\section{Discussion}
\label{discussion}

We evaluated six visual hand renderings, as described in \secref{hands}, displayed on top of the real hand, in two virtual object manipulation tasks in AR.

During the Push task, the Skeleton hand rendering was the fastest (\figref{results/Push-CompletionTime-Hand-Overall-Means}), as participants employed fewer and longer contacts to adjust the cube inside the target volume (\figref{results/Push-ContactsCount-Hand-Overall-Means} and \figref{results/Push-MeanContactTime-Hand-Overall-Means}).
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Participants consistently used few and continuous contacts for all visual hand renderings (Fig. 3b), with only less than ten trials, carried out by two participants, quickly completed with multiple discrete touches.
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However, during the Grasp task, despite no difference in completion time, providing no visible hand rendering (None and Occlusion renderings) led to more failed grasps or cube drops (\figref{results/Grasp-CompletionTime-Hand-Overall-Means} and \figref{results/Grasp-MeanContactTime-Hand-Overall-Means}).
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Indeed, participants found the None and Occlusion renderings less effective (\figref{results/Ranks-Grasp}) and less precise (\figref{questions}).
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To understand whether the participants' previous experience might have played a role, we also carried out an additional statistical analysis considering VR experience as an additional between-subjects factor, \ie VR novices vs. VR experts (\enquote{I use it every week}, see \secref{participants}).
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We found no statistically significant differences when comparing the considered metrics between VR novices and experts.

Interestingly, all visual hand renderings showed grip apertures very close to the size of the virtual cube, except for the None rendering (\figref{results/Grasp-GripAperture-Hand-Overall-Means}), with which participants applied stronger grasps, \ie less distance between the fingertips.
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Having no visual hand rendering, but only the reaction of the cube to the interaction as feedback, made participants less confident in their grip.
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This result contrasts with the wrongly estimated grip apertures observed by \textcite{al-kalbani2016analysis} in an exocentric VST-AR setup.
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Also, while some participants found the absence of visual hand rendering more natural, many of them commented on the importance of having feedback on the tracking of their hands, as observed by \textcite{xiao2018mrtouch} in a similar immersive OST-AR setup.

Yet, participants' opinions of the visual hand renderings were mixed on many questions, except for the Occlusion one, which was perceived less effective than more \enquote{complete} visual hands such as Contour, Skeleton, and Mesh hands (\figref{questions}).
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However, due to the latency of the hand tracking and the visual hand reacting to the cube, almost all participants thought that the Occlusion rendering to be a \enquote{shadow} of the real hand on the cube.

The Tips rendering, which showed the contacts made on the virtual cube, was controversial as it received the minimum and the maximum score on every question.
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Many participants reported difficulties in seeing the orientation of the visual fingers,
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while others found that it gave them a better sense of the contact points and improved their concentration on the task.
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This result are consistent with \textcite{saito2021contact}, who found that displaying the points of contacts was beneficial for grasping a virtual object over an opaque visual hand overlay.

To summarize, when employing a visual hand rendering overlaying the real hand, participants were more performant and confident in manipulating virtual objects with bare hands in AR.
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These results contrast with similar manipulation studies, but in non-immersive, on-screen AR, where the presence of a visual hand rendering was found by participants to improve the usability of the interaction, but not their performance~\cite{blaga2017usability,maisto2017evaluation,meli2018combining}.
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Our results show the most effective visual hand rendering to be the Skeleton one{. Participants appreciated that} it provided a detailed and precise view of the tracking of the real hand{, without} hiding or masking it.
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Although the Contour and Mesh hand renderings were also highly rated, some participants felt that they were too visible and masked the real hand.
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This result is in line with the results of virtual object manipulation in VR of \textcite{prachyabrued2014visual}, who found that the most effective visual hand rendering was a double representation of both the real tracked hand and a visual hand physically constrained by the virtual environment.
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This type of Skeleton rendering was also the one that provided the best sense of agency (control) in VR~\cite{argelaguet2016role, schwind2018touch}.

These results have of course some limitations as they only address limited types of manipulation tasks and visual hand characteristics, evaluated in a specific OST-AR setup.
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The two manipulation tasks were also limited to placing a virtual cube in predefined target volumes.
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Testing a wider range of virtual objects and more ecological tasks \eg stacking, assembly, will ensure a greater applicability of the results obtained in this work, as well as considering bimanual manipulation.
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Similarly, a broader experimental study might shed light on the role of gender and age, as our subject pool was not sufficiently diverse in this respect.
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However, we believe that the results presented here provide a rather interesting overview of the most promising approaches in AR manipulation.
