Animating L1 norm ball projections, as in
https://mathematica.stackexchange.com/questions/280517/intersecting-plane-and-l1-ball
https://mathematica.stackexchange.com/questions/280517/intersecting-plane-and-l1-ball
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makePlot[θ_]:=ContourPlot3D[{Cos[θ],Sin[θ]}.{x,y}==0,{x,-b,b},{y,-b,b},{z,-b,b},PlotPoints->60,MaxRecursion->4,MeshFunctions->Function[{x,y,z},Norm[{x,y,z},1]-1],Mesh->{{0}},MeshShading->{Red,None},BoundaryStyle->None,ViewPoint->{Cos[θ],Sin[θ],0},Boxed->False,Axes->None,ViewProjection->"Orthographic"];Manipulate[makePlot[θ],{{θ,π/2},0,2π}]
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plots=makePlot/@Table[t,{t,0,Pi/2,Pi/200}];ListAnimate[plots]
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Export["~/Desktop/l1-ball.gif",plots]
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~/Desktop/l1-ball.gif