Rational space curves are not “unit speed”

2007 ◽  
Vol 24 (4) ◽  
pp. 238-240 ◽  
Author(s):  
Rida T. Farouki ◽  
Takis Sakkalis
Keyword(s):  
Rational Space ◽  
Space Curves ◽  
Unit Speed

scholarly journals On the variety of rational space curves

2001 ◽  
Vol 122 (1) ◽  
pp. 359-369
Author(s):  
Z. Ran
Keyword(s):  
Rational Space ◽  
Space Curves

scholarly journals Using a bihomogeneous resultant to find the singularities of rational space curves

2013 ◽  
Vol 53 ◽  
pp. 1-25 ◽  
Author(s):  
Xiaoran Shi ◽  
Xiaohong Jia ◽  
Ron Goldman
Keyword(s):  
Rational Space ◽  
Space Curves

Double structures on rational space curves

2008 ◽  
Vol 281 (3) ◽  
pp. 434-441 ◽  
Author(s):  
Jon Eivind Vatne
Keyword(s):  
Rational Space ◽  
Space Curves

scholarly journals Kempe’s Universality Theorem for Rational Space Curves

2017 ◽  
Vol 18 (2) ◽  
pp. 509-536 ◽  
Author(s):  
Zijia Li ◽  
Josef Schicho ◽  
Hans-Peter Schröcker
Keyword(s):  
Rational Space ◽  
Space Curves ◽  
Universality Theorem

Symmetry detection of rational space curves

2015 ◽  
Vol 49 (2) ◽  
pp. 51-51
Author(s):  
Juan G. Alcázar ◽  
Carlos Hermoso ◽  
Georg Muntingh
Keyword(s):  
Symmetry Detection ◽  
Rational Space ◽  
Space Curves

scholarly journals Similarity detection of rational space curves

2018 ◽  
Vol 85 ◽  
pp. 4-24 ◽  
Author(s):  
Juan Gerardo Alcázar ◽  
Carlos Hermoso ◽  
Georg Muntingh
Keyword(s):  
Rational Space ◽  
Space Curves ◽  
Similarity Detection

scholarly journals Symmetry detection of rational space curves from their curvature and torsion

2015 ◽  
Vol 33 ◽  
pp. 51-65 ◽  
Author(s):  
Juan Gerardo Alcázar ◽  
Carlos Hermoso ◽  
Georg Muntingh
Keyword(s):  
Symmetry Detection ◽  
Rational Space ◽  
Space Curves ◽  
Curvature And Torsion

scholarly journals Space curves defined by curvature-torsion relations and associated helices

Filomat ◽  
2019 ◽  
Vol 33 (15) ◽  
pp. 4951-4966
Author(s):  
Sharief Deshmukh ◽  
Azeb Alghanemi ◽  
Rida Farouki
Keyword(s):  
Euclidean Space ◽  
Space Curves ◽  
General Polynomial ◽  
Slant Helix ◽  
Pythagorean Hodograph ◽  
Unit Speed ◽  
Circular Helix

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.

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