File:Surfaces of constant positive Gaussian curvature.png

The left-hand surface has a boundary, and the right-hand one has two singular points. Both are surfaces of revolution given by ${\displaystyle (\phi (v)\cos(u),\phi (v)\sin(u),\psi (v))}$ with ${\displaystyle \phi (v)=C\cos v}$, and ${\displaystyle \psi (v)=\int _{0}^{v}{\sqrt {1-C^{2}\sin ^{2}v}}\ dv}$. The left hand surface has ${\displaystyle C=1.4}$, and the right hand one ${\displaystyle C=0.6}$. ${\displaystyle C=1}$ is a sphere.

Image produced by SungSurf and JavaView with en:Elliptical Integral code from [1].