使用圓錐樣條曲線做函數近似轉換之研究

Approximate Conversion of Functions -- Using Conic Spline

徐志亮(Hsu Chie Liang)

指導教授 ： 李振華 ； 林基成

元智大學/工程學院/電機與資訊工程研究所/碩士(1993年)

摘要

通常繪圖或轉換軟體無法有效地使用高輸出裝置, 並佔用大量的檔案空
間, 因為這些方法使用許多點來描繪一個圖形。在此我們提出一個方法,
用以轉換可表示為R(t)=[X(t),Y(t)]的參數函式為數段樣條曲線。我們選
取反曲點作為切斷函式曲線的節點, 以使函式曲線被切割的段數盡可能地
少; 選擇圓錐樣條曲線做為本方法的基本曲線, 因為它的方法簡單, 計算
快速, 並具有易於修改的彈性。

關鍵字

圓錐樣條曲線 ； 近似轉換 ； 反曲點

並列摘要

Often plotting or conversion packages do not use high-
resolution output devices efficiently. Where such packages use
very large point file to describe a plot. In this thesis, we
will propose a new method which produces a conic spline to
approximate the parametric function which could be represented
by R(t) = [ X(t),Y(t) ]. We choose the knot in the inflection
point which makes the splited segments as less as possible. And
we select the conic spline as the primitive curve, because it's
simple, fast in computing time, and flexible. The most
important problem in this thesis is to find the accurate value
of cusps and inflection points to be the knots. We'll discuss
that in the approximte conversion steps.

並列關鍵字

Conic Spline ； Approximate Conversion ； Inflection Point