2013/06/16 by Fatma Şengüler-Çiftçi, Şengüler-Çiftçi, Fatma
Computer Science · Engineering · Mathematics · #53A04 #65D05 #65D17 #65D18 #68U07 #Advanced Numerical Analysis Techniques #Advanced Vision and Imaging #Differential Geometry (math.DG) #FOS: Mathematics #Robotic Mechanisms and Dynamics #math.DG #msc:53A04 #msc:65D05 #msc:65D17 #msc:65D18 #msc:68U07
paper · pdf · doi:10.48550/arxiv.1306.3689
20 pages, 8 figures
openalex publication_date 2013/06/16 · arxiv created 2014/01/27 · arxiv updated 2014/01/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.