The propagation of a (1+1)D spatial optical soliton beam at an oblique angle of incidence to a nonlocal nonlinear interface is studied by using numerical method. It is found that the intensity dependence of the propagation of a light beam at a nonlinear nonlocal interface can be portrayed by 5 node points of beam width of the incident soliton beam, which mark respectively 5 critical intensity value of the incident beam that cause the sudden changes of the propagation of the reflection or the transmission beam. It is also found that with the incident beam width keep unchanged and its power is increased, the 5 sudden change points of the propagation of the incident optical breathing beam can also arise, which illustrate that the power dependence is essentially intensity dependence. The change of the values of the 5 node points of beam width of the incident soliton beam with the change of nonlocality degree is also studied.