Mao Shi

Mao Shi, Jiansong Deng

In this paper, we propose a method to obtain a constrained approximation of a rational Bézier curve by a polynomial Bézier curve. This problem is reformulated as an approximation problem between two polynomial Bézier curves based on weighted least-squares method, where weight functions $ρ(t)=ω(t)$ and $ρ(t)=ω(t)^{2}$ are studied respectively. The efficiency of the proposed method is tested using some examples.

Mao Shi

This article considers the convergence of NURBS curve when weights approach infinity. We shows that limit of NURBS curve dose not exist when independent variables weights approach infinity. Further, pointwise convergence uniform convergence and $L^1$ convergence are researched.