Geometry / Read the grid

What does a domain query measure?

Predict the coordinates before you run the code.

Includes the model, inputs, required headers and a short run guide.

A helper name is not a substitute for its mathematical definition. OpenPFC can report a domain’s point count, dimensionality, bounds, extent and physical_volume. These quantities answer related but different questions.

Read the definitions

For size \((N_x,N_y,N_z)\), get_total_size counts \(N_xN_yN_z\) samples. extent subtracts lower from upper, respecting each axis’s endpoint convention. physical_volume uses the historical grid measure

\[V_h=N_xN_yN_z h_xh_yh_z.\]

On a fully periodic grid it equals the product of the extents. On a nonperiodic axis, the stored coordinate span is \((N_x-1)h_x\), so those products differ. This function does not introduce endpoint quadrature weights or compute a physical integral of a field.

for (bool periodic : {true, false}) {
  const auto grid = pfc::domain::create(
      pfc::GridSize{{5, 3, 2}}, pfc::PhysicalOrigin{{-1, 2, 0}},
      pfc::GridSpacing{{.5, 2, 3}}, {periodic, true, true});
  const auto length = pfc::domain::extent(grid);
  std::cout << periodic << ',' << pfc::domain::get_total_size(grid) << ','
            << pfc::domain::dimensionality(grid) << ',' << length[0] << ','
            << length[1] << ',' << length[2] << ','
            << pfc::domain::physical_volume(grid) << '\n';
}

Here both grids have 30 points and physical_volume=90. Making x nonperiodic changes its span from 2.5 to 2, and the product of the three coordinate spans from 90 to 72. Nothing has changed the stored sample count.

Ask for the quantity you need

openpfc run model.cpp input.json --launcher=none

The empty input is unused: edit the source constants. The program prints CSV. The regression checks both counts, dimensions, all extents and the historical volume convention. To describe a bounding box, use extent; to integrate a nonperiodic sampled function, choose an appropriate quadrature rule explicitly.

Try a grid with one sample in z and observe dimensionality. A singleton axis removes variation along that axis, but its spacing can still represent a chosen thickness. Dimensionality alone does not decide the physical units of an integral. Consult the domain query definitions when adapting a model.

The complete C++ model and starting input are available with this lesson.