Convergence of Geometric Interpolation Using B-splines
This paper investigates the convergence of an algorithm geometrically interpolating a given polygon using quadratic and cubic B-splines respectively. The geometric interpolation method views the polygon itself as the initial guess of the control polygon of the B-spline and reduces the approximate error by iteratively updating the control points with the deviation from the interpolated vertices to their nearest footpoints on the current B-spline curve. We demonstrate that the algorithm usually does not converge if the nearest points are searched on the whole curve and present a sufficient condition under which the algorithm is convergent, for quadratic and cubic B-splines respectively. Furthermore, we introduce a new strategy to update the control points incrementally. Experiments show that though our condition constrains the search range of the nearest points, it can still produce interpolation curves with high quality compared to the original method. In addition, the proposed control point updating strategy results in a faster convergent speed.
Yunhui Xiong Guiqing Li Aihua Mao
South China University of Technology,Guangzhou,China
国际会议
2011国际计算机辅助设计与图形学学术会议(CAD/Graphics 2011)
济南
英文
1-8
2011-09-15（万方平台首次上网日期，不代表论文的发表时间）