Title :
A subdivision scheme for approximating circular helix with NURBS curve
Author :
Pu, Xiongyin ; Liu, Weijun
Author_Institution :
Modern Equip. Res. Design Center, Chinese Acad. of Sci., Shenyang, China
Abstract :
An initial approximation circular helix with quadratic NURBS curve is represented by combining the algorithm for the planar NURBS circular arc and the height function defined by using the knot insertion and the degree elevation for linear NURBS. For given tolerance, a subdivision scheme based on de Boor algorithm for approximating NURBS helix curve is proposed. The modification subdivision scheme is easy and stabilized for keeping on improvement the approximation value and eliminates the blending algorithm for Bezier segments. Numerical examples are given to illustrate the efficiency of the method.
Keywords :
CAD; approximation theory; computational geometry; engineering graphics; splines (mathematics); Bezier segments; Boor algorithm; NURBS curve; approximation circular helix; computer aided geometric design; degree elevation; knot insertion; planar NURBS circular; quadratic NURBS curve; subdivision scheme; Approximation algorithms; Design automation; Error analysis; Geometry; Kinematics; Polynomials; Solid modeling; Spline; Surface reconstruction; Surface topography; Approximation; Helix; NURBS curves; Subdivision;
Conference_Titel :
Computer-Aided Industrial Design & Conceptual Design, 2009. CAID & CD 2009. IEEE 10th International Conference on
Conference_Location :
Wenzhou
Print_ISBN :
978-1-4244-5266-8
Electronic_ISBN :
978-1-4244-5268-2
DOI :
10.1109/CAIDCD.2009.5374879
