I have a triangulated mesh that I generated with the Delaunay 3D function in PyVista. I would like to calculate the surface area of the mesh adding up the areas of all the triangles. Is there a way to obtain the indices of the simplices triangles from the delaunay result?

import pyvista as pv cloud = pv.PolyData(points) volume = cloud.delaunay_3d(alpha = 2.5) shell = volume.extract_geometry() shell.plot()

I know I can do it with Scipy but for whatever reason Scipy generates an incorrect mesh (and does not have attributes I can adjust in the Delaunay method):

from scipy.spatial import Delaunay tri = Delaunay(points) print(tri.simplices) [[386 466 377 613] [159 386 377 613] [159 386 466 613] ... [696 709 695 691] [696 710 711 691] [696 697 711 691]]

My goal is to loop through the triangles and calculate the surface area of the mesh.

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## Answer

PyVista `PolyData`

objects already have an `area`

property that adds up the cell areas.

For example, consider random points on the unit sphere:

import numpy as np import pyvista as pv # random point cloud on a unit sphere rng = np.random.default_rng() N = 1000 # points thetas = rng.random(N)*np.pi phis = rng.random(N)*2*np.pi points = np.array([ np.sin(thetas)*np.cos(phis), np.sin(thetas)*np.sin(phis), np.cos(thetas), ]).T # triangulate and compute total area mesh = pv.PolyData(points) triangulated = mesh.delaunay_3d().extract_surface() print(triangulated.area, 4*np.pi)

For me this printed

12.47386243049973 12.566370614359172

The first value is the total area of our triangulated point cloud on a sphere, and the second value is the exact surface of a perfect unit sphere. Looks good.

Additionally, there are other similar attributes, for instance `volume`

for watertight surfaces (which you have):

>>> print(triangulated.volume, 4/3*np.pi) 4.127984347614561 4.1887902047863905

In other words, you don’t need the vertex indices if you’re only looking for the total area.

(If you *do* still want the vertices, the information is accessible via `triangulated.faces`

. My recommendation would be to look at `triangulated.faces.reshape(-1, 4)[:, 1:]`

which is a 2d array of shape `(n_cells, 3)`

, where each row corresponds to a given triangle and the three integers in the row are the indices of the three points forming the corresponding triangle.)

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