Cylindrical and spherical coordinates

convert_coordinates(mesh, system, axis=..., arrays=[...]) reads a mesh in cylindrical or spherical components about an axis: it records each point's (r, θ, z) or (r, θ, φ) as point data, and rewrites the named vector and tensor fields in the local basis of each point (a cell's at its centroid). The results of rotating machinery and pressure vessels are read this way: the radial, tangential and axial velocity of a rotor, the hoop and axial stress of a vessel. The points do not move; inverse=True turns local components back into Cartesian ones.

import meshioplusplus as mp

rotor = mp.read("rotor.vtu")
out = mp.convert_coordinates(rotor, "cylindrical", axis=(0, 0, 1), arrays=["U", "stress"])
u_r, u_theta, u_z = out.point_data["U"].T
r, theta, z = out.point_data["coords:cylindrical"].T

vessel = mp.read("vessel.vtu")
out, report = mp.convert_coordinates(
    vessel, "spherical", origin=(0, 0, 1.5), arrays=["sigma"], return_report=True
)
report["num_arrays"], report["num_singular"]

back = mp.convert_coordinates(out, "spherical", origin=(0, 0, 1.5), arrays=["sigma"],
                              inverse=True, record_coordinates=False)

The systems

With a the unit axis through the origin o, d = p − o, z = d · a, the radial vector ρ = d − z a, and e₁ the reference direction projected off the axis ((1, 0, 0) by default; (0, 1, 0) stands in when the reference lies along the axis):

System	coords:<system>	Local basis (rows of R)
cylindrical	(r, θ, z): `r =	ρ
spherical	(r, θ, φ): `r =	d

The spherical system follows the physics convention (ISO 80000-2): θ is measured from the axis, φ about it. Both bases are right-handed and orthonormal.

A vector v becomes R v and a tensor T becomes R T Rᵀ; with inverse=True they become Rᵀ v and Rᵀ T R, so the two directions round trip to rounding. The trace and the norm are unchanged, which makes a quick check: the von Mises stress of a converted tensor equals the original's.

Scope

• Arrays are point or cell data, by name; a name present as both converts both. A vector is (n, 3); a tensor (n, 9) (row-major) or (n, 3, 3). Anything else, or a missing name, is an error. A converted array becomes Float64; every other array passes through.
• Cell data is converted in the basis at the cell's centroid: the mean of its distinct nodes.
• On the axis (r = 0 cylindrically, or the spherical centre) the radial direction is undefined: e₁ stands in for it, the angle is 0, and the point counts in num_singular. A point on the axis but away from the spherical centre is singular too, because its φ is undefined, although its e_r (along the axis) is still exact.
• Data-only: points, connectivity, block order and regions are left bit-identical. 2-D points are read with z = 0.

Both engines, the C++ core and the numpy twin used when it declines, give the same values to rounding (tested to 1e-13).

Report

num_arrays (the arrays converted, a point and a cell array of one name counting twice) and num_singular (the points on the axis or at the centre; 0 with record_coordinates=False).

Everywhere else

Surface	Call
Python	convert_coordinates(mesh, system="cylindrical", *, axis=(0, 0, 1), origin=(0, 0, 0), reference=(1, 0, 0), arrays=(), inverse=False, record_coordinates=True, return_report=False)
Pipeline	{"Op": "ConvertCoordinates", "System": "cylindrical", "Axis": [0, 0, 1], "Origin": [0, 0, 0], "Reference": [1, 0, 0], "Arrays": ["U"], "Inverse": false, "RecordCoordinates": true}; counters NumArrays, NumSingular
Both CLIs	meshioplusplus coordinates IN OUT [--system cylindrical|spherical] [--axis X,Y,Z] [--origin X,Y,Z] [--reference X,Y,Z] [--arrays A,B] [--inverse] [--no-record] [--json]
C	mio_coordinate_opts_init(&o); o.system = MIO_COORDS_SPHERICAL; o.arrays = names; o.num_arrays = 1; mio_mesh* out = mio_convert_coordinates(mesh, &o, &num_arrays, &num_singular);
Fortran	out = m%convert_coordinates(system="spherical", arrays=[character(8) :: "U"], num_singular=ns, stat=ierr)
Julia	r = convert_coordinates(mesh; system="cylindrical", arrays=["U"]); r.mesh, r.num_arrays, r.num_singular
R	r <- mio_convert_coordinates(mesh, "cylindrical", arrays = "U"); r$mesh, r$num_arrays, r$num_singular
WASM	m.convertCoordinates(mesh, {system, axis, origin, reference, arrays, inverse, recordCoordinates}) returns {mesh, numArrays, numSingular}
MCP	tool convert_coordinates(input_path, output_path, system, axis, origin, reference, arrays, inverse, record_coordinates)