  Infrared observations of Sgr A* probe the region close to the event horizon
of the black hole at the Galactic center. These observations can constrain the
properties of low-luminosity accretion as well as that of the black hole
itself. The GRAVITY instrument at the ESO VLTI has recently detected continuous
circular relativistic motion during infrared flares which has been interpreted
as orbital motion near the event horizon. Here we analyze the astrometric data
from these flares, taking into account the effects of out-of-plane motion and
orbital shear of material near the event horizon of the black hole. We have
developed a new code to predict astrometric motion and flux variability from
compact emission regions following particle orbits. Our code combines
semi-analytic calculations of timelike geodesics that allow for out-of-plane or
elliptical motions with ray tracing of photon trajectories to compute
time-dependent images and light curves. We apply our code to the three flares
observed with GRAVITY in 2018. We show that all flares are consistent with a
hotspot orbiting at R$\sim$9 gravitational radii with an inclination of
$i\sim140^\circ$. The emitting region must be compact and less than $\sim5$
gravitational radii in diameter. We place a further limit on the out-of-plane
motion during the flare.
