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標題: Degree reduction of NURBS curves
作者: Lai, Y.L.
Wu, J.S.S.
Hung, J.P.
Chen, J.H.
關鍵字: degree reduction;global bound error;NURBS curves;optimum;b-spline curves;polynomial degree reduction;bezier curves;euclidean;approximation;jacobi-polynomials;coefficients;constraints;equals
Project: International Journal of Advanced Manufacturing Technology
期刊/報告no:: International Journal of Advanced Manufacturing Technology, Volume 27, Issue 11-12, Page(s) 1124-1131.
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 Bezier/B-spline curves.
ISSN: 0268-3768
DOI: 10.1007/s00170-004-2289-y
Appears in Collections:機械工程學系所

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