有理螺旋线几何及其应用
Geometry of rational helices and its applications
摘要：
本文试图展示一种关于有理勾股速端曲线（PH）的替代方法，特别是对于有理PH螺旋（即有理螺旋）的更自然的方法。它利用有理螺旋线的几何特征来获得这些曲线的更简单的构造，并将其应用于相关主题。这些应用之一是几何C1埃尔米特插值（即插值端点与相关的单位切线）的有理螺旋线。此外，我们还研究了有理螺旋线上有理旋转极小框架（RRMF）的存在性。提出了旋转最小标架的一种有理逼近方法。随后，我们部署了一个合理的扫描曲面建模的近似框架。所得到的算法说明了几个例子。
英文摘要：
The present paper attempts to show an alternative approach with regards to rational Pythagorean-hodograph (PH) curves and especially more natural approach for rational PH helices (i.e. rational helices). It exploits geometric features of rational helices to obtain a simpler construction of these curves and apply this to related subjects. One of these applications is Geometric C1 Hermite interpolation (i.e. interpolation of end points with associated unit tangents) by rational helices. Furthermore, we investigate the existence of rational rotation minimizing frames (RRMFs) on rational helices. A rational approximation procedure to rotation minimizing frames (RMFs) is suggested. Subsequently, we deploy the approximate frame for modeling a rational sweep surface. The resulting algorithms are illustrated by several examples.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
