On the limits of non-uniform rational B-spline surfaces with varying weights

Yue Zhang,Chun-Gang Zhu,Qing-Jie Guo

doi:10.1177/1687814017700547

Abstract

The non-uniform rational B-spline is a mathematical model commonly used in computer-aided design and manufacturing. For a non-uniform rational B-spline surface, when a single weight approaches infi...

Highlights

Machine parts in the mechanical processing, such as cam, blade, and mold are usually composed of complex curves or surfaces.[1,2] Outlines of them cannot be represented by simple mathematical models
We prove that regular control surface is the limit of the nonuniform rational B-spline (NURBS) surface when all of the weights approach infinity
We demonstrate that if a point set is the limit of a NURBS surface for a sequence of weights, this set must be a regular control surface induced by some regular decomposition

Summary

Introduction

Machine parts in the mechanical processing, such as cam, blade, and mold are usually composed of complex curves or surfaces.[1,2] Outlines of them cannot be represented by simple mathematical models. The NURBS method is effectively applied in many areas of computer-aided design and manufacturing (CAD/CAM), computer-aided geometric design (CAGD), and geometric modeling. It has diverse applications in isogeometric analysis,[4,5] reverse engineering,[6,7,8] computer numerical control (CNC) machining,[9,10,11] and so on

Objectives

Conclusion