Quadratic approximation to plane parametric curves and its application in approximate implicitization

Authors:
Ming Li;Xiao-Shan Gao;Shang-Ching Chou
Affiliations:
School of Computer Science, Cardiff University, Cardiff, UK;Key Lab of Mathematics Mechanization, Academia Sinica, Beijing, China;Department of Computer Science, Wichita State University, Wichita, USA
Venue:
The Visual Computer: International Journal of Computer Graphics
Year:
2006

Citing 0
Cited 3

Approximate implicitization of parametric surfaces by using compactly supported radial basis functions

Computers & Mathematics with Applications
Ambient Isotopic Meshing for Implicit Algebraic Surfaces with Singularities

CASC '09 Proceedings of the 11th International Workshop on Computer Algebra in Scientific Computing
Certified approximation of parametric space curves with cubic B-spline curves

Computer Aided Geometric Design

Quantified Score

Hi-index	0.01

Visualization

Abstract

Expressing complex curves with simple parametric curve segments is widely used in computer graphics, CAD and so on. This paper applies rational quadratic B-spline curves to give a global C1 continuous approximation to a large class of plane parametric curves including rational parametric curves. Its application in approximate implicitization is also explored. The approximated parametric curve is first divided into intrinsic triangle convex segments which can be efficiently approximated with rational quadratic Bézier curves. With this approximation, we keep the convexity and the cusp (sharp) points of the approximated curve with simple computations. High accuracy approximation is achieved with a small number of quadratic segments. Experimental results are given to demonstrate the operation and efficiency of the algorithm.