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頁籤選單縮合
題 名 | Interpolation of Massive Data Points Into a B-Spline Curve with Few Control Points=由大量點資料建構含少數控制點之B-spline曲線 |
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作 者 | 林清安; | 書刊名 | 中國機械工程學刊 |
卷 期 | 19:4 1998.08[民87.08] |
頁 次 | 頁379-390 |
分類號 | 446.01 |
關鍵詞 | 點資料; 建構; 控制點; B-spline曲線; CAD; B-spline curve; Curve fitting; Reverse engineering; |
語 文 | 英文(English) |
中文摘要 | This paper presents a methodology for which a composite B-spline curve can be automatically interpolated from a series of data points obtained through contact or non-contact measuring devices. In the first place, the methodology considers the issue of smoothing the measured point data, For a given allowable deviation, the step of data smoothing checks through the entire point data of find out a number of control-point sets, each set containing 4 control points which render a cubic B-spline curve. The initial point data can thus be approximated by a number of piecewise, C �� -continuous cubic B-spline curves. Each B-spline curve is next transformed into a set of new data points and the output data possesses the following property: curve regions with drastic changes of curvature possess denser points, while flat regions have looser density of data points. The property ensures that not only enough point data are provided to facilitate automatic curve fitting in the next stage, but also the computing time is saved for the regions with exceeding number fo data points. For the issue of automatic curve fitting, the constancy of third-order derivative on each curve segment of uniform cubic B-spline is used as the essential property to discover the joining points between each pair of adjacent curve segments. By interpolating these joining points, a set of control points can be found which become the basis to construct the geometric model of the composite B-spline curve. Hence, the joining points can be viewed as "feature points" in the curve-fitting process. Based on the proposed method, a B-spline curve fitted from massive data points may contain merely a few feature points and they facilitate the subsequent task of curve adjustment. |
英文摘要 | 此篇論文旨在探討如何將一連串的點資料 (由接觸式或非接觸式量測儀器所量得 ) 自動建構為一複合 B-spline 曲線。此文首先討論點資料平滑化的問題,其方法乃是在一個 可允許的公差範圍內,由整個點資料找出許多控制點區段,而每一區段含有四個控制點,因 此原輸入的點資料可被轉換為一段一段的 B-spline 曲線線段 (每一段曲線由四個控制點插 補而成 ),接下來再將每一曲線線段轉換為資料點。由此方法產生的新資料點有以下的特性 :曲線在曲率變化較大處將含有較密集的點,而較平坦處所含的資料點則較少。此特性不但 使下一個自動曲線建構的步驟能有適量的點資料輸入,且使資料點過份密集區的計算時間能 大幅縮短。在自動化曲線建構方面,本文利用三次方 B-spline 曲線含「三階微分為常數」 的特性來由點資料中尋找出兩條相鄰曲線線段的交接點,再由這些交接點求出控制點,即可 建構出複合 B-spline 曲線的幾何模型,因此,我們找出的曲線線段交接點即可視為曲線建 構過程中的「特徵點」。此文所提的方法,可使所建構的 B-spline 曲線含有非常少數的控 制點,以利往後設計變更時更改曲線造型之用。 |
本系統中英文摘要資訊取自各篇刊載內容。