Volume of the alpha shape

[stla]

Hello,

To get the volume of an alpha shape as, I do:

    double vol = 0.0;
    std::list<Cell_handle> cells;
    // as.get_alpha_shape_cells(std::back_inserter(cells),
    //                          Fixed_alpha_shape_3::EXTERIOR);
    as.get_alpha_shape_cells(std::back_inserter(cells),
                             Fixed_alpha_shape_3::INTERIOR);
    std::list<Cell_handle>::iterator it_cell;
    for(it_cell = cells.begin(); it_cell != cells.end(); it_cell++) {
      Cell_handle cell = *it_cell;
      Tetrahedron t(
          cell->vertex(0)->point(),
          cell->vertex(1)->point(),
          cell->vertex(2)->point(),
          cell->vertex(3)->point()
      );
      vol += fabs(t.volume());
    }

In general it is correct. But not always: take a cube having edge length 2, and take alpha=2, then the volume is 0 (while the alpha shape is the cube). It is correct (8) for alpha=5. For alpha=2 the volume is obtained from the EXTERIOR cells.

So what is the correct way to get the volume?

[sloriot]

For alpha=2, all cells are classified as EXTERIOR so there is no volume. You can refer to the definition here.

[stla]

Ok. I will return both the total volume of the exterior cells and the total volume of the interior cells for the user. Thanks.