球面と北半球・南半球
\( \boldsymbol{x}(u_{1}, v_{1}) = \begin{pmatrix} \cos u_{1} \hskip 0.1em \cos v_{1} \\ \cos u_{1} \hskip 0.1em \sin v_{1} \\ \sin u_{1} \end{pmatrix} \)

\( \left( - \dfrac{4 \pi}{9} \leq u_{1} \leq \dfrac{4 \pi}{9}, \, 0 \leq v_{1} \leq 2 \pi \right) \),

\( \boldsymbol{x}_{\pm}(u_{2}, v_{2}) = \begin{pmatrix} u_{2} \\ v_{2} \\ \pm \sqrt{1 - u_{2}^{2} - v_{2}^{2}} \end{pmatrix} \)

\( (u_{2}^{2} + v_{2}^{2} \leq 0.99) \)