Fig. 5.

Graphical representation of assumption (P3), in a parametrization of the sphere with 60 patches and one single element per patch. The three elements forming ${\pi }_{\mathbf{F}}(\mathbf{z})$ on the left are colored in different tones of gray, and the corresponding polygon ${\widehat{\pi }}_{\mathbf{F}}(\mathbf{z})$ is the hexagon shown in the middle. The mapping ${\mathbf{F}}_{\mathbf{z}}^{-1}\circ {\mathbf{F}}_m$ is an affine transformation