Creating a Structured Surface

Create a StructuredGrid surface from NumPy arrays

# sphinx_gallery_thumbnail_number = 2
import pyvista as pv
import numpy as np

From NumPy Meshgrid

Create a simple meshgrid using NumPy

# Make data
x = np.arange(-10, 10, 0.25)
y = np.arange(-10, 10, 0.25)
x, y = np.meshgrid(x, y)
r = np.sqrt(x ** 2 + y ** 2)
z = np.sin(r)

Now pass the NumPy meshgrid to PyVista

# Create and plot structured grid
grid = pv.StructuredGrid(x, y, z)
grid.plot()
../../_images/sphx_glr_create-structured-surface_001.png
# Plot mean curvature as well
grid.plot_curvature(clim=[-1, 1])
../../_images/sphx_glr_create-structured-surface_002.png

Out:

WARNING:root:DEPRECATED: ``.tri_filter`` is deprecated. Use ``.triangulate`` instead.

Generating a structured grid is a one liner in this module, and the points from the resulting surface can be accessed as a NumPy array:

print(grid.points)

Out:

[[-10.         -10.           0.99998766]
 [-10.          -9.75         0.98546793]
 [-10.          -9.5          0.9413954 ]
 ...
 [  9.75         9.25         0.76645876]
 [  9.75         9.5          0.86571785]
 [  9.75         9.75         0.93985707]]

From XYZ Points

Quite often, you might be given a set of coordinates (XYZ points) in a simple tabular format where there exists some structure such that grid could be built between the nodes you have. A great example is found in pyvista-support#16 where a strucutred grid that is rotated from the cartesian reference frame is given as just XYZ points. In these cases, all that is needed to recover the grid is the dimensions of the grid (nx by ny by nz) and that the coordinates are ordered appropriately.

For this example, we will create a small dataset and rotate the coordinates such that they are not on orthogonal to cartesian reference frame.

def make_point_set():
    """Ignore the contents of this function. Just know that it returns an
    n by 3 numpy array of structured coordinates."""
    n, m = 29, 32
    x = np.linspace(-200, 200, num=n) + np.random.uniform(-5, 5, size=n)
    y = np.linspace(-200, 200, num=m) + np.random.uniform(-5, 5, size=m)
    xx, yy = np.meshgrid(x, y)
    A, b = 100, 100
    zz = A * np.exp(-0.5 * ((xx / b) ** 2.0 + (yy / b) ** 2.0))
    points = np.c_[xx.reshape(-1), yy.reshape(-1), zz.reshape(-1)]
    foo = pv.PolyData(points)
    foo.rotate_z(36.6)
    return foo.points


# Get the points as a 2D NumPy array (N by 3)
points = make_point_set()
print(points[0:5, :])

Out:

[[ -38.43433214 -276.10381337    2.053703  ]
 [ -31.5324676  -270.97803641    2.42056395]
 [ -21.27897134 -263.36311805    3.0481165 ]
 [  -8.63003441 -253.96918846    3.96073208]
 [   3.43196509 -245.01115706    4.96820155]]

Now pretend that the (n by 3) NumPy array above are coordinates that you have, possibly from a file with three columns of XYZ points.

We simply need to recover the dimensions of the grid that these points make and then we can generate a pyvista.StructuredGrid mesh.

Let’s preview the points to see what we are dealing with:

import matplotlib.pyplot as plt

plt.figure(figsize=(10, 10))
plt.scatter(points[:, 0], points[:, 1], c=points[:, 2])
plt.axis("image")
plt.xlabel("X Coordinate")
plt.ylabel("Y Coordinate")
plt.show()
../../_images/sphx_glr_create-structured-surface_003.png

Out:

/home/travis/build/pyvista/pyvista/examples/00-load/create-structured-surface.py:100: UserWarning: Matplotlib is currently using agg, which is a non-GUI backend, so cannot show the figure.
  plt.show()

In the figure above, we can see some inherit structure to the points and thus we could connect the points as a structured gird. All we need to know are the dimensions of the grid present. In this case, we know (because we made this dataset) the dimensions are [29, 32, 1], but you might not know the dimensions of your pointset. There are a few ways to figure out the dimensionality of structured grid including:

  • manually conting the the nodes along the edges of the pointset

  • using a technique like principle component analysis to strip the rotation from the dataset and count the unique values along each axis for the new;y projected dataset.

# Once you've figured out your grid's dimensions, simple create the
# :class:`pyvista.StructuredGrid` as follows:

mesh = pv.StructuredGrid()
# Set the coordinates from the numpy array
mesh.points = points
# set the dimensions
mesh.dimensions = [29, 32, 1]

# and then inspect it!
mesh.plot(show_edges=True, show_grid=True, cpos="xy")
../../_images/sphx_glr_create-structured-surface_004.png

Total running time of the script: ( 0 minutes 4.709 seconds)

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