In this paper, we propose a novel method of representing the complex surface of a 3D object for a new aerial 3D display which can draw dots of light at an arbitrary position in a space. The aerial 3D display that we use in this research can create a dot of light at 50 kHz and can draw dots of light by vector scanning. The proposed method can generate point sequence data for the aerial 3D display from 3D surface models consisting of polygonal patches. The 3D surface model is polygonal model which are generally used in computer graphics. The proposed method represents the surface with contours consisting of intersections of an object and cross sections by a sequence of points for vector scanning. In this research, some polygonal models, for example face and hand, are examined at experiments. From the experiments of drawing, the polygonal models can successfully be drawn by the proposed method.