1. A display apparatus which is connected to a machine tool having structures including one or more movable structures, a driving mechanism unit driving the movable structures, a numerical controller controlling operation of the driving mechanism unit and an input device for inputting an operation signal into the numerical controller and which displays at least an image relating to the movable structures, the display apparatus comprising: a display on which the image is displayed; a model data storage storing therein at least three-dimensional model data relating to the movable structures and three-dimensional model data relating to other structures having a possibility of interfering with the movable structures in a movable area of the movable structures; a model generator which reads out the three-dimensional model data stored in the model data storage and receives a signal relating to positions of the movable structures from the numerical controller, and generates a three-dimensional model in which three-dimensional models of the other structures are arranged in a three-dimensional space to have a determined positional relationship and a three-dimensional model of a corresponding movable structure is arranged in the three-dimensional space to have a received positional relationship; an interference-caution-portion specifying processor which, when a signal which is for moving the movable structure and which relates to at least a moving direction of the movable structure is input from the input device into the numerical controller, receives the signal and executes a determination processing of determining, based on the three-dimensional model generated by the model generator, whether an interfering structure which will interfere with the movable structure when the movable structure moves in the received moving direction exists or not, and a specifying processing of, in a case where an interfering structure exists, specifying a portion of the movable structure having a possibility of interference with the interfering structure as an interference caution portion, and, in a case where an interfering structure does not exist, specifying a leading portion of the movable structure in the moving direction as an interference caution portion; and an image display unit which generates at least a display image of the movable structure based on the three-dimensional model generated by the model generator, and, in a case where an interference caution portion specified by the interference-caution-portion specifying processor exists, generates the display image in which the interference caution portion of the movable structure is highlighted and in which in the case where a determination is made that an interfering structure exists in the determination processing, an arrow starting from the interference caution portion and ending at an interfering portion of the interfering structure is illustrated, and in the case where a determination is made that an interfering structure does not exist, an arrow along the moving direction starting from the interference caution portion is illustrated, and displays the generated display image on the display.