Vector plot of magnetization

Questions
,
1

I would like to see the change of Magnetic Field of Polar-Anisotropic by changing magnetization definition.

The below magnetization image is R= cos(3phi), φ＝sin(3phi),z=0 in FEM software (equation maybe fault) in cylindrical cordinate.

Can Mathematica make these vector image to understand magnetization?
(FEM is not needed. It is OK by simple vector calculation)

Reference

スクリーンショット2024-08-104.57.41.jpg
スクリーンショット2024-08-104.57.41.jpg1006×632 137 KB

2

I would like to see the change of magnetization by direction definition.

I think below image is definition by R=cos(3Phi), Phi＝sin(3Phi),Z=0 (cylindrical coordinate) in FEM software.

Can Mathematica visualize this vector combination?
I would like to see the direction change by changing R, Phi, Z.

スクリーンショット2024-08-109.11.25.jpg
スクリーンショット2024-08-109.11.25.jpg788×676 135 KB

Reference

3

You may consider StreamPlot3D. VectorPlot3D, SliceVectorPlot3D.

4

Thanks for your comment

I will use 3D Vector Plot.
I am straggling how to input triangle function as vector plot definition.

スクリーンショット2024-08-110.27.14.jpg
スクリーンショット2024-08-110.27.14.jpg1120×950 199 KB

5

What is a triangle function?

6

Sorry I mean trigonometric functions.

To make polar anisotropic, I would like to change the direction by each position by using trigonometric function.

7

This is a way:

VectorPlot3D[RotationMatrix[Pi/3, {0, 0, 1}] . {x, y, z},
 {x, -1, 1}, {y, -1, 1}, {z, -1, 1} ]