  The color-magnitude diagrams (CMDs) of intermediate-age star clusters (less
than ~ 2 Gyr) are much more complex than those predicted by coeval, nonrotating
stellar evolution models. Their observed extended main sequence turnoffs
(eMSTOs) could result from variations in stellar age, stellar rotation, or
both. The physical interpretation of eMSTOs is largely based on the complex
mapping between stellar models -- themselves functions of mass, rotation,
orientation, and binarity -- and the CMD. In this paper, we compute continuous
probability densities in three-dimensional color, magnitude, and vsini space
for individual stars in a cluster's eMSTO, based on a rotating stellar
evolution model. These densities enable the rigorous inference of cluster
properties from a stellar model, or, alternatively, constraints on the stellar
model from the cluster's CMD. We use the MIST stellar evolution models to
jointly infer the age dispersion, the rotational distribution, and the binary
fraction of the Large Magellanic Cloud cluster NGC 1846. We derive an age
dispersion of ~ 70-80 Myr, approximately half the earlier estimates due to
nonrotating models. This finding agrees with the conjecture that rotational
variation is largely responsible for eMSTOs. However, the MIST models do not
provide a satisfactory fit to all stars in the cluster and achieve their best
agreement at an unrealistically high binary fraction. The lack of agreement
near the main-sequence turnoff suggests specific physical changes to the
stellar evolution models, including a lower mass for the Kraft break and
potentially enhanced main sequence lifespans for rapidly rotating stars.
