Degree reduction of NURBS curves

Yuan-Lung Lai, James Shih Shyn Wu, Jui Pin Hung, Jian Hong Chen

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


Higher degree curves are used in applications because they are easier to manipulate interactively but require heavy computation. Most of the equations for curves used popularly in CAD software are of degree 2 and 3, because two curves of degree 3 can guarantee 2nd derivative continuity at the connection point. This study proposes a different but simpler method than any put forward before to deal with degree reduction of free-form curves. The reduced curves use the simplest knot vector type, i.e., the open uniform knot vector. Unlike other methods, this study does not modify or refine the knot vectors but perturb the control points globally. After obtaining an initial condition, a radiating web-like search algorithm is applied to detect the optimum positions. These NURBS curve formats reach basic industrial standards for CAD/CAM/CNC applications. By defining a global bound error function, this algorithm can achieve an optimum solution not only for NURBS curves but also Bézier/B-spline curves.

Original languageEnglish
Pages (from-to)1124-1131
Number of pages8
JournalInternational Journal of Advanced Manufacturing Technology
Issue number11-12
Publication statusPublished - 2006 Feb 1

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Software
  • Mechanical Engineering
  • Computer Science Applications
  • Industrial and Manufacturing Engineering

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