A quantitative analysis of the evolution of a spherical surface artificially prepared from a potassium alum single-crystal during its regeneration is carried out in real growth experiments. The results are compared with the results of the numerical simulation based on the proposed regeneration process kinematical model. It is demonstrated that for many boundary conditions there is a close quantitative correspondence between the model and real experiments on the regeneration of single-crystal balls. It is shown that the most important parameter that has a quantitative effect on the growing regeneration surface evolution is the geometry of the roughness (protrusions and depressions), initially present on this surface. The rare quantitative discrepancies between the results of real growth and numerical experiments are due to the discrepancies between the geometry of the roughness set in the model and those actually present on the regenerating single-crystal ball. The proximity of the model to real regeneration processes allows us to accept, as they are proven, the basic postulates of the model. Namely, (i) the genetic predecessors of subindividuals are the protrusions that are initially presented on the regeneration surface. (ii) The rate of growth of all faces within the same crystallographic form is equal, regardless of whether the latest faces present on the polyhedral crystal, or they are localized on the subindividual's surfaces. (iii) The effects observed during the growth of the regeneration surface are the result of geometric selection either between the faces of each subindividual or between adjacent subindividuals in the course of which some subindividuals absorb their neighbors. Random differences in the initial protrusions geometry are the driving force for the latter.