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dc.contributor.authorWen, Ou Hsinen_US
dc.description.abstract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。zh_TW
dc.description.abstractThe 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.en_US
dc.description.tableofcontents中文摘要 I 英文摘要 II 第一章、介紹 1 1.1 目的與方法 2 1.2 文獻回顧 3 1.3 內容大綱 7 第二章、NURBS之基本原理與常用演算法 8 2.1 NURBS曲線/曲面數學理論 8 2.1.1 Bezier曲線/曲面的定義 8 2.1.2 B-Spline曲線/曲面的定義 10 2.1.3 Bezier曲線/曲面的定義 14 2.2 節點插入法 16 2.3 節點消去法 19 2.4 權重與曲線外形的關係 23 第三章、偏置取樣點的取得 28 3.1 偏置位置的取得 28 3.2 幾何不連續處之消去 33 第四章、偏置曲線的產生 38 4.1 以擬合方式產生偏置曲線 38 4.1.1 使用插值法擬合曲線 39 4.1.2 使用近似法擬合曲線 41 4.1.3 曲線誤差之計算 43 4.1.4 以擬合方式產生偏置曲線 44 4.2 以控制點偏置求取偏置曲線 48 4.3 以權重的改變縮小偏置曲線的誤差 51 第五章、程式執行範例與應用 56 5.1 程式執行範例 56 5.2 曲線偏置之應用 70 第六章、結論與展望 73 參考文獻 Reference -Ⅰ-zh_TW
dc.subjectError controlen_US
dc.subjectNURBS curveen_US
dc.subjectOffset curveen_US
dc.subjectCurve fittingen_US
dc.subjectControl polygon based methoden_US
dc.titleError based NURBS Curve Offseten_US
dc.typeThesis and Dissertationzh_TW
item.openairetypeThesis and Dissertation-
item.fulltextno fulltext-
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