## 4 Discussion  
The results demonstrated that exocentric distance judgment (Figure 4) was more accurate (93.9%) and slightly underestimated (0.4 cm) in the HMDs; exocentric distance judgment was less accurate (85.03%) and overestimated (1.93 cm) in the SWDs. A few studies reported similar results by comparing HMDs to one of a number of projection display types (all fall into the same category as SWDs),  
Figure 5: Horizontal position accuracy with respect to exocentric distance for the target displayed at (**a**) 65 cm, (**b**) 100 cm, and (**c**) 150 cm from the participant, where horizontal position accuracies in the SWDs were worsened as exocentric distance increases. [PERSON]’s law could explain the phenomena where the accuracy decreases as exocentric distance increases [4, 28]. The main effect of (**d**) exocentric distance and (**e**) size on horizontal position accuracy, where horizontal position accuracies improve as size and exocentric distance decreases. Figure 6: The main effect of (**a**) target distance and (**b**) size on vertical position accuracy. It shows that the overall vertical position estimates were worsened as both target distance and exocentric distance increases. which are in agreement with the findings of the present study. For example, [PERSON] [23] confirmed that immersed participants (wearing HMDs) were more precise, more linear, and less varied with their exocentric distance judgments than participants who used a desktop display. Similarly, [PERSON], [PERSON], [PERSON], [PERSON] and [PERSON] [26] reported a significant difference between the BackPro display (without viewpoint tracking) and the HMD conditions, where a better accuracy of size judgment was obtained from HMDs (86%) than BackPro display (77%). [PERSON] et al. [35] reasoned that the accuracy of exocentric distance judgment might be enhanced with HMDs rather than desktop displays, as HMDs are more advantageous than desktop displays in permitting information of deduced spatial relationships. In addition, the ability of HMDs to refresh the virtual target stereo information based on the tracking of the participants' location and orientation might be a reason for their better exocentric distance judgment. For instance, [PERSON], [PERSON], [PERSON], [PERSON] and [PERSON] [26] argued that display technologies with the ability to update 3D information based on the tracking of the users' location and orientation would provide better accuracy of size judgment. In addition, other studies reported exocentric distance judgment by comparing the real environment to a virtual environment. For instance, [PERSON] and [PERSON] [19] and [PERSON] et al. [36] both compared real environments and HMD, reported accurate and underestimated (20% lower than estimates in the real) distance judgments, respectively, in real and HMD conditions. Besides, [PERSON], [PERSON], [PERSON], [PERSON] and [PERSON] [9] also revealed that sizes in the SWD were perceived smaller than in the real world. [PERSON] and [PERSON] [6], [PERSON] et al. [37], and [PERSON], [PERSON] and [PERSON] [8] also reported that, under different distance and varied experimental setups, exocentric distance judgment accuracies of, respectively, 85%, 84%, and 80% in SWD, and these were perceived as smaller than in the real environment. The findings of the present study show that the exocentric distance judgment was imperceptibly improved in accordance with the past studies of VR. The possible reasons for the improvement of the judgment accuracy could be because of the direct reaching method employed in the present study and the display advancements. Indeed, accuracy results obtained using direct reaching was better as compared to the results reported in previous studies, where 86% and 77% accuracies were obtained using affordance judgment, respectively, in the HMDs and BackPro display [26]; 80% using gesture interaction [8]; 84% using perceptual matching [37]. Consequently, direct pointing could be considered as one of the reliable and promising interaction techniques in VR.