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([[-200.33034637, -199.62351341,    1.83323185],
       [-181.80403476, -199.62351341,    2.61184659],
       [-158.50699013, -199.62351341,    3.88246218],
       [-140.42331462, -199.62351341,    5.08735203],
       [-113.64744938, -199.62351341,    7.14852251]])

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:

[(640.6378803041428, 641.287784725254, 691.2426519530368),
 (-0.12622157168897274, 0.5236828494222863, 50.47855007720499),
 (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:

[(640.6378803041428, 641.287784725254, 691.2426519530368),
 (-0.12622157168897274, 0.5236828494222863, 50.47855007720499),
 (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	5.944e-03, 9.248e+00
Y Bounds	4.427e-02, 9.297e+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:

[(4.627080308767694, 4.670638655330208, 25.264652517472054),
 (4.627080308767694, 4.670638655330208, 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:

[(4.627080308767694, 4.670638655330208, 25.264652517472054),
 (4.627080308767694, 4.670638655330208, 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:

[(4.627080308767694, 4.670638655330208, 25.264652517472054),
 (4.627080308767694, 4.670638655330208, 0.0),
 (0.0, 1.0, 0.0)]