# Manifold set¶

The manifold set is typically named `manifolds.star`

, and it lists all the manifolds defined in all tomograms.
In this context, all manifolds are 2D surfaces embedded in 3D space.
Currently, only *spheres* and *spheroids* are supported.
Spheroids are sphere-like surfaces (blobs) whose deviation from a sphere is expressed using the Spherical Harmonics basis.
Spheres can be imported by using the program program_tomo_add_sphere, while spheroids can be fitted to membrane vesicles from initial spheres using the program relion_tomo_fit_blobs_3d.

The manifolds file contains one table for each tomogram, each named after the corresponding *tomogram name* (see tomogram set).
Each row of a table corresponds to one manifold, listing its:

number (

`rlnTomoManifoldIndex`

),type (

`rlnTomoManifoldType`

),and parameters (

`rlnTomoManifoldParams`

).

The parameter set varies depending on the manifold type: for spheres, the first 3 coefficients describe the position of the centre of the sphere, while the fourth describes its radius. For spheroids, the first 3 coefficients also describe the position, while the remaining ones are coefficients that describe the contribution of each Spherical Harmonics basis function. Please note that for spheroids, the fourth parameter is *not* equal to the radius, but to the radius multiplied by \({2\sqrt \pi}\).
Every consecutive parameter then distorts the sphere of that radius by applying higher-order Spherical Hamonics functions.

Given a set of manifolds, the program relion_tomo_sample_manifold allows the user to sample particles along each manifold, generating a novel particle set. Those particles are aligned such that their Z direction points perpendicularly to the surface normal of the manifold. This allows strong tilt priors to be applied during refinement in order to save time.