工学解析って何？！　日本オンリーワン株式会社

面白い曲面（その１）

脱線して、ここで面白い曲面とそれを表す方程式を示す。

===== Klein ========
x(u,v)=(3*(1+sin(v)) + 2*(1-cos(v)/2)*cos(u))*cos(v)
y(u,v)=(4+2*(1-cos(v)/2)*cos(u))*sin(v)
z(u,v)=-2*(1-cos(v)/2) * sin(u)
0<=u<=2*Pi,0<=v<=2*Pi



=====　Shell =====
x(u,v)=1.2^v*(sin(u)^2 *sin(v))
y(u,v)=1.2^v*(sin(u)^2 *cos(v))
z(u,v)=1.2^v*(sin(u)*cos(u))
0<=u<=Pi,-Pi/4<=v<=5*Pi/2



==== Trus =====
x(u,v)=(1+ 0.5*cos(u))*cos(v)
y(u,v)=(1+ 0.5*cos(u))*sin(v)
z(u,v)=0.5*sin(u)
0<=u<=2*Pi,0<=v<=2*Pi



===== Cosinus =====
x(u,v)=u
y(u,v)=v
z(u,v)=sin(pi*((u)^2+(v)^2))/2
-1<=u<=1,-1<=v<=1



===== Moebius =====
x(u,v)=cos(v)+u*cos(v/2)*cos(v)
y(u,v)=sin(v)+u*cos(v/2)*sin(v)
z(u,v)=u*sin(v/2)
-0.4<=u<=0.4,0<=v<=2*Pi