# Volumetric Analysis#

Calculate mass properties such as the volume or area of datasets

```import numpy as np

from pyvista import examples
```

Computing mass properties such as the volume or area of datasets in PyVista is quite easy using the `pyvista.DataSetFilters.compute_cell_sizes()` filter and the `pyvista.DataSet.volume` property on all PyVista meshes.

Let’s get started with a simple gridded mesh:

```# Load a simple example mesh
dataset.set_active_scalars("Spatial Cell Data")
```

We can then calculate the volume of every cell in the array using the `.compute_cell_sizes` filter which will add arrays to the cell data of the mesh core the volume and area by default.

```# Compute volumes and areas
sized = dataset.compute_cell_sizes()

# Grab volumes for all cells in the mesh
cell_volumes = sized.cell_data["Volume"]
```

We can also compute the total volume of the mesh using the `.volume` property:

```# Compute the total volume of the mesh
volume = dataset.volume
```

Okay awesome! But what if we have have a dataset that we threshold with two volumetric bodies left over in one dataset? Take this for example:

```threshed = dataset.threshold_percent([0.15, 0.50], invert=True)
threshed.plot(show_grid=True, cpos=[-2, 5, 3])
``` We could then assign a classification array for the two bodies, compute the cell sizes, then extract the volumes of each body. Note that there is a simpler implementation of this below in Splitting Volumes.

```# Create a classifying array to ID each body
rng = dataset.get_data_range()
cval = ((rng - rng) * 0.20) + rng
classifier = threshed.cell_data["Spatial Cell Data"] > cval

# Compute cell volumes
sizes = threshed.compute_cell_sizes()
volumes = sizes.cell_data["Volume"]

# Split volumes based on classifier and get volumes!
idx = np.argwhere(classifier)
hvol = np.sum(volumes[idx])
idx = np.argwhere(~classifier)
lvol = np.sum(volumes[idx])

print(f"Low grade volume: {lvol}")
print(f"High grade volume: {hvol}")
print(f"Original volume: {dataset.volume}")
```

Out:

```Low grade volume: 518.0
High grade volume: 35.0
Original volume: 729.0
```

Or better yet, you could simply extract the largest volume from your thresholded dataset by passing `largest=True` to the `connectivity` filter or by using `extract_largest` filter (both are equivalent).

```# Grab the largest connected volume present
largest = threshed.connectivity(largest=True)
# or: largest = threshed.extract_largest()

# Get volume as numeric value
large_volume = largest.volume

# Display it!
largest.plot(show_grid=True, cpos=[-2, 5, 3])
``` ## Splitting Volumes#

What if instead, we wanted to split all the different connected bodies / volumes in a dataset like the one above? We could use the `pyvista.DataSetFilters.split_bodies()` filter to extract all the different connected volumes in a dataset into blocks in a `pyvista.MultiBlock` dataset. For example, lets split the thresholded volume in the example above:

```# Load a simple example mesh
dataset.set_active_scalars("Spatial Cell Data")
threshed = dataset.threshold_percent([0.15, 0.50], invert=True)

bodies = threshed.split_bodies()

for i, body in enumerate(bodies):
print(f"Body {i} volume: {body.volume:.3f}")
```

Out:

```Body 0 volume: 518.000
Body 1 volume: 35.000
```
```bodies.plot(show_grid=True, multi_colors=True, cpos=[-2, 5, 3])
``` ## A Real Dataset#

Here is a realistic training dataset of fluvial channels in the subsurface. This will threshold the channels from the dataset then separate each significantly large body and compute the volumes for each!

Load up the data and threshold the channels:

```data = examples.load_channels()
channels = data.threshold([0.9, 1.1])
```

Now extract all the different bodies and compute their volumes:

```bodies = channels.split_bodies()
# Now remove all bodies with a small volume
for key in bodies.keys():
b = bodies[key]
vol = b.volume
if vol < 1000.0:
del bodies[key]
continue
# Now lets add a volume array to all blocks
b.cell_data["TOTAL VOLUME"] = np.full(b.n_cells, vol)
```

Print out the volumes for each body:

```for i, body in enumerate(bodies):
print(f"Body {i:02d} volume: {body.volume:.3f}")
```

Out:

```Body 00 volume: 66761.000
Body 01 volume: 16120.000
Body 02 volume: 1150.000
Body 03 volume: 5166.000
Body 04 volume: 2085.000
Body 05 volume: 12490.000
Body 06 volume: 152667.000
Body 07 volume: 32520.000
Body 08 volume: 18238.000
Body 09 volume: 152638.000
Body 10 volume: 1889.000
Body 11 volume: 31866.000
Body 12 volume: 9861.000
Body 13 volume: 108024.000
Body 14 volume: 1548.000
Body 15 volume: 27857.000
Body 16 volume: 1443.000
Body 17 volume: 8239.000
Body 18 volume: 12550.000
Body 19 volume: 18269.000
Body 20 volume: 2270.000
```

And visualize all the different volumes:

```bodies.plot(scalars="TOTAL VOLUME", cmap="viridis", show_grid=True)
``` Total running time of the script: ( 0 minutes 5.924 seconds)

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