Revision of the geometry coordinates api by biancagi · Pull Request #104 · mitadel/mito

biancagi · 2026-08-10T13:25:05Z

Summary

This PR revises the geometry coordinates API to provide a more compact and expressive interface for Cartesian, polar, and spherical coordinate systems.

In particular, Cartesian geometry is now represented by a dimension-specific type:

mito::geometry::cartesian<D>

which collects the coordinate type, coordinate factory, Euclidean metric, coordinate component functions, and basis vectors associated with the corresponding Cartesian space.

For example, the 2D Cartesian API becomes:

using coordinates_t = mito::geometry::cartesian<2>::coordinates_t;

constexpr auto x = mito::geometry::cartesian<2>::x;
constexpr auto y = mito::geometry::cartesian<2>::y;

constexpr auto e_x = mito::geometry::cartesian<2>::e_x;
constexpr auto e_y = mito::geometry::cartesian<2>::e_y;

auto coordinates =
    mito::geometry::cartesian<2>::coordinates({ 1.0, 2.0 });

Coordinates API

Introduce dimension-specific Cartesian geometry descriptors:
- geometry::cartesian<1>
- geometry::cartesian<2>
- geometry::cartesian<3>
Collect the Cartesian coordinate type, coordinate factory, Euclidean metric, coordinate functions, and basis vectors within the corresponding geometry type.

Replace index-based Cartesian coordinate accessors such as

cartesian::x_0<2>
cartesian::x_1<2>
cartesian::x_2<3>

with the more natural

cartesian<2>::x
cartesian<2>::y

cartesian<3>::x
cartesian<3>::y
cartesian<3>::z

Similarly rename Cartesian basis vectors from e_0, e_1, and e_2 to e_x, e_y, and e_z.
Move the polar and spherical APIs to geometry descriptor types as well:
```
geometry::polar
geometry::spherical
```
exposing their coordinate types, coordinate factories, Euclidean metrics, coordinate functions, and basis vectors as static members.

API migration

Update benchmarks, tests, tutorials, Python bindings, and VTK utilities to use the new interface.

In particular:

geometry::coordinates_t<2, geometry::CARTESIAN>

becomes

geometry::cartesian<2>::coordinates_t

and explicit component functions such as

functions::component<coordinates_t, 0>

can now be replaced by the coordinate-system API:

geometry::cartesian<2>::x

The same convention is adopted consistently for Cartesian, polar, and spherical coordinates throughout the codebase.

Copilot

Pull request overview

This PR revises MiTo’s geometry coordinates API by moving Cartesian (dimension-specific), polar, and spherical coordinate-system “descriptors” into mito::geometry::{cartesian<D>, polar, spherical} types that bundle coordinate types, factories, metrics, component functions, and basis vectors, then migrates call sites to the new interface across tutorials, tests, benchmarks, bindings, and VTK utilities.

Changes:

Introduces mito::geometry::cartesian<1/2/3> descriptor specializations and migrates Cartesian component/basis access to ::x/::y/::z and ::e_x/::e_y/::e_z.
Moves polar and spherical APIs under mito::geometry::polar / mito::geometry::spherical descriptor types and migrates many usages to ::coordinates_t.
Updates broad codebase usage (tutorials/tests/benchmarks/bindings/VTK helpers) to the new coordinate-type aliases and factories.

Reviewed changes

Copilot reviewed 105 out of 105 changed files in this pull request and generated 5 comments.

Show a summary per file

File	Description
tutorial/5_divergence_theorem_2D_in_3D/main.cc	Migrates tutorial to `geometry::cartesian<3>` descriptor API.
tutorial/4_divergence_theorem_2D/main.cc	Migrates tutorial to `geometry::cartesian<2>` descriptor API.
tutorial/3_fields/main.cc	Migrates tutorial to `geometry::cartesian<2>` descriptor API.
tests/mito.lib/quadrature/quadrature_triangle_2D.cc	Updates quadrature test to `cartesian<2>` accessors.
tests/mito.lib/quadrature/quadrature_square_3D.cc	Updates quadrature test to `cartesian<3>::coordinates_t` / factory.
tests/mito.lib/quadrature/quadrature_segment_3D.cc	Updates quadrature test to `cartesian<3>::coordinates_t` / factory.
tests/mito.lib/quadrature/quadrature_segment_1D.cc	Updates quadrature test to `cartesian<1>` descriptor API.
tests/mito.lib/operators/gradient_non_square.cc	Updates operator test to `cartesian<3>::x/y/z`.
tests/mito.lib/operators/calculus_vector_field.cc	Updates operator test to `cartesian<2>::x/y`.
tests/mito.lib/operators/calculus_scalar_field.cc	Updates operator test to `cartesian<2>::x/y`.
tests/mito.lib/operators/calculus_identities.cc	Updates identities test to `cartesian<2>` descriptor API.
tests/mito.lib/mesh/tetra_zero_subdivisions.cc	Updates mesh test coordinate type to `cartesian<3>::coordinates_t`.
tests/mito.lib/mesh/tetra_triangle_3D.cc	Updates mesh test coordinate type to `cartesian<3>::coordinates_t`.
tests/mito.lib/mesh/tetra_triangle_2D.cc	Updates mesh test coordinate type to `cartesian<2>::coordinates_t`.
tests/mito.lib/mesh/tetra_tetrahedron_3D.cc	Updates mesh test coordinate type to `cartesian<3>::coordinates_t`.
tests/mito.lib/mesh/tetra_segment_1D.cc	Updates mesh test coordinate type to `cartesian<1>::coordinates_t`.
tests/mito.lib/mesh/tetra_rectangle_2D.cc	Updates mesh test coordinate type to `cartesian<2>::coordinates_t`.
tests/mito.lib/mesh/tetra_multiple_subdivisions.cc	Updates mesh test coordinate type to `cartesian<2>::coordinates_t`.
tests/mito.lib/mesh/tetra_cube_3D.cc	Updates mesh test coordinate type to `cartesian<3>::coordinates_t`.
tests/mito.lib/mesh/summit_read_write.cc	Updates mesh test coordinate type to `cartesian<2>::coordinates_t`.
tests/mito.lib/mesh/sphere.cc	Updates mesh test coordinate type to `cartesian<3>::coordinates_t`.
tests/mito.lib/mesh/metis_partitioner.cc	Updates mesh test coordinate type to `cartesian<2>::coordinates_t`.
tests/mito.lib/mesh/metis_partitioner_single_partition.cc	Updates mesh test coordinate type to `cartesian<2>::coordinates_t`.
tests/mito.lib/mesh/metis_partitioner_mpi.cc	Updates mesh test coordinate type to `cartesian<2>::coordinates_t`.
tests/mito.lib/mesh/metis_partitioner_mpi_load_mesh.cc	Updates mesh test coordinate type to `cartesian<2>::coordinates_t`.
tests/mito.lib/mesh/metis_partitioner_load_mesh.cc	Updates mesh test coordinate type to `cartesian<2>::coordinates_t`.
tests/mito.lib/mesh/half_ball.cc	Migrates cartesian and spherical coordinate aliases to new descriptors.
tests/mito.lib/mesh/filter_ball.cc	Updates mesh test coordinate type to `cartesian<3>::coordinates_t`.
tests/mito.lib/mesh/erase_element.cc	Updates mesh test coordinate type to `cartesian<2>::coordinates_t`.
tests/mito.lib/mesh/erase_duplicates.cc	Updates mesh test coordinate type to `cartesian<2>::coordinates_t`.
tests/mito.lib/mesh/disk_polar_cartesian.cc	Migrates cartesian/polar coordinate aliases to new descriptors.
tests/mito.lib/mesh/disk_change_coordinates.cc	Migrates cartesian/polar coordinate aliases to new descriptors.
tests/mito.lib/mesh/build_mesh.cc	Updates mesh test coordinate type to `cartesian<2>::coordinates_t`.
tests/mito.lib/mesh/ball.cc	Updates mesh test coordinate type to `cartesian<3>::coordinates_t`.
tests/mito.lib/manifolds/surface_half_sphere_spherical.cc	Migrates spherical/cartesian coordinate aliases to new descriptors.
tests/mito.lib/manifolds/surface_half_sphere_cartesian.cc	Updates manifold test to `cartesian<3>::coordinates_t`.
tests/mito.lib/manifolds/spherical_gradient.cc	Updates manifold test to `spherical::coordinates_t`.
tests/mito.lib/manifolds/polar_gradient.cc	Updates manifold test to `polar::coordinates_t`.
tests/mito.lib/manifolds/manifold_elements_view.cc	Updates manifold test to `cartesian<2>::coordinates_t`.
tests/mito.lib/manifolds/euclidean_gradient.cc	Migrates euclidean gradient test to `cartesian<2>` descriptor API.
tests/mito.lib/io/vtk_mesh_writer_polar_coordinates.cc	Updates VTK writer test to `polar::coordinates_t`.
tests/mito.lib/io/vtk_mesh_writer_lattice_3D.cc	Updates VTK writer test to `cartesian<3>::coordinates_t`.
tests/mito.lib/io/vtk_mesh_writer_3D.cc	Updates VTK writer test to `cartesian<3>::coordinates_t`.
tests/mito.lib/io/vtk_mesh_writer_2D.cc	Updates VTK writer test to `cartesian<2>::coordinates_t`.
tests/mito.lib/io/vtk_cloud_writer.cc	Updates VTK writer test to `cartesian<3>::coordinates_t`.
tests/mito.lib/io/vtk_cloud_writer_spherical_coordinates.cc	Updates VTK writer test to `spherical::coordinates_t`.
tests/mito.lib/io/summit_to_summit_mesh_2D.cc	Updates Summit IO test to `cartesian<2>::coordinates_t`.
tests/mito.lib/io/summit_mesh_reader_segment_3D.cc	Updates Summit reader test to `cartesian<3>::coordinates_t`.
tests/mito.lib/io/summit_mesh_reader_3D.cc	Updates Summit reader test to `cartesian<3>::coordinates_t`.
tests/mito.lib/io/summit_mesh_reader_2D.cc	Updates Summit reader test to `cartesian<2>::coordinates_t`.
tests/mito.lib/io/parallel_vtk_mesh_writer.cc	Updates parallel VTK writer test to `cartesian<3>::coordinates_t`.
tests/mito.lib/io/parallel_vtk_mesh_field_writer.cc	Updates parallel VTK field writer test to `cartesian<3>::coordinates_t`.
tests/mito.lib/io/parallel_vtk_cloud_writer.cc	Updates parallel VTK cloud writer test to `cartesian<3>::coordinates_t`.
tests/mito.lib/io/parallel_vtk_cloud_field_writer.cc	Updates parallel VTK cloud field writer test to `cartesian<3>::coordinates_t`.
tests/mito.lib/integration/write_tetra_mesh_to_vtk.cc	Updates integration test to `cartesian<3>::coordinates_t`.
tests/mito.lib/integration/quadrature_load_mesh_2D.cc	Updates integration test to `cartesian<2>::x/y` and `coordinates_t`.
tests/mito.lib/integration/quadrature_load_mesh_2D_mpi.cc	Updates MPI integration test to `cartesian<2>::x/y` and `coordinates_t`.
tests/mito.lib/integration/quadrature_flip_segment_3D.cc	Updates integration test to `cartesian<3>::coordinates_t` / factory.
tests/mito.lib/integration/divergence_theorem.cc	Updates integration test to `cartesian<2>::x/y` and `e_x/e_y`.
tests/mito.lib/geometry/triangle_3D.cc	Updates geometry test to `cartesian<3>::coordinates_t` and factory.
tests/mito.lib/geometry/triangle_2D.cc	Updates geometry test to `cartesian<2>::coordinates_t`.
tests/mito.lib/geometry/tetrahedron_3D.cc	Updates geometry test to `cartesian<3>::coordinates_t` (plus formatting).
tests/mito.lib/geometry/spherical_metric_space.cc	Updates metric space test to `spherical::coordinates_t`.
tests/mito.lib/geometry/segment_2D.cc	Updates geometry test to `cartesian<2>::coordinates_t`.
tests/mito.lib/geometry/polar_metric_space.cc	Updates metric space test to `polar::coordinates_t`.
tests/mito.lib/geometry/point.cc	Migrates point test cartesian/polar coordinate aliases to descriptors.
tests/mito.lib/geometry/metric.cc	Migrates metric test to `cartesian<2>` descriptor API.
tests/mito.lib/geometry/induced_metric_triangle.cc	Migrates induced metric tests to `cartesian<2/3>` descriptors.
tests/mito.lib/geometry/induced_metric_segment.cc	Migrates induced metric segment tests to `cartesian<1/2/3>` descriptors.
tests/mito.lib/geometry/induced_metric_non_cartesian.cc	Migrates non-cartesian induced metric tests to polar/spherical descriptors.
tests/mito.lib/geometry/euclidean_submanifold_metric_3D.cc	Updates test to `cartesian<3>::coordinates_t` and factory.
tests/mito.lib/geometry/euclidean_metric_space.cc	Updates metric space test to `cartesian<2>::coordinates_t`.
tests/mito.lib/geometry/euclidean_metric_3D.cc	Updates metric test to `cartesian<3>::coordinates_t`.
tests/mito.lib/geometry/euclidean_metric_2D.cc	Updates metric test to `cartesian<2>::coordinates_t`.
tests/mito.lib/geometry/euclidean_metric_1D.cc	Updates metric test to `cartesian<1>::coordinates_t`.
tests/mito.lib/geometry/cube_volume.cc	Updates geometry test to `cartesian<3>::coordinates_t`.
tests/mito.lib/geometry/coordinates.cc	Updates coordinates test to `cartesian<2>::coordinates(...)`.
tests/mito.lib/geometry/coordinate_transformation.cc	Migrates transformation tests to cartesian/polar/spherical descriptors.
tests/mito.lib/geometry/coordinate_system.cc	Updates coordinate system test to `cartesian<2>::coordinates_t` / factory.
tests/mito.lib/geometry/cell_directors.cc	Updates test to `cartesian<3>::coordinates_t`.
tests/mito.lib/geometry/barycenter_triangle_3D.cc	Updates barycenter test to `cartesian<3>::coordinates(...)`.
tests/mito.lib/geometry/barycenter_triangle_2D.cc	Updates barycenter test to `cartesian<2>::coordinates(...)`.
tests/mito.lib/geometry/barycenter_tetrahedron_3D.cc	Updates barycenter test to `cartesian<3>::coordinates(...)`.
tests/mito.lib/geometry/barycenter_segment_3D.cc	Updates barycenter test to `cartesian<3>::coordinates(...)`.
tests/mito.lib/geometry/barycenter_segment_2D.cc	Updates barycenter test to `cartesian<2>::coordinates(...)`.
tests/mito.lib/geometry/barycenter_segment_1D.cc	Updates barycenter test to `cartesian<1>::coordinates(...)`.
tests/mito.lib/geometry/arc_length_integration.cc	Migrates arc-length integration test to `cartesian<1/2>::coordinates_t`.
tests/mito.lib/fields/polar_metric_field.cc	Touches polar-field test coordinate aliasing.
tests/mito.lib/fem/isoparametric_triangle.cc	Updates FEM test to `cartesian<2>::coordinates_t`.
tests/mito.lib/fem/isoparametric_segment.cc	Updates FEM test to `cartesian<1>::coordinates_t`.
tests/mito.lib/fem/fem_field.cc	Updates FEM test to `cartesian<2>::x/y` and `coordinates_t`.
tests/mito.lib/fem/block_mass.cc	Updates FEM test to `cartesian<2>::coordinates_t`.
tests/mito.lib/fem/block_mass_segment.cc	Updates FEM test to `cartesian<1>::coordinates_t`.
tests/mito.lib/fem/block_grad_grad.cc	Updates FEM test to `cartesian<2>::coordinates_t`.
tests/mito.lib/fem/block_grad_grad_segment.cc	Updates FEM test to `cartesian<1>::coordinates_t`.
tests/mito.lib/discrete/mesh_field.cc	Updates discrete test to `cartesian<3>::coordinates_t`.
tests/mito.lib/constraints/dirichlet.cc	Updates constraints test to `cartesian<2>::x/y` and `coordinates_t`.
lib/mito/io/vtk/vtk_point.h	Updates coordinate type aliasing for VTK point insertion logic.
lib/mito/geometry/spherical/api.h	Introduces `geometry::spherical` descriptor struct API.
lib/mito/geometry/polar/api.h	Introduces `geometry::polar` descriptor struct API.
lib/mito/geometry/cartesian/api.h	Introduces `geometry::cartesian<1/2/3>` descriptor specializations.
extensions/mito/mito.cc	Updates Python bindings to new `cartesian<D>::coordinates_t` aliases.
benchmarks/mito.lib/pdes/poisson.cc	Updates benchmark to `cartesian<2>::x/y` and `coordinates_t`.
benchmarks/mito.lib/operators/laplacian.cc	Updates benchmark to `cartesian<2>::x/y` and `coordinates_t`.
benchmarks/mito.lib/integration/integration.cc	Updates benchmark to `cartesian<2>::x/y` and `coordinates_t`.

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…stead of the more verbose geometry::coordinates_t<dim, family>

… more verbose {functions::component<coordinates_t, dim>} Also, changed api of cartesian coordinates from {x_0}, {x_1}, {x_2} to x, y, z.

From {mito::geometry::cartesian::x<2>} to {mito::geometry::cartesian<2>::x}

Copilot

Pull request overview

Copilot reviewed 117 out of 117 changed files in this pull request and generated 3 comments.

Suppressed comments (3)

tests/mito.lib/fields/polar_metric_field.cc:15

using mito::geometry::POLAR; is now unused because the coordinates type uses a fully-qualified mito::geometry::POLAR. This can trigger unused-using warnings and is easy to avoid by using the imported POLAR (or by removing the using).

// use polar coordinates
using mito::geometry::POLAR;

// the type of coordinates
using coordinates_t = mito::geometry::coordinates_t<2, mito::geometry::POLAR>;

lib/mito/geometry/cartesian/api.h:40

This comment contains a non-breaking space character between “2D” and “Euclidean”, which is hard to spot and can be annoying in diffs/searches. Replacing it with a normal space keeps the file ASCII-clean.

    // cartesian geometry in 2D Euclidean space

lib/mito/geometry/cartesian/api.h:70

This comment contains a non-breaking space character between “3D” and “Euclidean”, which is hard to spot and can be annoying in diffs/searches. Replacing it with a normal space keeps the file ASCII-clean.

    // cartesian geometry in 3D Euclidean space

        const geometry::coordinates_t<3, geometry::SPHERICAL> & coord,
        vtkSmartPointer<vtkPoints> & pointsVtk) -> void
    {
-        // cartesian coordinates in 2D
-        using cartesian_coord_t = mito::geometry::coordinates_t<3, mito::geometry::CARTESIAN>;
+        // cartesian coordinates in 3D
+        using cartesian_coord_t = mito::geometry::cartesian<3>::coordinates_t;


        const geometry::coordinates_t<2, geometry::POLAR> & coord,
        vtkSmartPointer<vtkPoints> & pointsVtk) -> void
    {
        // cartesian coordinates in 2D
-        using cartesian_coord_t = mito::geometry::coordinates_t<2, mito::geometry::CARTESIAN>;
+        using cartesian_coord_t = mito::geometry::cartesian<2>::coordinates_t;


+    // cartesian geometry in 1D
    template <int D>
-    using coordinates_t = cartesian_coordinates_t<D>;
+    struct cartesian;

-    // the Euclidean metric tensor field
-    template <int D>
-    constexpr auto euclidean_metric =
-        geometry::euclidean_metric<cartesian_coordinates_t<D>>::field();
+    // cartesian geometry in 1D Euclidean space


biancagi requested a lite review from Copilot August 10, 2026 13:25

Copilot started reviewing on behalf of biancagi August 10, 2026 13:25 View session

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Comment thread tutorial/5_divergence_theorem_2D_in_3D/main.cc

Comment thread lib/mito/io/vtk/vtk_point.h Outdated

Comment thread lib/mito/io/vtk/vtk_point.h Outdated

Comment thread extensions/mito/mito.cc Outdated

Comment thread tests/mito.lib/fields/polar_metric_field.cc

biancagi force-pushed the coordinates-api branch from 1105994 to dd7cdf1 Compare August 10, 2026 13:41

biancagi added 4 commits August 26, 2026 06:46

tests and benchmarks: use {geometry::<family>::coordinates_t<dim>} in…

e0c3636

…stead of the more verbose geometry::coordinates_t<dim, family>

tests and benchmarks: use {geometry::<family>::x<dim>} instead of the…

10d874d

… more verbose {functions::component<coordinates_t, dim>} Also, changed api of cartesian coordinates from {x_0}, {x_1}, {x_2} to x, y, z.

improve coordinates api

416761f

From {mito::geometry::cartesian::x<2>} to {mito::geometry::cartesian<2>::x}

io/vtk: fix typo in comment

dd58b98

biancagi force-pushed the coordinates-api branch from dd7cdf1 to dd58b98 Compare August 26, 2026 04:55

biancagi self-assigned this Aug 26, 2026

biancagi requested review from Pawel024 and a lite review from Copilot August 26, 2026 04:56

Copilot started reviewing on behalf of biancagi August 26, 2026 04:57 View session

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Revision of the geometry coordinates api - #104

Revision of the geometry coordinates api#104
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biancagi commented Aug 10, 2026

Summary

Coordinates API

API migration

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