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Swirl function : ウィキペディア英語版
Swirl function
In mathematics, swirl functions are special functions defined as follows〔Trott, M. Graphica 1: The World of Mathematica Graphics. The Imaginary Made Real: The Images of Michael Trott. Champaign, IL: Wolfram Media, pp. 36–37 and 86, 1999. 〕:
: S(k,n,r,\theta)=\sin(k\cos(r) -n\theta)
where ''k'', ''n'' are integers.
''n'' is the number of blades, ''k'' is related to the shape of each blade.
==Symmmetry==
The function ''S''(''k'',''n'',''r'',''θ'') satisifies the following relations:
;mirror symmetry
*f(-k, n, r, \theta)=-f(k, n, r, -\theta)
*f(-k, n, r, \theta)=-f(k, -n, r, \theta)
*f(-k, -n, r, \theta)=-f(k, n, r, \theta)
*f(-k, n, r, -\theta)=-f(k, n, r, \theta)
* f(-k, n, r, \theta)=-f(k, n, -r, -\theta)
* f(-k, n, -r, -\theta)=-f(k, n, r, \theta)
* f(-k, -n, -r, \theta)=-f(k, n, r, \theta)
* f(-k, n, -r, -\theta)=-f(k, n, r, \theta)
;full symmetry
*f(k, -n, r, \theta)=f(k, n, r, -\theta)
*f(k, -n, r, -\theta)=f(k, n, r, \theta)
* f(k, n, -r, \theta)=f(k, n, r, \theta)
* f(k, n, -r, \theta)=f(k, n, r, \theta)
* f(k, n, -r, \theta)=f(k, -n, r, -\theta)
* f(k, -n, -r, -\theta)=f(k, n, r, \theta)
* f(k, n, -r, \theta)-f(k, n, r, \theta)
;rotation symmetry
: S\left(k,n,r,\theta+\frac\right)=S(k,n,r,\theta)

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
ウィキペディアで「Swirl function」の詳細全文を読む



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