# 1.2-create-tri-surface

%matplotlib inline
from pyvista import set_plot_theme
set_plot_theme('document')

# 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, :]
array([[-197.58765542, -198.28684883, 1.98822521], [-175.84882467, -198.28684883, 2.9836459 ], [-161.80819309, -198.28684883, 3.78176903], [-136.67169993, -198.28684883, 5.50319475], [-112.29205961, -198.28684883, 7.45444972]])

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

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

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)

x = np.arange(10, dtype=float)
xx, yy, zz = np.meshgrid(x, x, )
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

Run the triangulation on these points

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

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)

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.show(cpos="xy")