中文摘要：

针对曲面上曲线偏置方法存在的不足,提出一种流形网格曲面上测地B样条曲线偏置方法。该方法将流形网格曲面上曲线偏置的问题转换为平面曲线偏置的问题。对于给定的流形网格曲面上测地B样条曲线,将测地B样条曲线所在的区域用离散指数映射的方法进行局部参数化;利用基于控制顶点偏移的方法,将参数域上的曲线进行偏置;利用参数匹配的方法将偏置后的曲线映射到流形网格曲面上,完成曲面上曲线的偏置。针对平面偏置曲线出现的自交,提出了一种新的检测与去除自交的方法,能够有效地去除自交。试验结果表明：该方法不仅健壮、有效,能够满足交互设计要求,而且偏置曲线的表达式与源曲线具有相同形式。

英文摘要：

In allusion to deficiencies of the existing methods of curve offset on surface, an offset method of geodesic B-spline curves on manifold triangulation surface is proposed in this study. In this method, the offset problem of curves on manifold triangulation is converted to simpler problem that offset of curves on plane. As for a given geodesic B-spine curve on manifold triangulation surface, firstly, the region where geodesic B-spline curve is parameterized locally using discrete exponential maps; secondly, the curve in the parameter domain is offset using the method based on shifting control points; finally, the offset curve is mapped to the manifold triangulation surface using parameter matching, and finishing the work that offset of curve on surface. According to the self-intersections that appeared in the offset curve on plane, a new approach that detecting and eliminating self-intersections is proposed, which can eliminate self-intersection effectively. robust, effective, and able to meet the interactive design consistent with the source curve. The results show that the proposed method is not only requirements, but also the expression of offset curve.