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頁籤選單縮合
題名 | An Optimization Approach for Curve Fitting by Parabolic Curve Segments=拋物線曲線綴合最佳化方法 |
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作者姓名(中文) | 呂維成; 黃俊明; | 書刊名 | 中國機械工程學刊 |
卷期 | 20:2 1999.04[民88.04] |
頁次 | 頁107-119 |
分類號 | 448.945 |
關鍵詞 | 拋物線曲線; 最佳化; CAD; NURBS curve; Curve fitting; |
語文 | 英文(English) |
中文摘要 | 本文提出一種拋物線曲線綴合法。曲線綴合的過程包括:(1)點資料的前處理,(2) 曲線段交點的粹取,(3)產生粗略綴合曲線,以及(4)曲線修正。點資料的前處理係先由數條 近似的拋物線綴合曲線段表示該原始點資料,然後由這些曲線段輸出平滑分佈的點資料。平 滑化點資料經由拋物線評估函數的運算,可自動偵測出拋物線B-Spline曲線段的交點。利 用這些交點的位置與切線方向特徵,數條相接於這些特徵交點之連續拋物線B-Spline曲線 段因而組成了粗略綴合曲線。經由B-Spline曲線轉換成NURBS曲線的法則,綴合曲線模型 被賦予局部修正的功能;藉由調整綴合曲線的控制點與weights,使綴合曲線與點資料之間小 於容許誤差。利用本文的方法,將產生一條由少數控制點構成的特徵基(feature-based) B- Spline曲線,並可方便做曲線特徵造形的編修。本研究發展的雛型電腦系統對兩種不同型 態的點資料執行,並驗證了本文所提出之法則。 |
英文摘要 | This paper presents a methodology for curve fitting by parabolic curve segments. The process of curve fitting consists of data preprocessing, joining points extraction1 rough curve fitting, and curve correction. Data preprocessing is achieved by firstly approximating a number of parabolic curve segments to the original data points, and then generating smoother point data from these segments. A parabola- based evaluation function is applied through the smoothed data points to discover the boundary points of curve segments, with which the fitted curve is divided by a number of continuous parabolic curve segments. The boundary points and their tangents are constrained to create a rough uniform B-spline curve, which possesses only a few curve segments. An algorithm is then proposed to convert the uniform B-spline curve into a NURBS curve that is adopted to locally improve the curve segments in the rough fitted B-spline curve. Curve fitting by using the algorithm of this paper, a feature-based curve model with fewer control points will be created, in which a high edit-ability for the curve's features is embedded. A prototype computer system is also developed to verify the methodology proposed in this paper. |
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