# Compare Field Across Mesh Regions#

Here is some velocity data from a glacier modelling simulation that is compared across nodes in the simulation. We have simplified the mesh to have the simulation node value already on the mesh.

This was originally posted to pyvista/pyvista-support#83.

The modeling results are courtesy of Urruty Benoit and are from the Elmer/Ice simulation software.

```import numpy as np

import pyvista as pv
from pyvista import examples

mesh["magnitude"] = np.linalg.norm(mesh["ssavelocity"], axis=1)
mesh
```
PolyDataInformation
N Cells1106948
N Points557470
N Strips0
X Bounds-2.506e+06, 2.743e+06
Y Bounds-2.143e+06, 2.240e+06
Z Bounds0.000e+00, 0.000e+00
N Arrays3
NameFieldTypeN CompMinMax
ssavelocityPointsfloat643-4.341e+039.677e+03
node_valuePointsint6410.000e+002.300e+01
magnitudePointsfloat6416.649e-031.013e+04

Here is a helper to extract regions of the mesh based on the simulation node.

```def extract_node(node):
idx = mesh["node_value"] == node
return mesh.extract_points(idx)
```
```p = pv.Plotter()
for node in np.unique(mesh["node_value"]):
loc = extract_node(node).center
p.show(cpos="xy")
```
```vel_dargs = dict(scalars="magnitude", clim=[1e-3, 1e4], cmap='Blues', log_scale=True)

mesh.plot(cpos="xy", **vel_dargs)
```
```a = extract_node(12)
b = extract_node(20)
```
```pl = pv.Plotter()
pl.show(cpos='xy')
```

plot vectors without mesh

```pl = pv.Plotter()
pl.camera_position = [
(-1114684.6969340036, 293863.65389149904, 752186.603224546),
(-1114684.6969340036, 293863.65389149904, 0.0),
(0.0, 1.0, 0.0),
]
pl.show()
```

Compare directions. Normalize them so we can get a reasonable direction comparison.

```flow_a = a.point_data['ssavelocity'].copy()
flow_a /= np.linalg.norm(flow_a, axis=1).reshape(-1, 1)
flow_b = b.point_data['ssavelocity'].copy()
flow_b /= np.linalg.norm(flow_b, axis=1).reshape(-1, 1)

# plot normalized vectors
pl = pv.Plotter()
pl.camera_position = [
(-1044239.3240694795, 354805.0268606294, 484178.24825854995),
(-1044239.3240694795, 354805.0268606294, 0.0),
(0.0, 1.0, 0.0),
]
pl.show()
```

flow_a that agrees with the mean flow path of flow_b

```agree = flow_a.dot(flow_b.mean(0))

pl = pv.Plotter()
pl.add_mesh(a, scalars=agree, cmap='bwr', scalar_bar_args={'title': 'Flow agreement with block b'})
```agree = flow_b.dot(flow_a.mean(0))