
Surface(x,y,z) = f(u,v)                                20-april-2005
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alphabetical order of surface formulas in parametric form:


Bohemian Dome
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x = a*cos(u)  
y = b*cos(v) + a*sin(u) 
z = c*sin(v)
      
Boy Surface
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x = (f1 * cos(2*u) + f2) / f3      f1 = Sqrt2 * sqr(cos(v))
y = (f1 * sin(2*u) + f2) / f3      f2 = cos(u) * sin(2*v)
z =   3 * sqr(cos(v)   ) / f3      f3 = 2 - Sqrt2 * sin(3*u) * sin (2*v)
    0 <= u <= 2 Pi     0 <= v <= Pi / 2

Cresent
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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
    0 <= u <= 1,  0 <= v <= 1

Hyperboloid
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f1 = sqrt(1+u*u);
x = r1 * f1 * cos(v);
y = r2 * f1 * -sin(v);
z = r3 * u;
    -Pi/2 <= u <= Pi/2,  0 <= v <= 2*Pi

SuperEllipsoid
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cv=          cos(v) ^ f1;
x = a * cv * cos(u) ^ f2;
y = b * cv * sin(u) ^ f2;
z = c *      sin(v) ^ f1;

Supertoroid
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r = r1 + r2 * cos(v)        r1: main radius
x = r * cos(u)              r2: ring radius
y = r * sin(u)^              0 <= u <= 2 pi
z = r1 * sin(phi)            0 <= v <= 2 pi

Steiner surface
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x = cos(v) cos(v) sin(2u) / 2
y = sin(u) sin(2v) / 2
z = cos(u) sin(2v) / 2
    0 <= u <= pi,  0 <= v <= pi

Cross Cap
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x = cos(u) * sin(2*v)
y = sin(u) * sin(2*v)
z = cos(v) * cos(v) - cos(u) * cos(u) * sin(v) * sin(v)
    0 <= u <= 2,  0 <= v <= / 2

Teardrop
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r = r1 * sin(u) * sin(u/2)^n1
x = r * sin(v)
y = r * cos(v)
z = r2 * cos(u)
    0 <= u <= pi,   -Pi <= v <= Pi

Horn
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x = (2 + u cos(v)) sin(2 pi u)
y = (2 + u cos(v)) cos(2 pi u) + 2 u
z = u sin(v)
    0 <= u <= 1,  0 <= v <= pi


Whitney Umbrella
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There is a singularity at (0,0,0)
and a self intersection along the line x=y=0.
x = 0.5 sin2(u) cos(2 v)
y = 0.5 sin2(u) sin(2 v)
z = sin(u) sin(v)
    0 <= u <= pi,  0 <= v <= 2 pi


Twisted Pipe Surface
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x = cos(v) * (2 + cos(u)) / sqrt(1 + sin(v)2)
y = sin(v + 2pi/3) * (2 + cos(u + 2pi/3)) / sqrt(1 + sin(v)2)
z = sin(v - 2pi/3) * (2 + cos(u - 2pi/3)) / sqrt(1 + sin(v)2)
    0 <= u <= 2 pi,  0 <= v <= 2 pi

