Viewing 3d Field Lines of an unstructured dataset

I have tried to view field lines of an uncomplete regular grid vector field with first pyVista Streamlines and then with plotly without success... I have yet good results with other 2d streamplots :

2d streamplot of the data

Could someone help me with this ? I found no answer... Here is my data : https://wetransfer.com/downloads/7f3c4ae01e5922e753ea708134f956e720230214141330/bf11ab

import pandas as pd
import numpy as np
import pyvista as pv
import plotly.graph_objects as go
df = pd.read_csv("mix_griddata.csv")
X = df['X']
Y = df['Y']
Z = df['Z']
Vx = df['Vx']
Vy = df['Vy']
Vz = df['Vz']
fig = go.Figure(data=go.Streamtube(
x = X,
y = Y,
z = Z,
u = Vx,
v = Vy,
w = Vz,
starts = dict(
x = X.sample(frac=0.01,replace=False),
y = Y.sample(frac=0.01,replace=False),
z = Z.sample(frac=0.01,replace=False)
),
sizeref =1,
colorscale = 'Portland',
showscale = False,
maxdisplayed = 30000000
))
fig.update_layout(
scene = dict(
aspectratio = dict(
x = 1,
y = 1,
z = 1
)
),
margin = dict(
t = 10,
b = 10,
l = 10,
r = 10
)
)
fig.show(renderer="browser")
#Streamlines
mix_FD_grid = np.load("C:/Users/hd377/OneDrive - ensam.eu/0-Thesis/Fibres_Direction_in_allvolume/mix/mix_FD_grid.npy")
origin = (0,0,0)
mesh = pv.UniformGrid(dimensions=mix_FD_grid[:,:,:,0].shape, spacing=(1, 1, 1), origin=origin)
vectors = np.empty((mesh.n_points, 3))
vectors[:, 0] = mix_FD_grid[:,:,:,0].flatten()
vectors[:, 1] = mix_FD_grid[:,:,:,1].flatten()
vectors[:, 2] = mix_FD_grid[:,:,:,2].flatten()
mesh['vectors'] = vectors
stream, src = mesh.streamlines(
'vectors', return_source=True, max_steps = 20000, n_points=200, source_radius=25, source_center=(15, 0, 30)
)
p = pv.Plotter()
p.add_mesh(mesh.outline(), color="k")
p.add_mesh(stream.tube(radius=0.1))
p.camera_position = [(182.0, 177.0, 50), (139, 105, 19), (-0.2, -0.2, 1)]
p.show() 

The plotly window does appear in my browser but no tube are visible at all, and the axes values are false.
The pyVista does show something, but in the wrong direction, and clearly not what expected (longitudinal flux circumventing a central cone).

I'll only be tackling PyVista. It's hard to say for sure and I'm only guessing, but your data is probably laid out in the wrong order.

1. For starters, your data is inconsistent to begin with: your CSV has 1274117 rows whereas your multidimensional array has shape (37, 364, 100, 3), for a total of 1346800 vectors. And your question title says "unstructured", but your PyVista attempt uses a uniform grid with.
2. Secondly, your CSV doesn't correspond to a regular grid in the first place, e.g. at the end of the file you have 15 rows starting with 368.693,36.971999999999994, then 8 rows starting with 369.71999999999997,36.971999999999994, then a single row starting with 370.74699999999996,36.971999999999994. In a regular grid you'd get the same number of items in each block.
3. Thirdly, your CSV has an unusual (MATLAB-smelling) layout that the order of axes is z-x-y (rather than either x-y-z or z-y-x). This is a strong clue that your data is mangled due to memory layout issues when flattened. But the previous two point mean that I can't verify how your 4d array was created, I have to take it for granted that it's correct.

Just plotting your raw data makes it obvious that the data is mangled in your original version (with some style cleanup):

import numpy as np
import pyvista as pv

mix_FD_grid = np.load("mix_FD_grid.npy")

origin = (0, 0, 0)
mesh = pv.UniformGrid(dimensions=mix_FD_grid.shape[:-1], spacing=(1, 1, 1), origin=origin)
vectors = np.empty_like(mesh.points)
vectors[:, 0] = mix_FD_grid[..., 0].ravel()
vectors[:, 1] = mix_FD_grid[..., 1].ravel()
vectors[:, 2] = mix_FD_grid[..., 2].ravel()
mesh.point_data['vectors'] = vectors

mesh.plot()

The fragmented pattern you can see is a hallmark of data mangling due to mistaken memory layout.

If we assume the layout is more or less sane, trying column-major layout ("F" for "Fortran", also used by MATLAB) seems to make a lot more sense:

vectors[:, 0] = mix_FD_grid[..., 0].ravel('F')
vectors[:, 1] = mix_FD_grid[..., 1].ravel('F')
vectors[:, 2] = mix_FD_grid[..., 2].ravel('F')
mesh.point_data['vectors'] = vectors

mesh.plot()

So we can try using streamlines using that:

stream, src = mesh.streamlines(
    'vectors', return_source=True, max_steps=20000, n_points=200, source_radius=25, source_center=(15, 0, 30)
)

p = pv.Plotter()
p.add_mesh(mesh.outline(), color="k")
p.add_mesh(stream.tube(radius=0.1))
p.show()

It doesn't look great:

So, you said that the streamlines should be longitudinal, but here they are clearly transversal. Can it be that the x and y field components are swapped? I can't tell, so let's try!

import numpy as np
import pyvista as pv

mix_FD_grid = np.load("mix_FD_grid.npy")

origin = (0, 0, 0)
mesh = pv.UniformGrid(dimensions=mix_FD_grid.shape[:-1], spacing=(1, 1, 1), origin=origin)
vectors = np.empty_like(mesh.points)
vectors[:, 0] = mix_FD_grid[..., 1].ravel('F')  # swap 0 <-> 1
vectors[:, 1] = mix_FD_grid[..., 0].ravel('F')  # swap 0 <-> 1
vectors[:, 2] = mix_FD_grid[..., 2].ravel('F')
mesh.point_data['vectors'] = vectors

stream, src = mesh.streamlines(
    'vectors', return_source=True, max_steps=20000, n_points=200, source_radius=25, source_center=(15, 0, 30)
)

p = pv.Plotter()
p.add_mesh(mesh.outline(), color="k")
p.add_mesh(stream.tube(radius=0.1))
p.show()

Now we're talking!

Bonus: y field component on a volumetric plot:

mesh.plot(volume=True, scalars=vectors[:, 1], show_scalar_bar=False)