# Create Triangulated Surface#

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

Note

We will use a filter from PyVista to perform our triangulation: delaunay_2d.

```import numpy as np
import pyvista as pv
```

## 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, :]
```

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 = ...
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. See `pyvista.UnstructuredGridFilters.delaunay_2d()`.

```help(cloud.delaunay_2d)
```

Apply the `delaunay_2d` filter.

```surf = ...

# And plot it with edges shown
surf.plot(show_edges=True)
```

## Clean Edges & Triangulations#

```# Create the points to triangulate
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
```
```cloud.plot(cpos="xy")
```

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

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