空间曲线基于内在几何量的高质量采样和B样条拟合

为解决均匀参数采样在许多情况下得到质量不高的采样点,进而生成不理想的B样条拟合曲线,提出空间曲线基于内在几何量的均匀采样方法,以获得给定总数且具有代表性的采样点.首先定义基于弧长、曲率和挠率加权组合的特征函数,通过调整组合参数更好匹配不同的曲线形状;然后提出空间曲线基于内在几何量的自适应采样方法,迭代生成满足给定距离阈值的采样点.采用最大绝对误差和均方根误差作为评价指标,与均匀弧长采样方法和基于弧长和曲率平均的均匀采样方法进行对比,并通过实例进行验证.结果表明,文中方法在采样质量和B样条拟合结果上获得明显改善.

High-Quality Sampling and B-Spline Fitting for Spatial Curves Using Intrinsic Geometric Quantities

Uniform parametric sampling often provides low-quality sampled points and leads to unsatisfactory B-spline fitting curves.To resolve this problem,a uniform sampling method is proposed for spatial curves using intrinsic geometric quantities,so as to obtain a prescribed number of representative points.Firstly,the characteristic function is defined as a weighted combination of arc length,curvature and torsion,and it can more closely match various curve shapes by adjusting the combination parameters.Then an adaptive sampling method is proposed for spatial curves using intrinsic geometric quantities,which iteratively generates sampled points until a given distance threshold is satisfied.By using the evaluation indicators of maximum absolute error and root mean square error,numerical examples are implemented when comparing with uniform sampling in arc length and uniform sampling in the average of arc length and curvature.The experimental results show that the proposed method remarkably improves sampling quality and B-spline fitting results.