赵宏艳 王国瑾. 过测地线的优化曲面设计[J]. 计算机研究与发展, 2009, 46(2): 289-294.
 引用本文: 赵宏艳 王国瑾. 过测地线的优化曲面设计[J]. 计算机研究与发展, 2009, 46(2): 289-294.
Zhao Hongyan and Wang Guojin. Design of Optimized Surface Passing Through a Given Geodesic[J]. Journal of Computer Research and Development, 2009, 46(2): 289-294.
 Citation: Zhao Hongyan and Wang Guojin. Design of Optimized Surface Passing Through a Given Geodesic[J]. Journal of Computer Research and Development, 2009, 46(2): 289-294.

## Design of Optimized Surface Passing Through a Given Geodesic

• 摘要: 给定一条曲线，构造以其为测地线的曲面，这是服装鞋帽类产品的设计/制造业中的一个现实课题.已有研究结果是构造出以给定曲线为公共测地线的曲面束，然后用拟合数据点的方法来确定最终曲面.这种通用方法受到曲面参数及其表示方法的影响，且没有对曲面的光顺程度加以考虑.从服装材料的特性和设计思想出发，提出一种利用能量优化来确定最终曲面的新方法.通过改变曲面表示形式和引入能量函数，方便而有效地确定了过给定测地线的一张优化曲面.给出了在插值拟合等约束条件下的相应算法.实例表明，所给算法很好地模拟了成衣的光顺设计与加工，在计算机辅助设计/制造(CAD/CAM)中富有应用价值.

Abstract: Given a space curve, to design a surface with it as a geodesic is in urgent need of garment manufacture and shoe making industry. The existing research proposed to construct a surface pencil with the curve as a common geodesic, and then specify the final surface among them by fitting scanned data. Such a method highly depends on surface parameterization and representation, and gives no consideration to surface fairness, which is important in practice. According to the material characteristic of garment and the designing concept, this paper provides a new method to specify the final surface in an energy optimization way. It first changes the representation of the surface pencil, so as to establish a relation between the free variable and the surface expression. After that, it introduces a proper energy function, and then determines the optimization surface by solving the minimum energy equation. In this way, global smoothness is realized. The authors also consider surface modification with different constraints such as interpolating or fitting some points or curves. Experiments show that the new method can simulate the garment modeling and processing efficiently and effectively. The method provided is especially applicable and useful in CAD/CAM.

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