POLYGON SMOOTHING NURBS CURVES AND SURFACES

摘要

In conventional spline geometric shape design, each part of a designed object always evolves the same number of control 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 introduced parameters provide additional facilities for the freeform geometric object design. The most significant feature of this newly proposed spline scheme is that the number of control points used for different parts of a geometric 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 conventional NURBS, the proposed technique allows the designers to produce a much richer set of geometric shapes with a relatively smaller set of control points.