Breather surface

Breather surface

s.

Parametrization

:egin{align}x & {} = frac{2left(1-a^2 ight)cosh(au)sinh(au)}{aleft(sqrt{1-a^2}cosh^2(au)+left(a,sin^2left(sqrt{1-a^2}v ight) ight) ight)}-u \ \y & {} = frac{2sqrt{1-a^2}cosh(u)left(-sqrt{1-a^2}cos(v)cosleft(sqrt{1-a^2}v ight)-sin(v)sinleft(sqrt{1-a^2}v ight) ight)}{aleft(sqrt{1-a^2}cosh^2(au)+left(a,sin^2left(sqrt{1-a^2}v ight) ight) ight)} \ \z & {} = frac{2sqrt{1-a^2}cosh(au)left(-sqrt{1-a^2}sin(v)cosleft(sqrt{1-a^2}v ight)+cos(v)sinleft(sqrt{1-a^2}v ight) ight)}{aleft(sqrt{1-a^2}cosh^2(au)+left(a,sin^2left(sqrt{1-a^2}v ight) ight) ight)}end{align}where 0 < "a" < 1.

ee also

* Breather

References

* [http://xahlee.org/surface/breather_p/breather_p.html Xah Lee Web - Surface Gallery]


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