## 1 Introduction
Even though there are not many studies in the exocentric space, it seems most of them agreed on the underestimation [19; 20; 21]. [PERSON] et al. [22] bolstered the case that the virtual space has been compacted by indicating the underestimation of both depth and frontal extents. Similarly, [PERSON], [PERSON] and [PERSON] [8] and [PERSON] and [PERSON] [6] reported compression in the frontal plane in stereoscopic widespread displays (SWDs). Moreover, [PERSON] et al. (2011) looked at egocentric and exocentric distance estimation and discovered underestimation in both cases, where compression in exocentric conditions was higher. [PERSON] et al. (2017) reported that modern head-mounted displays (HMDs) have improved the accuracy of space perception. However, [PERSON], [PERSON], [PERSON] and [PERSON] [22] indicated that the exocentric distance judgment in VR is either underestimated when objects are oriented in both sagittal and frontal planes or sometimes veridically perceived when the objects are oriented in a frontal plane. Researchers have discussed the possible reasons for the inaccuracy of judgment in stereoscopic exocentric spaces. For example, [PERSON] [23] listed the display type, the geometric field of view (GFOV), scene contrast, texture, stimulus size, navigational interface, and feedback as the likely factors that affect exocentric distance estimations. [PERSON] et al. [24] reasoned that distances are assessed more precisely in larger displays as they actuate a more grounded emotional feeling of being available in the virtual space. [PERSON] et al. [25] claimed that feedback combined with a sufficiently vast GFOV could permit sensibly accurate exocentric distance estimations. [PERSON] and [PERSON] [19] identified that size-constancy phenomena caused misperception, whereby sizes and distances seem to be smaller when seen through a truncated field of view. [PERSON] and [PERSON] [18] reported that the availability of stereoscopic depth cues resulted in a higher estimation accuracy in the cave automatic virtual environment (CAVE). In addition, [PERSON], [PERSON] and [PERSON] [8] have shown how the accuracy of judgment varies with distance because, as the exocentric distance increases, the accuracy of estimation decreases, whereas the effect of egocentric distance was not significant. [PERSON] et al. [26] reported the influence of VR displays on virtual space perceptions and claimed that examining it is valuable for a variety of applications. Out of the previous studies, only a few of them exhibited the same 3D content through various VR displays that allowed for an examination between them, all of which had compared HMDs to a projection display--i.e., only one type of SWD. For instance, [PERSON] [23] reported that participants using HMD have been precise, more linear, and more consistent with their exocentric distance judgments than participants who used a desktop display. On the other hand, [PERSON], [PERSON], [PERSON], [PERSON] and [PERSON] [26] found no significant difference between the stereo back-projection (BackPro) display condition with a tracked viewpoint and the HMD conditions; they also found significant underestimation in the BackPro condition (when the viewpoint was not tracked). [PERSON] and [PERSON] [19] reported mixed results via comparing the real environment, a monitor, a fixed HMD (no head rotation), and a tracked HMD (with head rotation), and found that the underestimates in all the VR conditions were significantly lower than the real condition, and the estimates in the tracked HMD were significantly smaller than the other two display (monitor and fixed HMD) conditions.