Research On Sampling Methods For Spatial Curves Using Intrinsic Geometric Quantities

Curve sampling methods can approximately represent the profiles of curves by selecting a sequence of points located on the curves,which is a hot research problem in computer aided geometric design and some related areas.Existing curve sampling methods are mainly focused on obtaining sampled points on planar curves,only a few methods can also be applied to the case of spatial curves,but without considering the inherent characteristics of spatial curves.So,these methods have some drawbacks in various applications.High-quality sampling methods must consider intrinsic geometric quantities of spatial curves,such as arc length,curvature and torsion,and explore the impact of these three factors in sampling results.This thesis proposes sampling methods for spatial curves,so as to select representative sampled points to better represent the actual shape of curves.Firstly,a characteristic function which is based on a weighted combination of arc length,curvature and torsion is constructed.Then a uniform sampling method for spatial curves using intrinsic geometric quantities is proposed.This method can adjust the weights in the characteristic function according to the actual curve shape to obtain a prescribed number of high-quality sampled points.Secondly,an adaptive sampling method using intrinsic geometric quantities is proposed for spatial curves,which is suitable for more complicated curve shapes.Compared with the uniform sampling method for spatial curves using intrinsic geometric quantities,this method does not fix the number of sampled points and iteratively obtains sampled points that meet the specified distance threshold,which improves sampling quality.Finally,compared with the state-of-the-art sampling methods,the results demonstrate that the proposed methods significantly improve the B-spline fitting results of spatial curves.