# 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 Traingulations¶

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([[-195.33087704, -196.68361973,    2.14521611],
[-177.17593253, -196.68361973,    3.00832161],
[-158.71611811, -196.68361973,    4.10172479],
[-135.5600617 , -196.68361973,    5.76682319],
[-112.23285819, -196.68361973,    7.69935955]])
```

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:

```[(640.2590658397567, 639.5863399361687, 687.6519214726571),
(3.2602260632090037, 2.5875001596209586, 50.653081696109474),
(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:

```[(640.2590658397567, 639.5863399361687, 687.6519214726571),
(3.2602260632090037, 2.5875001596209586, 50.653081696109474),
(0.0, 0.0, 1.0)]
```

```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
```
PolyDataInformation
N Cells100
N Points100
X Bounds4.666e-02, 9.281e+00
Y Bounds2.587e-02, 9.253e+00
Z Bounds0.000e+00, 0.000e+00
N Arrays0

Run the triangulation on these points

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

```[(4.663633749724465, 4.639613562413302, 25.218782834786982),
(4.663633749724465, 4.639613562413302, 0.0),
(0.0, 1.0, 0.0)]
```

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

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

```[(4.663633749724465, 4.639613562413302, 25.218782834786982),
(4.663633749724465, 4.639613562413302, 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.show(cpos="xy")
``` Out:

```[(4.663633749724465, 4.639613562413302, 25.218782834786982),
(4.663633749724465, 4.639613562413302, 0.0),
(0.0, 1.0, 0.0)]
```

Total running time of the script: ( 0 minutes 3.106 seconds)

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