A calibration platform may obtain measurements for aligning a real-world coordinate system and a display coordinate system. For example, the calibration platform may display, via an optical see-through head-mounted display (OST-HMD), a three-dimensional virtual object and receive, from a positional tracking device, information that relates to a current pose of a three-dimensional real-world object to be aligned with the three-dimensional virtual object. The calibration platform may record a three-dimensional position of a plurality of points on the three-dimensional real-world object based on the current pose of the three-dimensional real-world object, based on an indication that the plurality of points on the three-dimensional real-world object respectively corresponds with a plurality of points on the three-dimensional virtual object. Accordingly, based on the obtained measurements, the calibration platform may generate a transformation function to provide a mapping between three-dimensional points in the real-world coordinate system and three-dimensional points in the display coordinate system.