# Create Triangulated Surface#

Create a surface from a set of points through a Delaunay triangulation. This example uses `pyvista.PolyDataFilters.delaunay_2d()`.

```from __future__ import annotations

import numpy as np

import pyvista as pv

# Seed random numbers for reproducibility
rng = np.random.default_rng(seed=0)
```

## Simple Triangulations#

First, create some points for the surface.

```# Define a simple Gaussian surface
n = 20
x = np.linspace(-200, 200, num=n) + rng.uniform(-5, 5, size=n)
y = np.linspace(-200, 200, num=n) + rng.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([[-198.63038313, -204.71680329,    1.71090121],
[-181.24950128, -204.71680329,    2.38012408],
[-162.4850016 , -204.71680329,    3.28594053],
[-141.67682891, -204.71680329,    4.5091358 ],
[-112.65677129, -204.71680329,    6.52176016]])
```

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)
```

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, [0])
points = np.column_stack((xx.ravel(order="F"), yy.ravel(order="F"), zz.ravel(order="F")))
# Perturb the points
points[:, 0] += rng.random(len(points)) * 0.3
points[:, 1] += rng.random(len(points)) * 0.3
# Create the point cloud mesh to triangulate from the coordinates
cloud = pv.PolyData(points)
cloud
```
PolyDataInformation
N Cells100
N Points100
N Strips0
X Bounds2.520e-02, 9.288e+00
Y Bounds2.986e-03, 9.297e+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)
```

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.insert(ids, 0, len(ids))

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

p = pv.Plotter()