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With the last task, we investigated virtual aiming performance across the BendDesk surface. Other than in the previous tasks participants did not move their finger towards the target, but had to adjust both fingers inside the source area along a virtual aiming path to hit the target. We compared whether virtual aiming was supported with or without a grid displayed on the surface.

Task design and procedure The experimental task is depicted in Figure 12. The system displayed the source, a gray colored circle with a diameter of 200 px (19.5 cm) and the target, a white colored circle with a diameter of 30 px (2.9 cm). The distance between source and target was 800 px (78.1 cm). Participants had to position the left and right index finger inside the source area until an imagined line drawn through both finger tips would hit the target area. The system gave visual feedback by rendering circles beneath the touches. When participants felt that they would have hit the target they released both fingers and the system displayed a gray line through both touches towards the target area. Then, the interactive area went blank and the next trial appeared.

Trials appeared in ten different movement directions (with two repetitions each). Targets within the horizontal plane: (1) 90◦, (2) 80◦, (3) 70◦; target within the curve: (4) 60◦; and targets across the curve and in the vertical plane: (5) 50◦, (6) 40◦, (7) 30◦, (8) 20◦, (9) 10◦, and (10) 0◦. The order of trials was randomized. Participants worked throughout a block with a uniform grid on the system’s surface (we displayed a 26 x 26 grid with a cell size of about 40 px × 40 px, or 3.9 cm × 3.9 cm) and throughout another block without a grid but a solid blue-colored surface. This resulted in 10 (angle) × 2 (background) experimental conditions. We further controlled the virtual aiming direction by presenting the source either in the right or left corner of the horizontal area (upward aiming), or in the right or left corner of the vertical area (downward aiming). This resulted in a total number of 160 virtual aiming operations. As dependent variable we measured the aiming error (Figure 13), i.e., the deviation between the virtual aiming path and the target area, or in other words the spatial misjudgment (given in px).

We hypothesized the following outcomes:

• H6: The aiming error is smaller for virtual aiming within one plane than across the curve and different planes.

• H7: The aiming error is smaller for virtual aiming with a grid displayed on the surface than without a grid.

Results The data were analyzed with a 10 × 2 analysis of variance (ANOVA) with the within-subject factor angle and background. Aiming errors are depicted in Figure 14. The ANOVA revealed a significant main effect of the factor angle (F(9,158) = 17.24;p < 0.01). Aiming errors were smallest when source and target were within the same plane, i.e., virtual aiming at 90◦ (mean error 9 px) was significantly more accurate than at all other angles (mean error 43 px).

ITS 2010: Displays November 7-10, 2010, Saarbrucken, Germany

Furthermore, aiming at 90◦ and 0◦ was supported by the grid displayed on the surface: Aiming errors for the 90◦ angle were 65% (8 px) smaller with displayed grid (mean 5 px) than without the grid (mean 13 px). For the 0◦ angle the aiming errors were 57% (19 px) smaller with the grid (mean 14 px) than without the grid (mean 3 px). However, the background did not have any effect on the other angles, yielding a significant interaction (F(9,153) = 2.61;p < 0.01). The factor background alone did not show any significant effect on aiming errors.

Finally, the results from the virtual aiming task showed that virtual aiming is most accurate for the orthogonal angles (0◦, 90◦) when a grid is displayed on the surface. This is only partially in line with our hypotheses H6 and H7.

Exhaustion considerations As pointed out earlier, users had to use their entire arm to drag objects across the curve and onto the vertical surface. We believed that these movements would lead to muscle fatigue in short time. Therefore, we conducted an informal test to gain a rough estimate when dragging movements become inconvenient. We repeated the cross-dragging task and let users drag objects across the curve in both directions without dropping the arm onto the surface. We asked the participants to stop the test as soon as they felt muscle fatigue. Furthermore, we asked users to express any signs of fatigue during the test.

Results In the first four minutes, no participant reported any signs of fatigue. After four minutes six participants expressed signs of fatigue in their upper arm. On average, each participant conducted this task for about 7:30 minutes. However, after 12 minutes two participants commented that they could do the test “the whole day”. Both stopped the test after about 15 minutes without any symptoms of fatigue.

Most participants (16/18) perceived the downward dragging as more comfortable than the reverse direction because of the inward rotation of the hand during the movement. For the downwards direction, they could almost let their arm fall down. This confirms our observations in the second user test.

Ten participants thought that their dragging speed on the curved area was much slower than on the other areas. Additionally, five of them thought that they had to use more pressure on the curve to drag the object. 13 participants stated that diagonal dragging through the curve was inconvenient.

Figure 12: Experimental design for virtual aiming task.

aiming error source area target

Figure13: Twofingertouchesinthesourceareadefine a straight line towards the target. The aiming error is the deviation between this virtual aiming path and the target area.



Solid color Uniform grid same curve opposite surface

Figure 14: Distance from target depending on angle.

Our user population is not representative for an ergonomic analysis of the BendDesk system as most users were male and between 24 and 32 years old. Nevertheless, in contrast to our assumptions, all users were able to perform the dragging task for a rather long period without any fatigue. In future work, we will explore the ergonomic aspects of interaction gestures in more detail.

DISCUSSION The evaluation of BendDesk revealed three main findings: First, dragging on a planar surface is faster and straighter than dragging across the curve, although the distances were constant for all dragging tasks. This is a rather unexpected finding, as Fitts’ Law [9] would have predicted constant movement durations over all areas. The increased movement durations across the curve went along with a higher curvature in hand paths. From a cognitive point of view, the curved hand path is similar to motor behavior observed when avoiding obstacles. Jax and Rosenbaum [14] found in their study that the anticipation of obstacles led to more curved hand paths, even when the obstacle was not present. This suggests that our participants perceived the curve as a kind of obstacle, which they tended to avoid. Considering the motor behavior, we assume that the more curved hand paths in the curve also results from the more complex motor activity involved in curve dragging: The participants performed horizontal dragging basically by pushing or pulling the hand backwards or forwards. Analogously, they dragged the target on the vertical surface by lifting or lowering the arm. In

ITS 2010: Displays November 7-10, 2010, Saarbrucken, Germany contrast, when moving across the curve, users tended to turn in the entire hand while moving it upwards and downwards, which yields a more complex movement. One person stated afterwards that the tendon in his index finger hurt if he did not turn the hand, while another person reported that he was afraid of drilling his index finger into the surface and, thus, turned the hand. Furthermore, four users wanted to change from the index to the middle finger when they unintentionally released an object during the dragging because they considered the middle finger as stronger and more stable.

Second, the angle had nearly no effect on the duration of dragging operations. However, we noticed a significant increase in trajectory length when the angle is increased. In order to gain more insights into the causes for this effect, we plotted out the trajectories for each angle (Figure 9). Two effects become apparent: First, at higher angles participants tended to minimize the dragging distance on the curve. Some users even separated the movement into a short path across the curve and a long path for the remaining movement. Second, the higher the angle the higher the spreading of trajectories beside the direct line. This also matches Figure 10 that indicates an increased variance for higher angles. Furthermore, our observations revealed that most users optimized their dragging operations to reduce muscle exertion. We noticed that some users dragged downwards by letting the arm quickly fall straight downwards and across the curve before dragging the object to the target, as shown in Figure 1(a). Another frequent movement was an upward dragging, where the user firstly dragged the object across the curve using a stiff bent arm and finished the dragging by turning hand and lower arm with the upper arm as rotation axis, as shown in Figure 1(b). Moreover, two users reported that approaching the curve in a flat angle feels uncomfortable. In general, we noticed that users tried to create a convenient movement trajectory despite the task to acquire the target as fast as possible.

Finally, the virtual aiming task revealed the complexity of imagined instead of manual aiming gestures. Participants severely misjudged the spatial relations towards the target. However, at orthogonal angles (0◦, 90◦) the aiming error was lowest, probably because the table borders provided alignment guides. This is further supported by the observed improvement of virtual aiming at 0◦ and 90◦ when a grid was present. In this case participants could easily touch the grid lines to hit the target. We assume that the complexity of virtual aiming depends on the required cognitive mapping between the 3D and the GUI space. If the user aims at a target on the same surface, she has to compensate for the perspective distortion of the plane, where, according to [27], those effects are stronger on horizontal surfaces. If the target is placed on the opposite area, the user has to perform a threedimensional non-linear transformation of the table shape to the rectangular control space.

We presented an interactive desk system that merges a vertical and a horizontal display with a curve into a spatially cohesive surface. This provides a large interactive area that users can reach in a comfortable sitting position. We intro- duced a technique to project on the curved surface, as well as algorithms for multi-touch detection under strong distortions. The system enables seamless dragging gestures across all areas. Nevertheless, our user studies suggest that the curve represents a slight but noticeable physical barrier. It leads to longer interaction times when crossing it and some users tend to minimize the dragging distances in that area when approaching it with a flat angle. Furthermore, it impairs the user’s spatial perception.

For application designers, this means that the three areas should not be considered as a single interactive surface. Users will more likely reduce the number of interactions across the curve, and the user interface should not require crossdragging with flat angles. Instead, the characteristics of the curve must be taken into account and can even be exploited to divide the surface into logical units. For example, an application could use the horizontal display to create content that is stored in the curve before it is assembled at the vertical area. That is, the three areas would represent steps in a workflow. Another scenario is remote collaboration, where the vertical space represents a public space showing content visible to all co-workers, while the horizontal area is a private space for individual content. In these cases, the curve could act as an intermediate storage, or as a “dock” or “taskbar”.

In future work, we will investigate the factors influencing the dragging performance in further detail. We plan to conduct tests with different curve radii and varying angles between the large areas. Furthermore, we want to explore the application domain of BendDesk. We intend to identify the desk tasks that are suitable for the transfer to our system and determine the role each area plays in particular applications. Moreover, we plan to involve additional input modalities. For example, our diffusor layer can be replaced with an Anoto pattern that allows both touch and precise pen input [3, 15]. Additionally, we plan to find the limitations of such a system opposed to a common desk setup. Finally, we want to fathom to which extent the vision of a multi-touch based desk environment in the shape of BendDesk is practicable.

This work was funded in part by the German B-IT Foundation. We thank Christian Remy for his helpful comments on this paper.

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