效地控制离散曲面形状,设计者可以通过控制B样条度量函数的形状,使得所生成离散曲面满足工业生产需求。

In order to solve the geometric design problem of known surface feature line,this paper proposes an algorithm to design discrete surface through designing a B-spline as march-function.Firstly,imagining that the given discrete curve is a geodesic,the the discrete Frenet frame of the given discrete curve is calculated in order to get the curve feature.Then,the surface constrain condition is computed through geodesic feature.Finally,the B-spline march-function which satisfies the surface constrain condition is designed.Test results show that this algorithm can control the shape of discrete surface effectively to meet the needs of industry production by control the shape of B-spline.