Breather (Parametric)

Breather Parametric 003
breather p st
breather p st
breather p sw
breather p sw
Breather animation with bb from 1 to 0. (by Paul Nylander)
       Parametric Breather Surface Parametric Equations

   wsqr := 1 - aa * aa;
        w := sqrt(wsqr);
 denom := aa * (sqr(w * cosh(aa * u)) + sqr(aa * sin(w * v)))

    x = -u + (2 * wsqr * cosh(aa * u) * sinh(aa * u) / denom)
    y = 2 * w * cosh(aa * u) * (-(w * cos(v) * cos(w * v)) - (sin(v) * sin(w * v))) / denom
    z = 2 * w * cosh(aa * u) * (-(w * sin(v) * cos(w * v)) + (cos(v) * sin(w * v))) / denom

DiniKuenBreather.pdf