Abstract:

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 parameterized using discrete exponential maps and its normal coordinates will be obtained, then under the prerequisite 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 vertices,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.

Key words: exponential map; , mesh parameterization, reuse; , geodesic B-spline

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。
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关键词: 指数映射, 网格参数化, 复用, 测地B样条