A display operating device includes a position detecting section, an axis decision section, a movement determining section, a display section, and a first rotation processing section. The position detecting section is configured to detect three positions on a touch surface. The axis decision section is configured to decide a first axis using first and second positions which are two of the three positions. The movement determining section is configured to determine whether or not a third position, which is the remaining one of the three positions, is moving. The first rotation processing section is configured to, when with the 3D object displayed on the display section the three positions are detected and the third position is determined to be moving, rotate the 3D object by a first predetermined angle about the first axis.