Streamlines

Integrate a vector field to generate streamlines.

This example generates streamlines of blood velocity. An isosurface of speed provides context. The starting positions for the streamtubes were determined by experimenting with the data.

import numpy as np

import pyvista as pv
from pyvista import examples

Carotid

Download a sample dataset containing a vector field that can be integrated.

mesh = examples.download_carotid()

Run the stream line filtering algorithm using random seed points inside a sphere with radius of 2.0.

streamlines, src = mesh.streamlines(
    return_source=True,
    max_time=100.0,
    initial_step_length=2.0,
    terminal_speed=0.1,
    n_points=25,
    source_radius=2.0,
    source_center=(133.1, 116.3, 5.0),
)

Display the results. Please note that because this dataset’s velocity field was measured with low resolution, many streamlines travel outside the artery.

p = pv.Plotter()
p.add_mesh(mesh.outline(), color="k")
p.add_mesh(streamlines.tube(radius=0.15))
p.add_mesh(src)
p.add_mesh(mesh.contour([160]).extract_all_edges(), color="grey", opacity=0.25)
p.camera_position = [(182.0, 177.0, 50), (139, 105, 19), (-0.2, -0.2, 1)]
p.show()

Static Scene

Interactive Scene

Blood Vessels

Here is another example of blood flow:

mesh = examples.download_blood_vessels().cell_data_to_point_data()
mesh.set_active_scalars("velocity")
streamlines, src = mesh.streamlines(
    return_source=True, source_radius=10, source_center=(92.46, 74.37, 135.5)
)

boundary = mesh.decimate_boundary().extract_all_edges()

sargs = dict(vertical=True, title_font_size=16)
p = pv.Plotter()
p.add_mesh(streamlines.tube(radius=0.2), lighting=False, scalar_bar_args=sargs)
p.add_mesh(src)
p.add_mesh(boundary, color="grey", opacity=0.25)
p.camera_position = [(10, 9.5, -43), (87.0, 73.5, 123.0), (-0.5, -0.7, 0.5)]
p.show()

Static Scene

Interactive Scene

A source mesh can also be provided using the pyvista.DataSetFilters.streamlines_from_source() filter, for example if an inlet surface is available. In this example, the inlet surface is extracted just inside the domain for use as the seed for the streamlines.

source_mesh = mesh.slice('z', origin=(0, 0, 182))  # inlet surface
# thin out ~40% points to get a nice density of streamlines
seed_mesh = source_mesh.decimate_boundary(0.4)
streamlines = mesh.streamlines_from_source(seed_mesh, integration_direction="forward")
# print *only* added arrays from streamlines filter
print("Added arrays from streamlines filter:")
print([array_name for array_name in streamlines.array_names if array_name not in mesh.array_names])

Added arrays from streamlines filter:
['IntegrationTime', 'Vorticity', 'Rotation', 'AngularVelocity', 'Normals', 'ReasonForTermination', 'SeedIds']

Plot streamlines colored by the time along the streamlines.

sargs = dict(vertical=True, title_font_size=16)
p = pv.Plotter()
p.add_mesh(
    streamlines.tube(radius=0.2),
    scalars="IntegrationTime",
    clim=[0, 1000],
    lighting=False,
    scalar_bar_args=sargs,
)
p.add_mesh(boundary, color="grey", opacity=0.25)
p.add_mesh(source_mesh, color="red")
p.camera_position = [(10, 9.5, -43), (87.0, 73.5, 123.0), (-0.5, -0.7, 0.5)]
p.show()

Static Scene

Interactive Scene

Kitchen

kpos = [(-6.68, 11.9, 11.6), (3.5, 2.5, 1.26), (0.45, -0.4, 0.8)]

mesh = examples.download_kitchen()
kitchen = examples.download_kitchen(split=True)

streamlines = mesh.streamlines(n_points=40, source_center=(0.08, 3, 0.71))

p = pv.Plotter()
p.add_mesh(mesh.outline(), color="k")
p.add_mesh(kitchen, color=True)
p.add_mesh(streamlines.tube(radius=0.01), scalars="velocity", lighting=False)
p.camera_position = kpos
p.show()

Static Scene

Interactive Scene

Custom 3D Vector Field

nx = 20
ny = 15
nz = 5

origin = (-(nx - 1) * 0.1 / 2, -(ny - 1) * 0.1 / 2, -(nz - 1) * 0.1 / 2)
mesh = pv.ImageData(dimensions=(nx, ny, nz), spacing=(0.1, 0.1, 0.1), origin=origin)
x = mesh.points[:, 0]
y = mesh.points[:, 1]
z = mesh.points[:, 2]
vectors = np.empty((mesh.n_points, 3))
vectors[:, 0] = np.sin(np.pi * x) * np.cos(np.pi * y) * np.cos(np.pi * z)
vectors[:, 1] = -np.cos(np.pi * x) * np.sin(np.pi * y) * np.cos(np.pi * z)
vectors[:, 2] = np.sqrt(3.0 / 3.0) * np.cos(np.pi * x) * np.cos(np.pi * y) * np.sin(np.pi * z)

mesh['vectors'] = vectors

stream, src = mesh.streamlines(
    'vectors', return_source=True, terminal_speed=0.0, n_points=200, source_radius=0.1
)

cpos = [(1.2, 1.2, 1.2), (-0.0, -0.0, -0.0), (0.0, 0.0, 1.0)]
stream.tube(radius=0.0015).plot(cpos=cpos)

Static Scene

Interactive Scene