Gallinari said he had scarcely touched a ball since the N.B.A. was placed on hiatus, restricting himself to exercises he can do in his condo and, of course, checking in constantly with family members. Gallinari’s younger brother, Federico, is a redshirt sophomore on the basketball team at Rochester University, an N.A.I.A. school in Rochester Hills, Mich. Their father, Vittorio, a former professional basketball player in Italy, is frequently in the United States on business and is currently in Denver, where Danilo played for five and a half seasons. The rest of the family, including the brothers’ mother, Marilisa, is in Italy — but travel restrictions prevent her from visiting Danilo’s grandparents roughly 30 minutes away.