دانلود رایگان مقاله بلندی درجه T اسپلاین

1. Introduction

T-splines (Sederberg et al., 2003, 2004) address many limitations inherent in the NURBS representation, such as local refinement (Sederberg et al., 2004; Scott et al., 2012), watertightness via merging (Ipson, 2005; Sederberg et al., 2003) and trimmed NURBS conversion (Sederberg et al., 2008). T-splines have proved to be an important technology across several disciplines including industrial, architectural and engineering design, manufacturing and engineering analysis. Knot insertion and degree elevation algorithms are two fundamental algorithms which are used to enrich a spline space (Farin, 2002). Degree elevation is the process of raising the degree of a curve or a surface while keeping the shape unchanged. For NURBS, these issues have been well studied (Farin, 2002; Wang and Deng, 2007; Huang et al., 2005). For T-splines, the local refinement algorithm has also been well studied (Sederberg et al., 2004; Scott et al., 2012; Morgenstern and Peterseim, 2015). However, no previous articles address degree elevation for T-splines.

6. Results and conclusion

We conclude by presenting some numerical experimentations about these three degree elevation algorithms for T-splines. The key issue to compare the algorithms is the number of resulting anchors. Thus all the examples are shown with the index T-meshes in this section. The first example is a T-spline defined on a T-mesh refined from a tensor-product T-mesh along the diagonal faces. Using the general T-spline degree elevation (Fig. 12b), just similar as the behavior of local refinement algorithm in Sederberg et al. (2004), the resulting T-spline is almost a tensor-product B-spline. However, for both analysis-suitable T-spline degree elevation algorithms, the resulting T-splines are very reasonable (Fig. 12c and d).