中文摘要：

把指数映射参数化方法引入到网格曲面上自由曲线的设计中，提出一种网格曲面上测地B样条曲线复用操作方法。指数映射局部微分同胚的性质，可以保证局部网格参数化的有效性。对于生成的测地B样条曲线，采用离散指数映射方法参数化其控制顶点，得其法坐标，在保证法坐标不变的前提下，通过改变参数化区域，可以实现测地B样条曲线实时滑动、旋转、缩放等效果。测地B样条曲线生成和局部网格参数化都不依赖于网格模型的整体规模，适用性强。试验结果表明，基于离散指数映射的网格曲面上曲线设计与复用方法健壮、有效，能满足曲面上曲线的交互设计要求。

英文摘要：

By introducing exponential mapping parameterization into curve design on the surface, a reuse approach of geodesic B--spline curve on mesh surface was proposed. The exponential map had the property of local differentiable homeomorphism, which can guarantee the effectiveness of mesh parameterization. As for the generated geodesic B--spline curve, its control points were parameter- ized using discrete exponential maps and its normal coordinates will be obtained, then under the pre- requisite conditions that those normal coordinates remained unchanged, the geodesic B--spline curve could be moved, rotated and scaled by changing parameterized region. The generation of geodesic B-- spline curve and the parameterization of local mesh did not depend on the scale of overall mesh verti- ces,so it had wide adaptability. The results show that, the method is robust, effective, and able to meet the requirements of curve interaction design on surface.