求解具有规定测地曲率曲线的高效几何方法

An Efficient Geometric Method for Tracing Curves with Prescribed Geodesic Curvature on Parametric Surfaces

在诸如自动铺带、自动铺丝等应用场景中,需要设计出具有规定测地曲率的曲面曲线。通过分析发现,现有的方法在计算这类曲线时存在一些不足。有鉴于此,这里提出一种高效的具有规定测地曲率曲线的求解方法。本方法依据基本微分几何学原理,不需建立目标曲线复杂的数学模型。另一方面,在计算过程中利用多点加权平均以保证曲线的设计精度。本方法可保证目标曲线完全位于参数曲面上,且对于不同的参数曲面具有统一的求解格式。利用本文提出的方法设计了B样条曲面上一系列等测地曲率曲线。结果表明,该方法在计算效率上不仅显著高于现有的几何法,且一般情况下要优于现有的数值解法。

In many applications such as automated tape placement and automated fiber placement,the geodesic curvature of target curve is specified.However,it is found that existing methods show some shortcomings in calculating such curves.In view of this,it provides an efficient geometric method for tracing curves with prescribed geodesic curvature on parametric surfaces.This method is based on the basic principle of differential geometry.On the other hand,multi-point weighted average is utilized to ensure the design accuracy.The proposed geometric approach could ensure that the target curve lies completely on the parametric surface and has a uniform solution format for different surfaces.A series of curves with equal geodesic curvature on b-spline surfaces are designed through this method.Experimental results demonstrate that our algorithm is generally more efficient than existing geometric methods and numerical methods.