# 3d Vector Wrap of Half sphere

How I can plot the flowing image using Mathematica?

Thanks,

## 1 Answer

The lighting is a bit hard to get right without ray-tracing (though possible in Mathematica on Mac). Here is a first attempt, feel free to improve.

vpts = Catenate@
Table[FromSphericalCoordinates[{1.0, \[Theta], \[Phi]}], {\[Theta],
Range[0, Pi/2, Pi/16] // Rest}, {\[Phi],
Most[Range[-Pi, Pi, Pi/12]] + 0.001}];
SliceVectorPlot3D[{y, -x, z}, "CenterSphere", {x, -1, 1}, {y, -1,
1}, {z, -1, 1}, VectorPoints -> vpts,
VectorColorFunction -> (Blend[{Green, Red}, #3] &),
VectorColorFunctionScaling -> False, VectorScaling -> None,
VectorSizes -> 1.5,
PlotStyle -> Directive[{Opacity[1], GrayLevel[0.3]}],
Lighting -> (DirectionalLight[White, {Append[#, 15], {0, 0, 0}}] & /@
CirclePoints[3]), Boxed -> False, Axes -> False,
ViewVector -> {{0, -10, 2.5}, {0., 0., 0.}},
ViewVertical -> {0, 0, 1}]
`

• Thank you, What about instead of curling the vector are perpendicular to the plan of the sphere, I mean not tangent just perpendicular in the upper half like hedgehog, Commented Aug 23, 2023 at 23:32
• you replace {y, -x, z} with {x, y, z} Commented Aug 24, 2023 at 8:26
• Thanks, it works, What about the 2d projection of the above image? Like 2d vectors in the plane and no sphere? Commented Aug 24, 2023 at 19:58