I have a set of points $(x_i,y_i,u(x_i,y_i))\in\mathbb{R}^3$, $i=1,\dots N$, over a surface $S$ (experimental data). I need to calculate the integral of a function $F$ over that surfave.

If the points were points over a volumen I could use some mesh software (tetgen, for example) and build a mesh, and after that calculate anything. My problem is that it is a surface only, so if I try to use some mesh software I going to calculate a volumen...

How can I build, starting with the given points, a 2D (faces) mesh, for then iterate over each face in order to calculate the integral?

In this momment, I just need ideas about how to compute that "2D mesh". If exists a software that generates the mesh would be perfect.

I have a set of points $(x_i,y_i,u(x_i,y_i))\in\mathbb{R}^3$, $i=1,\dots N$, over a surface $S$ (from experimental data). I need to calculate the integral of a function $F$ over that surface.

If the points were points over a volume I could use some mesh software (tetgen, for example) and build a mesh, and after that calculate everything. My problem is that it is a surface only, so if I try to use some mesh software I am going to calculate a volume...

How can I build, starting with the given points, a 2D (face) mesh, then iterate over each face in order to calculate the integral?

At the moment, I just need some suggestions about how to compute that "2D mesh". If there exists software that generates the mesh that would be perfect.