Cylindrical coordinates

In our paper, we presented the helicity measures starting from a volume in cylindrical coordinates. This was mainly useful for giving an intuitive explanation, but can be skipped in the implementation (see the heliq.helicity module). However, it can still be useful to analyze the cylindrical sections because in some cases they can nicely visualize the helical features of a structure.

cylindrical_sections(data: numpy.ndarray, rho: Optional[Union[float, Sequence[float]]] = None, n_theta: int = 360) → numpy.ndarray

Get cylindrical sections from a volume in Cartesian coordinates

The volume should be aligned such that the helical axis goes through the center and is parallel to the z-axis.

Note that the pixels will not be square (different width and height) and that the real width of the pixels will be different at different cylindrical sections. If the voxel size is \(d\), then the height of the pixels is also \(h = d\), and the width can be calculated using \(w = d \cdot \rho \cdot \arctan{ \left( 360° / n_{\theta} \right) }\).

Parameters

• data – A 3D array containing the volumetric data of the object.

• rho – A list of the radii at which to create cylindrical sections, expressed in voxels, the default radii are calculated using rho = numpy.arange(0, min(data.shape[:2])).

• n_theta – The number of pixels in the θ-direction of the cylindrical sections.

Returns

A 3D array with axes (z, θ, ρ).