Please use this identifier to cite or link to this item: http://hdl.handle.net/11455/1650
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
摘要: 
本論文之目的在於發展一個方法,以使用者輸入之誤差值為基準,對一已知NURBS曲線求取同為NURBS格式的偏置曲線。
曲線/曲面的偏置計算為幾何處理的重要部份之一,在電腦輔助設計與製造(CAD/CAM)上的使用尤為廣泛,如切削刀具路徑之產生及模具設計等。過去以NURBS曲線發展的模型皆是以直線或圓弧來逼近偏置曲面,因此偏置後的近似曲線只能達到0次或1次連續,若要達到曲線平滑則必須作相當大量的分割。若能直接求取NURBS格式偏置曲線將可達到較高的連續性,並能大幅縮減偏置後曲線的資料量,且方便以偏置後曲線作局部的修改。
本論文所採的方法為對建構完成之NURBS曲線模型上之點集合作均勻取樣,在取樣點上對曲線求取其切線向量,法線向量,再配合偏置量求出取樣點之偏置位置;然後根據距離關係刪除過密之偏置點,便能得到距離均勻的偏置點。以偏置點作為誤差調整的依據,配合擬合曲線的方法或控制點偏置分割的方法而得到偏置曲線,再以調整偏置曲線控制點權重的方法使其誤差減少,最後分別探討各個方法結果之特性與分析其誤差變化。

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.
URI: http://hdl.handle.net/11455/1650
Appears in Collections:機械工程學系所

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