[15pt]Diff Geometry(arc length parametrization)

2008-07-23 12:30 am
an ellipse is parametrized by
x(t) = a cos t
y(t) = b sin t

0<b<a
0≦t≦2π


find the arc length parametrization s ├──> (x(s),y(s))
更新1:

using s (arc length) as a parameter so that (x(s),y(s)) and (x(t),y(t)) represent the same curve eg (x(t),y(t)) = (Rcos t,Rsin t) t from 0 to 2Pi (x(s),y(s))=(Rcos(s/R),Rsin(s/R)) s from 0 to 2PiR

回答 (1)

2008-07-24 7:29 am
✔ 最佳答案
要使用Elliptic Integral。

圖片參考:http://i187.photobucket.com/albums/x22/cshung/7008072201899.png

假設1st quadrant搞定了其它Quadrant就可以使用它了,只要改改正負號。

2008-07-23 23:38:50 補充:
Incomplete elliptic integral of the second kind 使用了這裏的定義。

http://mathworld.wolfram.com/EllipticIntegraloftheSecondKind.html
參考: 從不抄襲。, 從不抄襲。


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