Skip to main content
eScholarship
Open Access Publications from the University of California

Space curves defined by curvature–torsion relations and associated helices

  • Author(s): Deshmukh, S
  • Alghanemi, A
  • Farouki, RT
  • et al.
Abstract

© 2019, University of Nis. All rights reserved. The relationships between certain families of special curves, including the general helices, slant helices, rectifying curves, Salkowski curves, spherical curves, and centrodes, are analyzed. First, characterizations of proper slant helices and Salkowski curves are developed, and it is shown that, for any given proper slant helix with principal normal n, one may associate a unique general helix whose binormal b coincides with n. It is also shown that centrodes of Salkowski curves are proper slant helices. Moreover, with each unit–speed non–helical Frenet curve in the Euclidean space E3, one may associate a unique circular helix, and characterizations of the slant helices, rectifying curves, Salkowski curves, and spherical curves are presented in terms of their associated circular helices. Finally, these families of special curves are studied in the context of general polynomial/rational parameterizations, and it is observed that several of them are intimately related to the families of polynomial/rational Pythagorean–hodograph curves.

Many UC-authored scholarly publications are freely available on this site because of the UC's open access policies. Let us know how this access is important for you.

Main Content
Current View