  We compute the generating function of random planar quadrangulations with
three marked vertices at prescribed pairwise distances. In the scaling limit of
large quadrangulations, this discrete three-point function converges to a
simple universal scaling function, which is the continuous three-point function
of pure 2D quantum gravity. We give explicit expressions for this universal
three-point function both in the grand-canonical and canonical ensembles.
Various limiting regimes are studied when some of the distances become large or
small. By considering the case where the marked vertices are aligned, we also
obtain the probability law for the number of geodesic points, namely vertices
that lie on a geodesic path between two given vertices, and at prescribed
distances from these vertices.
