Polygon Smoothing Nurbs Curves and Surfaces

Q. Li (UK)


CAGD, NURBS, shape parameters, tension control, poly gon smoothing.


In conventional spline geometric shape design, each part of a designed object always evolves the same number of con trol points. This has been a disadvantage of the spline based geometric shape design schemes as much more points than necessary may be required to specify a shape. In this paper, NURBS are generalized into Polygon Smoothing NURBS (PS-NURBS) by introducing a new set of shape parameters into conventional spline basis functions. The newly intro duced parameters provide additional facilities for the free form geometric object design. The most significant fea ture of this newly proposed spline scheme is that the num ber of control points used for different parts of a geomet ric shape can be varied according to design requirements. With this technique, a geometric shape can be designed to approximate the specified control polygon or control mesh smoothly with any required precision. Compared with con ventional NURBS, the proposed technique allows the de signers to produce a much richer set of geometric shapes with a relatively smaller set of control points.

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