This paper presents a new approach based on light striping for reconstructing a 3D model from a real object. The proposed system consists of a light plane projector, camera and cube frame with LEDs attached. As in other light striping systems, the correspondence problem is solved by projecting light plane onto an object inside a frame. However, we use only cross-ratios and vanishing points to set up the world coordinates of the object, while the intrinsic and extrinsic parameters of the camera and the position of light source are not required. As such, the proposed system does not calibrate the camera and the light source. Furthermore, the computed 3D point data does not require any registration process because the data is directly measured based on unified world coordinates. Experimental results proved the accuracy of the measurements and consistency of the outcomes without any knowledge of the camera and light source parameters.