These images show mobius transformations stereographically projected onto the Riemann sphere. Note in particular that when projected onto a sphere, the special case of a fixed point at infinity looks no different to having the fixed points in an arbitrary location.
| Elliptic | Hyperbolic | Loxodromic | |
| One fixed point at Infinity |  |
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| Full Size | Full Size | Full Size | |
| Fixed points diametrically opposite |  |
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| Full Size | Full Size | Full Size | |
| Fixed points in an arbitrary location |  |
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| Full Size | Full Size | Full Size |
