Create Triangulated Surface

Create a surface from a set of points through a Delaunay triangulation.

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

Simple Triangulations

First, create some points for the surface.

# Define a simple Gaussian surface
n = 20
x = np.linspace(-200, 200, num=n) + np.random.uniform(-5, 5, size=n)
y = np.linspace(-200, 200, num=n) + np.random.uniform(-5, 5, size=n)
xx, yy = np.meshgrid(x, y)
A, b = 100, 100
zz = A * np.exp(-0.5 * ((xx / b) ** 2.0 + (yy / b) ** 2.0))

# Get the points as a 2D NumPy array (N by 3)
points = np.c_[xx.reshape(-1), yy.reshape(-1), zz.reshape(-1)]
points[0:5, :]

Out:

array([[-204.14829829, -196.62362683,    1.80092653],
       [-182.5521267 , -196.62362683,    2.73426786],
       [-160.14758257, -196.62362683,    4.01390766],
       [-138.83439864, -196.62362683,    5.52000156],
       [-118.44486895, -196.62362683,    7.17547029]])

Now use those points to create a point cloud PyVista data object. This will be encompassed in a pyvista.PolyData object.

# simply pass the numpy points to the PolyData constructor
cloud = pv.PolyData(points)
cloud.plot(point_size=15)

Out:

[(640.4307389872978, 646.2137442908282, 693.2589977868738),
 (-2.441270141366246, 3.3417351621642553, 50.386988658209866),
 (0.0, 0.0, 1.0)]

Now that we have a PyVista data structure of the points, we can perform a triangulation to turn those boring discrete points into a connected surface.

surf = cloud.delaunay_2d()
surf.plot(show_edges=True)

Out:

[(640.4307389872978, 646.2137442908282, 693.2589977868738),
 (-2.441270141366246, 3.3417351621642553, 50.386988658209866),
 (0.0, 0.0, 1.0)]

Masked Triangulations

x = np.arange(10, dtype=float)
xx, yy, zz = np.meshgrid(x, x, [0])
points = np.column_stack((xx.ravel(order="F"),
                          yy.ravel(order="F"),
                          zz.ravel(order="F")))
# Perturb the points
points[:, 0] += np.random.rand(len(points)) * 0.3
points[:, 1] += np.random.rand(len(points)) * 0.3
# Create the point cloud mesh to triangulate from the coordinates
cloud = pv.PolyData(points)
cloud

PolyData	Information
N Cells	100
N Points	100
X Bounds	2.049e-03, 9.296e+00
Y Bounds	2.409e-02, 9.278e+00
Z Bounds	0.000e+00, 0.000e+00
N Arrays	0

Run the triangulation on these points

surf = cloud.delaunay_2d()
surf.plot(cpos="xy", show_edges=True)

Out:

[(4.649158510057484, 4.650947530159079, 25.33699996306456),
 (4.649158510057484, 4.650947530159079, 0.0),
 (0.0, 1.0, 0.0)]

Note that some of the outer edges are unconstrained and the triangulation added unwanted triangles. We can mitigate that with the alpha parameter.

surf = cloud.delaunay_2d(alpha=1.0)
surf.plot(cpos="xy", show_edges=True)

Out:

[(4.649158510057484, 4.650947530159079, 25.33699996306456),
 (4.649158510057484, 4.650947530159079, 0.0),
 (0.0, 1.0, 0.0)]

We could also add a polygon to ignore during the triangulation via the edge_source parameter.

# Define a polygonal hole with a clockwise polygon
ids = [22, 23, 24, 25, 35, 45, 44, 43, 42, 32]

# Create a polydata to store the boundary
polygon = pv.PolyData()
# Make sure it has the same points as the mesh being triangulated
polygon.points = points
# But only has faces in regions to ignore
polygon.faces = np.array([len(ids),] + ids)

surf = cloud.delaunay_2d(alpha=1.0, edge_source=polygon)

p = pv.Plotter()
p.add_mesh(surf, show_edges=True)
p.add_mesh(polygon, color="red", opacity=0.5)
p.show(cpos="xy")

Out:

[(4.649158510057484, 4.650947530159079, 25.33699996306456),
 (4.649158510057484, 4.650947530159079, 0.0),
 (0.0, 1.0, 0.0)]