${\displaystyle x=\int \limits _{0}^{u}{\sqrt {a^{2}\sin ^{2}\alpha +b^{2}\cos ^{2}\alpha }}d\alpha +{\frac {{\sqrt {a^{2}-b^{2}}}\sin u\left({\sqrt {a^{2}-b^{2}}}\cos u+a\right)}{\sqrt {a^{2}\sin ^{2}u+b^{2}\cos ^{2}u}}}}$

${\displaystyle y=b\left[{\frac {{\sqrt {a^{2}-b^{2}}}\cos u+a}{\sqrt {a^{2}\sin ^{2}u+b^{2}\cos ^{2}u}}}\right]\cos v}$

${\displaystyle z=b\left[{\frac {{\sqrt {a^{2}-b^{2}}}\cos u+a}{\sqrt {a^{2}\sin ^{2}u+b^{2}\cos ^{2}u}}}\right]\sin v}$

where ${\displaystyle a}$ and ${\displaystyle b}$ are parameters. For the plot ${\displaystyle a=1.7}$ and ${\displaystyle b=1.2}$.