Tranguloid Trefoil
Rendered by Paul Bourke
Surface by Roger Bagula
April 2002
![](tranguloid1.jpg)
x = 2 sin(3 u) / (2 + cos(v))
y = 2 (sin(u) + 2 sin(2 u)) / (2 + cos(v + 2 pi / 3))
z = (cos(u) - 2 cos(2 u)) (2 + cos(v)) (2 + cos(v + 2 pi / 3)) / 4
-pi <= u <= pi
-pi <= v <= pi
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![](tranguloid2.jpg)
Sample C source code
![](tranguloid3.jpg)
![](mathematica.gif)
![](tranguloid4.jpg)
![](tranguloid5.jpg)
![](tranguloid6.jpg)
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