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Suppose I have some vector field equations $(f(\theta,\phi), g(\theta,\phi))$. The StreamPlot can be created easily in 2D, but I would like to visualize the stream line plot in a 3D spherical surface $(\theta,\phi)$, so how can it be done? As an example:

StreamPlot[{Cot[\[Theta]]Cos[\[Phi]],- Sin[\[Phi]]}, {\[Phi],-\[Pi],\[Pi]},{\[Theta],0,\[Pi]}, StreamColorFunction->Hue] 

Ideally, the front of spherical surface should be partially transparent so that the flow line at the rear end can be visualized at the same time.

Suppose I have some vector field equations $(f(\theta,\phi), g(\theta,\phi))$. The StreamPlot can be created easily in 2D, but I would like to visualize the stream line plot in a 3D spherical surface $(\theta,\phi)$, so how can it be done? As an example:

StreamPlot[{Cot[θ]Cos[ϕ],- Sin[ϕ]}, {ϕ,-π,π},{θ,0,π}, StreamColorFunction->Hue] 

Ideally, the front of spherical surface should be partially transparent so that the flow line at the rear end can be visualized at the same time.