The data set collected during the night of the discovery of a minor body constitutes a too-short arc (TSA), resulting in failure of the differential correction procedure. This makes it necessary to recover the object during subsequent nights to gather more observations that will allow a preliminary orbit to be calculated. In this work, we present a recovery technique based on sampling the admissible region (AdRe) by the constrained Delaunay triangulation. We construct the AdRe in its topocentric and geocentric variants, using logarithmic and exponential metrics, for the following near-Earth-asteroids: (3122) Florence, (3200) Phaethon, 2003 GW, (1864) Daedalus, 2003 BH84 and 1977 QQ5; and the main-belt asteroids: (1738) Oosterhoff, (4690) Strasbourg, (555) Norma, 2006 SO375, 2003 GE55 and (32811) Apisaon. Using our sampling technique, we established the ephemeris region for these objects, using intervals of observation from 25 minutes up to 2 hours, with propagation times from 1 up to 47 days. All these objects were recoverable in a field of vision of 95' × 72', except for (3122) Florence and (3200) Phaethon, since they were observed during their closest approach to the Earth. In the case of 2006 SO375, we performed an additional test with only two observations separated by 2 minutes, achieving a recovery of up to 28 days after its discovery, which demonstrates the potential of our technique.