A note on convergence analysis of NURBS curve when weights approach infinity

TL;DR

This paper investigates the convergence behavior of NURBS curves as their weights tend to infinity, revealing that the limit does not exist in general, and explores various types of convergence.

Contribution

It provides a detailed analysis of the convergence properties of NURBS curves under extreme weight conditions, which was previously not well understood.

Findings

Limit of NURBS curve does not exist when weights approach infinity.

Pointwise, uniform, and L^1 convergence are analyzed.

Convergence behavior depends on the independence of weights.

Abstract

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.