## 8 Experimental Results
### Perception of the Contribution of Haptic Feedback over AR Visualization  
In Task 1, as explained in Section 7.3, participants were told that they could _inspect_ the figures with their hand. Starting from this premise, users can be split into two groups taking into consideration their exploration movements. Five participants moved their hand up and down to explore the AR figure, interpreting the slices that were generated in the palm of the hand. This group was coincident with the design hypothesis and the implementation described in Section 5.2. On the other hand, 4 participants tended to explore the figure following the edges of its volume. For example, a participant tried to explore the sphere by moving the hand over its entire surface. Due to the operation mode of the Ultrahaptics, if the ultrasound is blocked with part of the hand, the haptic feedback is not properly received. Hence, in this case, it is not possible to inspect the bottom side of the figures with the palm facing up.  
When asked if they think that, when provided haptic feedback, high-fidelity volume-based interpretation is sufficient by its own to identify the figures, aggregated results reveal an average rating of 2.11 over 5 (\(\sigma\): 1.19), with 1 being completely insufficient and 5 being completely sufficient. Thus, according to the participants, haptic feedback does not seem sufficient and AR visual info is needed.  
Table 1 collects the opinion of the users with respect to the hardest and easiest figures to interpret based only on haptic representation. Seven participants identify the torus as the most complicated figure to interpret, while five think that the cube and the cone are the easiest ones. The most contradictory shape is the arrow, with a coincident number of participants (4) voting as it being hard or easy.  
\begin{table}
\begin{tabular}{l c c} \hline \hline  & \
\begin{tabular}{c} **Hardest Figure** \\ **(Number of Votes)** \\ \end{tabular} & \multicolumn{2}{c}{**Easiest Figure**} \\  &
\begin{tabular}{c} **(Number of Votes)** \\ \end{tabular} & \multicolumn{2}{c}{**(Number of Votes)**} \\ \hline Torus & 7 & Cube & 6 \\ Arrow & 4 & Cone & 5 \\ Sphere & 4 & Arrow & 4 \\ House & 3 & Sphere & 3 \\ Cone & 2 & Pyramid & 3 \\ Cube & 1 & House & 2 \\ Pyramid & 1 & Cylinder & 1 \\ Cylinder & 1 & Hemisphere & 1 \\ Hemisphere & 1 & Octahedron & 1 \\ Octahedron & 0 & Torus & 0 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Number of votes for the hardest (left) and easiest (right) figures as voted by the participants.  
Figure 13: Stages of the users study.  
During the tests, several participants have indicated that features such as the tip of the cone or the tip of the pyramid and the octahedron are much better appreciated. At the time of guessing in Task 2, these users have tried to find those characteristics that seem relevant to them.  
Figure 14 shows a box plot of the interpretability value given by the users to each figure. In the image, median values for each figure are represented as circles. As it can be seen in the image, the figures that present a greater disparity of results are the hemisphere and the torus. On the contrary, figures in which the users have most agreed are the pyramid and the cone.  
Figure 15 gathers the times required by each user on Task 1 since they begin to explore the figures until they form an opinion about it. The light blue line shows the average times for each figure. Times required by users range between 5 and 65 s. There is a statistically significant difference between inspection times among users, as revealed by a one-way ANOVA test (\(F(8,81)=5.627\), p\(\circ\)). A Tukey post hoc test shows that the inspection time was significantly lower for U1, U2, U5, and U6 when compared to U7 and U8.