Explicit matrix representation for NURBS curves and surfaces

Authors:
Ligang Liu;Guojin Wang
Affiliations:
State Key Lab of CAD&CG, Zhejiang University, Hangzhou 310027, PR China and Institute of Computer Images and Graphics, Zhejiang University, Hangzhou 310027, PR China;State Key Lab of CAD&CG, Zhejiang University, Hangzhou 310027, PR China and Institute of Computer Images and Graphics, Zhejiang University, Hangzhou 310027, PR China
Venue:
Computer Aided Geometric Design
Year:
2002

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Matrix representation for NURB curves and surfaces

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Abstract

The matrix forms for curves and surfaces were largely promoted in CAD/CAM. In this paper we have presented two matrix representation formulations for arbitrary degree NURBS curves and surfaces explicitly other than recursively. The two approaches are derived from the computation of divided difference and the Marsden identity respectively. The explicit coefficient matrix of B-spline with equally spaced knot and Bézier curves and surfaces can be obtained by these formulae. The coefficient formulae and the coefficient matrix formulae developed in this paper express non-uniform B-spline functions of arbitrary degree in explicit polynomial and matrix forms. They are useful for the evaluation and the conversion of NURBS curves and surfaces in CAD/CAM systems.