  We study the link between an expanding coronal shock and the energetic
particles measured near Earth during the Ground Level Enhancement (GLE) of 17
May 2012. We developed a new technique based on multipoint imaging to
triangulate the 3-D expansion of the shock forming in the corona. It uses
images from three vantage points by mapping the outermost extent of the coronal
region perturbed by the pressure front. We derive for the first time the 3-D
velocity vector and the distribution of Mach numbers, $M_{FM}$, of the entire
front as a function of time. Our approach uses magnetic field reconstructions
of the coronal field, full magneto-hydrodynamic simulations and imaging
inversion techniques. We find that the highest $M_{FM}$ values appear near the
coronal neutral line within a few minutes of the Coronal Mass Ejection (CME)
onset; this neutral line is usually associated with the source of the
heliospheric current and plasma sheet. We illustrate the variability of the
shock speed, shock geometry and Mach number along different modeled magnetic
field lines. Despite the level of uncertainty in deriving the shock Mach
numbers, all employed reconstruction techniques show that the release time of
GeV particles occurs when the coronal shock becomes super-critical
($M_{FM}>3$). Combining in-situ measurements with heliospheric imagery, we also
demonstrate that magnetic connectivity between the accelerator (the coronal
shock of 17 May 2012) and the near-Earth environment is established via a
magnetic cloud that erupted from the same active region roughly five days
earlier.
