# Integrate Data
# ==============

# Integrate data over a surface using the
# `pyvista.DataSetFilters.integrate_data()` filter.
import pyvista as pv
from pyvista import examples

# This example calculates the total flow rate and average velocity inside a
# blood vessel.  The boundary object is only used for plotting the shape of
# the dataset geometry.  The inlet surface is generated by slicing the domain.
# Fluid flowing into the domain is in the negative z-direction, so
# a new array, `normal_velocity`, is created.
dataset = examples.download_blood_vessels()
boundary = dataset.decimate_boundary().extract_all_edges()
inlet_surface = dataset.slice('z', origin=(0, 0, 182))
inlet_surface['normal_velocity'] = -1 * inlet_surface['velocity'][:, 2]

# The velocity in the inlet is shown.
pl = pv.Plotter()
pl.add_mesh(boundary, color='grey', opacity=0.25)
pl.add_mesh(
    inlet_surface,
    scalars='normal_velocity',
    component=2,
    scalar_bar_args=dict(vertical=True, title_font_size=16),
    lighting=False,
)
pl.add_axes()
pl.camera_position = pv.CameraPosition(
    position=(10, 9.5, -43), focal_point=(87.0, 73.5, 123.0), viewup=(-0.5, -0.7, 0.5)
)
pl.show()

# The total flow rate is calculated using the
# `pyvista.DataSetFilters.integrate_data()` filter.  Note that the data
# is a `pyvista.UnstructuredGrid` object with only 1 point and 1 cell.
integrated_data = inlet_surface.integrate_data()
integrated_data

# Each array in `integrated_data` stores the integrated data.
integrated_data['normal_velocity']

# An additional `Area` or `Volume` array is added.
print(f'Original arrays: {inlet_surface.array_names}')
new_arrays = [
    name for name in integrated_data.array_names if name not in inlet_surface.array_names
]
print(f'New arrays      : {new_arrays}')

# Display the total flow rate, area of inlet surface, and average velocity.
total_flow_rate = integrated_data['normal_velocity'][0]
area = integrated_data['Area'][0]
average_velocity = total_flow_rate / area
print(f'Total flow rate : {total_flow_rate:.1f}')
print(f'Area            : {area:.0f}')
print(f'Average velocity: {average_velocity:.3f}')

# Volume Integration
# ==================

# You can also integrate over a volume. Here, we effectively sum the cell and
# point data across the entire volume. You can use this to compute mean values
# by dividing by the volume of the dataset.
# Note that the calculated volume is the same as `pyvista.DataSet.volume`.
# Also note that the center of the dataset is the "point" of the integrated
# volume.
integrated_volume = dataset.integrate_data()
center = integrated_volume.points[0]
volume = integrated_volume['Volume'][0]
mean_density = integrated_volume['density'][0] / volume
mean_velocity = integrated_volume['velocity'][0] / volume

print(f'Center          : {center}')
print(f'Volume          : {volume:.0f}')
print(f'Mean density    : {mean_density:.4f}')
print(f'Mean velocity   : {mean_velocity}')

# ----------------------------------------------------------------------
# Generated by sphinx-examples-as-code https://github.com/pyvista/sphinx-examples-as-code