@Article{JICS-7-072,
author = {L. Yang, J.c. Li and G.h. Chen},
title = {A Class of Quasi-Quartic Trigonometric BÉZier Curves and Surfaces},
journal = {Journal of Information and Computing Science},
year = {2024},
volume = {7},
number = {1},
pages = {072--080},
abstract = {A new kind of quasi-quartic trigonometric polynomial base functions with a shape parameter λ 
over  the  space  Ω=span  {1,  sint,  cost,  sint2t,  cos2t}  is  presented,  and  the  corresponding  quasi-quartic 
trigonometric  Bézier  curves  and  surfaces  are  defined  by  the  introduced  base  functions.  The  quasi-quartic 
trigonometric Bézier curves inherit most of properties similar to those of quartic Bézier curves, and can be 
adjusted easily by using the shape parameter λ. The jointing conditions of two pieces of curves with G2 and 
C4  continuity  are  discussed.  With  the  shape  parameter  chosen  properly,  the  defined  curves  can  express 
exactly any plane curves or space curves defined by parametric equation based on{1, sint, cost, sint2t, cos2t} 
and  circular  helix  with  high  degree  of  accuracy  without  using  rational  form.  The  corresponding  tensor 
product surfaces can also represent precisely some quadratic surfaces, such as sphere, paraboloid, cylindrical 
surfaces,  and  some  complex  surfaces.  The  relationship  between  quasi-quartic  trigonometric  Bézier  curves 
and  quartic  Bézier  curves  is  also  discussed,  the  larger  is  parameter  λ,  and  the  more  approach  is  the  quasi-
quartic trigonometric Bézier curve to the control polygon. Examples are given to illustrate that the curves and 
surfaces can be used as an efficient new model for geometric design in the fields of CAGD. 
},
issn = {1746-7659},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/jics/22664.html}
}