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Geodesics on the paraboloid. This was a test picture after replacing the canned DSolve routines with
own Runge Kutta routines which is necessary when doing the evolution on manifolds with different
charts and also allows a bit more control in general like assuring that the flow stays on the unit tangent
bundle. The surface is the elliptic paraboloid z=x^{2} + 2 y^{2}.

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Same picture but with wave fronts added.

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Geodesics and wave fronts on the monkey saddle surface
z = 6 x y^{2}2x^{3}3y^{4}.
