Oct 10, 2007
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----Catenoid----
X = 2*cosh(v/2)*cos(u)
Y = 2*cosh(v/2)*sin(u)
Z = v
With U[ -pi, pi] And V[ -pi, pi]
----Shoe----
X = u
Y = v
Z = 1/3*u^3 - 1/2*v^2
With U[ -2, 2] And V[ -2, 2]
----Heliciodal----
X = sinh(v)*sin(u)
Y = -sinh(v)*cos(u)
Z = 3*u
With U[ -pi, pi] And V[ -pi, pi]
----Cresent---
X = (2 + sin(2* pi* u) *sin(2 *pi* v)) *sin(3* pi *v)
Y = (2 + sin(2* pi *u) *sin(2 *pi *v)) *cos(3* pi *v)
Z = cos(2* pi *u) *sin(2* pi* v) + 4 *v - 2
With U[ 0, 1] And V[ 0, 1]
----Hyperhelicoidal----
X = (sinh(v)*cos(3*u))/(1+cosh(u)*cosh(v))
Y = (sinh(v)*sin(3*u))/(1+cosh(u)*cosh(v))
Z = (cosh(v)*sinh(u))/(1+cosh(u)*cosh(v))
With U[ -pi, pi] And V[ -pi, pi]
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