## 8 Experimental Results
### UHK-Based Haptic Expressiveness for Shape/Volume Identification  
In Task 2 (guessing the figure only with haptic feedback support), the expressiveness of the mid-air haptic representation for different geometric figures is analyzed: 44.4% of users indicated that the  
Figure 14: Box plot of the interpretability given to each figure by the users, with 1 meaning that the figure is not interpretable and 5 meaning the figure is perfectly interpretable. Figure 15: Time required by each user for the inspection of the figures in Task 1.  
process of guessing figures seems extremely difficult (1 over 5), and 44.4% found it difficult (2 over 5). Only 1 user found it easy. Recall that the user answers the relevant questionnaire without getting any confirmation on the hits and failures. Despite its limitations, results indicate that participants are able to interpret more figures than expected, offering an acceptable success rate. Times required by each user to guess the shapes can be seen in Figure 16. A Wilcoxon Soigned-Rank Test indicates that the difference between inspection and guessing times is not statistically significant (\(Z=-1.630\), \(p=0.103\)). Figure 17 presents the confusion matrix between the correct answers and the participants' guesses in the form of a heat map. In the vertical axis appears the correct answer, and in the horizontal one appears the user guess. On the diagonal of the matrix, the number of right answers for each figure can be seen. The more green a cell is, the more users guessed correctly that figure. As can be seen in Figure 17, the _cone_ has been guessed properly 55.5% (5/9) of the time, while the _torus_ has the most hits with 77% (7/9). The _house_ on its side has been properly guessed the 66.6% (6/9) of the time. Although users have indicated that haptic feedback is not enough to identify figures, the data indicates that this is possible. In fact, by choosing a set of easily recognizable and non-misleading figures (e.g., cone and pyramid), it would be possible to transmit graphic information to the user in a haptic manner. The presented matrix serves as a guide to select that hypothetical set of figures. Most users indicated that, when identifying the _torus_, they were not able to properly distinguish the central hole. Instead, they did the divination on the basis that this figure had the lowest height of all. This problem is due to the lack of accuracy of the device as indicated in Section 4. Figure 18 shows the performance for each participant and the relationship between the figures perceived by users as more difficult (black lower triangle, labeled as 1/5) and easier (blue lower triangle (5/5)) and their actual results (upper triangle in green is a hit, while red is a fail). It would be expected that most hits have occurred over figures labeled as easy, with failures concentrating on those labeled as difficult to interpret. Taking for example the participant U7, we can see that the three figures that the user found easy to interpret (hemisphere, house, and pyramid), were not afterwards guessed. However, two of the figures that the participant said were hard to interpret were two hits (cone and octahedron). In general, it seems that users' perception of figures that are easy and difficult to interpret does not correspond to the results obtained. However, it seems that there is a set of figures that are the most successful in general (cone, house, and torus). We have grouped participants into two groups y taking into consideration the number of hits (G1: \(\geq\)5 hits; G2: \(<\)5 hits). A Shapiro test is carried out over the hit frequency, and the test cannot reject the null hypothesis of normality for the  
Figure 16: Time required by each user for the guessing process for each figure in Task 2.  
distribution (\(W=0.94,p=0.61\)). Then, a Welch Two Sample test for unequal variances cannot state a real difference in performance between the two groups. Figure 17: Confusion matrix heat map of the Task 2 guessing process.