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標題: 誤差控制之NURBS曲線偏置
Error based NURBS Curve Offset
作者: 歐星文
Wen, Ou Hsin
關鍵字: 誤差控制;Error control;NURBS曲線;偏置曲線;NURBS curve;Offset curve;Curve fitting;Control polygon based method
出版社: 機械工程學系

The purpose of this thesis is to develop a method to offset a NURBS(Non-Uniform Rational B-Spline) curve based on input error bound, and the offset curve should have the same format as the source curve.
The designing of offset curves and surfaces is an essential task in CAD/CAM such as tool-path generation and pattern design. In previous work, offset curves are usually fitted with small straight lines or arc segments, and the continuity of the offsets reaches only zero or one. To obtain satisfying smooth offset curves, a large number of segments are required. For offset curves with NURBS format, it is easier to obtain curves with higher continuity and the required data memory is much less then using straight lines and arcs.
The approach consists of following steps: (1) data points are sampled on source curve uniformly; (2) find tangent and normal vector of each sampling point; (3) find offset of sampling points with offset distance; (4) delete those offset points considered too close to one another; (5) use curve fitting method or control polygon based method to find the offset curve and to control the error of the curve using offset sampling points; (6) adjust the weights of control points of offset curve to reduce the error of the curve. At last, the advantages and disadvantages of each method and its influences on the change of errors are analyzed.
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