# 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.