1. A virtual endoscopic image display apparatus comprising: a memory configured to store computer-executable instructions; and a processor configure to execute the stored instructions, which when executed by the processor perform the following operations: generates, based on a three-dimensional image of a subject to be examined, a virtual endoscopic image by a virtual endoscope, simulating imaging performed by an endoscope inserted into the subject to be examined; displays the virtual endoscopic image; sets a path of the virtual endoscope in the three-dimensional image of the subject to be examined; receives specification of a point of interest in the virtual endoscopic image; obtains an operation amount after specification of the point of interest has been received; obtains, based on the operation amount, a distance of movement of the virtual endoscope on the path from an initial viewpoint; and sets, based on the distance of movement, view line vectors by sequentially changing the view line vectors from an initial view line vector with its start point located at the initial viewpoint to a shortest view line vector, which connects a viewpoint on the path at a shortest distance from the point of interest and the point of interest to each other, by moving, along the path, a viewpoint of the virtual endoscope on the path from the initial viewpoint closer to the point of interest and also by changing the direction of a view line of the virtual endoscope closer to a direction toward the point of interest, wherein the processor is further configured to: sequentially generate the virtual endoscopic image based on the view line vector, sequentially display the virtual endoscopic image based on change of the view line vectors, sequentially set the view line vectors in such a manner that the direction of a view line gradually becomes closer to a direction toward the point of interest as the viewpoint becomes closer to the point of interest, and employ the initial view line vector, the shortest view line vector, and the movement distance to sequentially calculate and set view line vectors corresponding to the movement distance.