Elbow-Anchored Interaction: Designing Restful Mid-Air Input

A key aspect of designing mid-air input concerns the mapping function for translating the hand motion to the cursor position on the screen. Myer et al. [37] suggest that directly mapping (ray-casting) hand motion provides an easy association for the user to keep track of the cursor. However, it tends to be imprecise. Similar findings were suggested by Vogel et al. [46] in their comparison of absolute, relative, and hybrid mappings of hand movements. The absolute mapping affords efficient input, at the cost of being erroneous, making it impractical. Cockburn et al. [14] also compared ray-casting with large 2D movements and movements in 3D volume. The 2D movements tend to be more precise and accurate than raycasting. 3D volume mappings are slower, less accurate, and more physically demanding than others. Solutions to implement natural but precise mid-air pointing include using a target-oriented approach [9, 13], velocity-oriented approach [33], or by allowing the user to manually switch between the absolute and relative mapping modes [15] - which require explicit mode switching to mitigate erroneous input.
设计空中输入的一个关键方面涉及将手部运动转换为屏幕上光标位置的映射函数。Myer 等人。[ 37]建议直接映射（光线投射）手部运动为用户提供了一个简单的关联，以跟踪光标。然而，它往往是不精确的。Vogel 等人[ 46]在手部运动的绝对、相对和混合映射的比较中提出了类似的发现。绝对映射提供了有效的输入，代价是错误的，使其不切实际。Cockburn 等人[ 14]还比较了具有较大 2D 运动和 3D 体积运动的光线投射。2D 运动往往比光线投射更精确和准确。3D 体积映射比其他映射速度更慢、精度更低、物理要求更高。 实现自然但精确的空中指向的解决方案包括使用面向目标的方法[ 9，13]，面向速度的方法[ 33]，或允许用户在绝对和相对映射模式之间手动切换[ 15] -这需要明确的模式切换以减少错误的输入。

The literature also presents approaches for 2D plane mappings. Chattopadhyay and Bolchini [12] tested a menu based on directional movements (360 degrees) that required XY-plane movements of up to 18.9cms, with a starting position at about shoulder level. The mid-air keyboard, Vulture [32], was implemented as a plane sized 20 x 5.5cm. Cockburn et al. [14] used a square with sides of one cubit (a measure based on forearm length, 45.72 cms).
文献还提出了 2D 平面映射的方法。Chattopadhyay 和 Bolchini [ 12]测试了一种基于定向运动（360 度）的菜单，该菜单要求 XY 平面运动高达 18.9 厘米，起始位置约为肩部水平。空中键盘 Vulture [ 32]是一个 20 x 5.5 cm 的平面。Cockburn 等人。[ 14]使用一个边长为一肘的正方形（基于前臂长度的测量，45.72 厘米）。

Previous work has also examined, to a minimal extent, spherical 3D input spaces. For instance, joint-centered kinespheres [31] are spherical 3D input spaces centered at joints. They tested three joints as the center of kinespheres: shoulder, elbow, and wrist, and found that wrist offers the highest performance (throughput) and comfort, followed by elbow and shoulder. Guinness et al. [19] propose a spherical input space defined by the user. In longitudinal user tests against planar and hyperplanar spaces, they found no significant difference in performance, arguing that their LeapMotion implementation which, does not provide precise forearm angle estimation, may have contributed to the results. Their participants were seated on an office chair with their elbow rested on a desk. In our studies, we use a motion capture system and a more ecologically valid setup that includes a large display and couch. Both aforementioned works use the ISO 9241-9 “ring of circles” task, which consists of targets arranged as a ring around the center of the screen; as a result, the performance at the edges and corners of the input space was not examined. We consider this to be a significant gap, as biomechanical and environment constraints can impact performance unevenly in the space. In contrast, we devised a protocol for capturing performance measurements uniformly across the available motor-input space. Another example of spherical mapping, although not intended as a general-purpose input space, is Virtual Shelves [28] which projects a menu on a spherical space around the user. Similar to Virtual Shelves, TickTockRay [24] aims at providing a self-contained method for mid-air input in VR environments. But such an approach does not include the necessary parameters for casual elbow-anchored input.
以前的工作也检查了，在最小程度上，球形 3D 输入空间。例如，以关节为中心的运动球[ 31]是以关节为中心的球形 3D 输入空间。他们测试了三个关节作为动力球的中心：肩膀，肘部和手腕，发现手腕提供最高的性能（吞吐量）和舒适度，其次是肘部和肩膀。Guinness 等人[ 19]提出了一个由用户定义的球形输入空间。在针对平面和超平面空间的纵向用户测试中，他们发现性能没有显着差异，认为他们的 LeapMotion 实现无法提供精确的前臂角度估计，可能对结果有所贡献。他们的参与者坐在办公椅上，手肘放在桌子上。在我们的研究中，我们使用了一个动作捕捉系统和一个更生态有效的设置，包括一个大显示器和沙发。 上述两个作品都使用 ISO 9241-9“圆环”任务，该任务由围绕屏幕中心排列的环形目标组成;因此，没有检查输入空间边缘和角落的性能。我们认为这是一个显著的差距，因为生物力学和环境限制可能会影响空间中的性能。相比之下，我们设计了一个协议，用于在可用的电机输入空间中均匀地捕获性能测量。球面映射的另一个例子，虽然不是作为通用输入空间，是虚拟货架[ 28]，它将菜单投影到用户周围的球面空间上。与 Virtual Shelves 类似，TickTockRay [ 24]旨在为 VR 环境中的半空输入提供一种独立的方法。但是这种方法不包括用于随意肘锚定输入的必要参数。

In summary, researchers have studied a variety of methods that bound the 2D and 3D input spaces for mid-air interactions, but far less is known about how these apply to various casual postures.
总之，研究人员已经研究了各种方法，这些方法将 2D 和 3D 输入空间绑定到空中交互，但对这些方法如何应用于各种休闲姿势知之甚少。

Mid-air interactions can benefit from an assessment of human biomechanical properties and upper limb ergonomics to offer an ideal user experience. König et al. [26] note the impact of hand tremors [45] on mid-air pointing imprecision. Temporal window averaging [37] or Kalman filter [42] techniques are needed to smoothen the pointing behavior. Another major issue with mid-air pointing is the “Gorilla Arm Syndrome” or arm fatigue [21]. Nancel et al. [39] investigated mid-air pan and zoom techniques for wall-displays and found that mid-air gestures are less efficient and more fatiguing than device-based gestures. Several methods have studied human fatigue in the context of mid-air input [21, 22, 29, 48]. As with these studies, we use the Borg CR10 tool in our evaluation of elbow-anchored interactions to assess the degree of fatigue induced by our approach in comparison to full-arm interactions.
空中交互可以受益于对人体生物力学特性和上肢人体工程学的评估，以提供理想的用户体验。König 等人[ 26]注意到手震[ 45]对空中指向不精确的影响。需要时间窗口平均[ 37]或卡尔曼滤波器[ 42]技术来平滑指向行为。空中指向的另一个主要问题是“大猩猩手臂综合症”或手臂疲劳[ 21]。Nancel 等人[ 39]研究了壁挂显示器的空中平移和缩放技术，发现空中手势比基于设备的手势效率更低，更容易疲劳。有几种方法研究了在半空输入的情况下人体疲劳[ 21，22，29，48]。与这些研究一样，我们使用博格 CR10 工具评估肘锚定相互作用，以评估与全臂相互作用相比，我们的方法引起的疲劳程度。

Several studies suggest to limit the interaction time for which the arm/hand is raised in the air to mitigate fatigue effects [16, 23, 44]. Hincapie-Ramos et al. [21] identified that movements further away from the user's waist will lead to higher fatigue and should be avoided. Liu et al. [30] explored arms-down positions with both hands at the sides of the body for interacting with a large display. Despite these suggestions, it is still unclear whether rested elbow interactions or interactions closer to the body can provide any significant performance benefits [10].
几项研究建议限制手臂/手在空中抬起的相互作用时间，以减轻疲劳效应[ 16，23，44]。Hincapie-Ramos 等人[ 21]发现，远离用户腰部的运动将导致更高的疲劳，应避免。Liu 等人。[ 30]探索了双手放在身体两侧的手臂向下位置，以与大型显示器进行交互。尽管有这些建议，但仍然不清楚休息的肘部相互作用或更靠近身体的相互作用是否可以提供任何显着的性能优势[ 10]。

Nunnari et al. [41] observed subjects performing a 3D docking task while sitting on a chair and found that muscle load distribution is higher when subjects vary their posture. Their results suggest that postural variability may prevent over-exertion of key muscles, such as the shoulder, which is usually identified as the culprit for fatigue in mid-air gestural input [21]. In touch-based interaction, shoulder-dominant arm strokes are also known to require more muscle effort than their elbow counterparts, although with improved performance in target selection tasks [7]. Gesture execution and movements tend to change over the duration of an interaction, as individuals relax and adopt more comfortable positions [16]. However, certain postures encumber gesture execution. For instance, the degrees-of-freedom of hand trajectories are limited when the elbow is rested on a surface. Aslan et al. [6] also observed variation in gesture patterns. In the domain of virtual reality, Wentzel et al. [47] measured the maximum reach of an individual arm's and apply a non-linear transformation to extend user's virtual reach. Similarly, Ergo-O [34] decouples the physical and visual spaces and shrinks the physical space so that more objects lie within user's reach.
Nunnari 等人[ 41]观察了坐在椅子上执行 3D 对接任务的受试者，发现当受试者改变姿势时，肌肉负荷分布更高。他们的研究结果表明，姿势变化可能会防止关键肌肉的过度劳累，例如肩膀，这通常被认为是空中手势输入疲劳的罪魁祸首[ 21]。在基于触摸的交互中，肩膀占主导地位的手臂划水也比肘部划水需要更多的肌肉努力，尽管在目标选择任务中的表现有所改善[ 7]。手势执行和动作往往会在互动的持续时间内发生变化，因为个人放松并采取更舒适的姿势[ 16]。然而，某些姿势阻碍手势执行。例如，当手肘搁置在表面上时，手轨迹的自由度是有限的。阿斯兰等人[ 6]也观察到手势模式的变化。 在虚拟现实领域，Wentzel 等人。[ 47]测量了单个手臂的最大范围，并应用非线性变换来扩展用户的虚拟范围。类似地，Ergo-O [ 34]将物理空间和视觉空间合并，并缩小物理空间，以便用户可以触及更多对象。

The above studies point at the need to consider system ergonomics and upper limb biomechanics to facilitate restful mid-air interactions. However, very little is known about the specific parameters needed to develop such interactions or how the constraints of a restful posture affect mid-air input. In particular, it is unclear if any advantage gained from diminished fatigue also negatively impacts the performance of such type of mid-air input.
上述研究指出，需要考虑系统人体工程学和上肢生物力学，以促进宁静的空中互动。然而，很少有人知道的具体参数需要开发这样的互动或如何约束的休息姿势影响半空中的输入。特别是，目前还不清楚从减少疲劳中获得的任何优势是否也会对这种类型的空中输入的性能产生负面影响。

The joint motions we used in coding our observational study are: 1) Shoulder Horizontal Adduction/Abduction 2) Shoulder Flexion/Extension 3) Elbow Flexion/Extension 4) Shoulder Medial/Lateral Rotation 5) Wrist Deviation 6) Wrist Flexion

Eight (8) participants, including 3 females, from our organization were invited into a space resembling a common living room and which included a large couch and TV. We instructed participants to sit on the couch in their most comfortable posture and perform a set of three different gestures: Swipe, Wave, and Slap. These three gesture labels were selected as they involve directional properties and can be distinguished from one another. The instructions on these three gestures were kept vague intentionally to support variability.We avoided using labels solely associated with any UI interactions such as drag, select, or move to prevent legacy bias [36]. For example, Swipe has a digital counterpart, but Slap and Wave gestures do not. While we acknowledge that the meaning of the term “comfort” may be subjectively distinct to each participant, we repeatedly asked participants to be relaxed and to assume they were in their own living room. Each participant performed Swipe, Wave and Slap gestures 3 times, in four directions (up, down, left, right) and with each hand. Variation in direction is important because the interaction of the body with furniture poses constraints to movement that are potentially asymmetric. These were captured in two of their most preferred body postures. The participants’ body postures varied from sitting with their legs on the couch, resting their body on an arm rest, resting their arm on the back rest or on a cushion, among other postures they deemed to be comfortable (Figure 2). Interestingly, none of the participants chose to lie down. This could possibly be because the participants were not comfortable lying down in a professional environment.
我们组织的八（8）名参与者（包括 3 名女性）被邀请进入一个类似公共客厅的空间，其中包括一张大沙发和电视。我们指导参与者以最舒适的姿势坐在沙发上，并执行一组三种不同的手势：滑动，挥手和拍打。选择这三个手势标签是因为它们涉及方向属性并且可以彼此区分。这三个手势的说明故意保持模糊以支持可变性。我们避免使用仅与任何 UI 交互相关的标签，例如拖动，选择或移动，以防止遗留偏见[ 36]。例如，滑动有一个数字对应物，但拍打和挥手手势没有。虽然我们承认“舒适”一词的含义可能对每个参与者来说主观上是不同的，但我们一再要求参与者放松，并假设他们在自己的客厅里。 每个参与者在四个方向（上，下，左，右）和每只手上执行滑动，挥动和拍打手势 3 次。方向的变化很重要，因为身体与家具的相互作用对潜在不对称的运动构成了约束。这些照片是以它们最喜欢的两种姿势拍摄的。参与者的身体姿势各不相同，从坐在沙发上，把身体放在扶手上，把手臂放在靠背上或垫子上，以及其他他们认为舒适的姿势（图 2）。有趣的是，没有一个参与者选择躺下。这可能是因为参与者不愿意躺在专业环境中。

We videotaped the sessions and recorded participants’ comments. Sessions on average lasted an hour long.
我们对会议进行了录像，并记录了参与者的评论。会议平均持续一个小时。

Two authors independently annotated each of the performed gestures based on the frequency of upper limb joints using Anvil [25], a video annotation tool. Video annotations were grouped into seven categories: motion joints, elbow position while rested, elbow position at the start of gesture execution, posture, gesture, gender, and hand. We define rested position as the neutral position of the joints when the participant is not doing a gesture and starting position as the position of the joints just before carrying out the gesture.
两位作者使用 Anvil [ 25]（一种视频注释工具）根据上肢关节的频率独立注释了每个执行的手势。视频注释分为七类：运动关节，休息时的肘部位置，手势执行开始时的肘部位置，姿势，手势，性别和手。我们将休息位置定义为参与者没有做手势时关节的中性位置，将开始位置定义为执行手势之前关节的位置。

First, each gesture is characterized in terms of joint motions that are utilized in the movement. The movements are characterised by six joint motions [40]: shoulder horizontal abduction/adduction, shoulder flexion/extension, elbow flexion/extension, shoulder medial/lateral rotation , wrist flexion/extension, wrist deviation (Figure 3). One gesture can have annotations corresponding to multiple joint motions. For example, a swipe-left motion with the right hand may involve shoulder horizontal abduction/adduction, shoulder medial/lateral rotation as well as elbow flexion/extension. In the majority of cases participants brought their hand to a common starting position that was usually higher than the resting position. Since this motion is meant as an accomodation, and is not part of the gesture semantics, we did not count it.
首先，每个姿势的特征在于在运动中使用的关节运动。这些运动的特征在于六个关节运动[ 40]：肩部水平外展/内收、肩部屈曲/伸展、肘部屈曲/伸展、肩部内侧/外侧旋转、手腕屈曲/伸展、手腕偏离（图 3）。一个姿势可以具有对应于多个关节运动的注释。例如，用右手向左滑动运动可以涉及肩部水平外展/内收、肩部内侧/外侧旋转以及肘部屈曲/伸展。在大多数情况下，参与者将他们的手带到一个通常高于休息位置的共同起始位置。由于这项动议是作为一种迁就，而不是手势语义的一部分，我们没有把它计算在内。

The joint motions are associated with different upper limb segments. Combined, wrist deviation and wrist flexion/extension move the hand, shoulder medial/lateral rotation and elbow flexion/extension has an effect on the forearm, and finally shoulder flexion/extension and shoulder horizontal abduction/adduction move the upper arm [40]. Figure 3 depicts these joint motions and their effect on the upper limb segments.
关节运动与不同的上肢节段相关联。结合起来，腕部偏离和腕部屈曲/伸展移动手，肩部内侧/外侧旋转和肘部屈曲/伸展对前臂产生影响，最后肩部屈曲/伸展和肩部水平外展/内收移动上臂[ 40]。图 3 描绘了这些关节运动及其对上肢节段的影响。

In Figure 4 we present a summary of the distribution of the joint motions for participants in each of the two postures in our study. We observed that the majority of movements involved participants lifting their elbow in order to bring the hand to a higher initial position for gesture execution. Those who anchored the elbow were either seated with the elbow rested on the arm rest, for example, or were interested in executing the gestures without affecting their seated posture.
在图 4 中，我们总结了我们研究中两种姿势的参与者的关节运动分布。我们观察到，大多数动作涉及参与者抬起肘部，以便将手带到更高的初始位置进行手势执行。例如，那些固定手肘的人要么坐在手肘放在扶手上，要么有兴趣在不影响坐姿的情况下执行手势。

Figure 4 Results are fully described in text.

We also observe that full arm motions are dominant in our observations, followed by forearm and hand movements (Figure 5-top). We note that a full arm motion is the one where we observed a major movement of the shoulder, while the other joints may also be moving simultaneously. Movements of the wrist were particularly high for the ‘Wave’ gesture, which dominated the counts presented in Figure 5-bottom. Users interpreted the ‘Wave’ motion in their actions literally.
我们还观察到，在我们的观察中，全臂运动占主导地位，其次是前臂和手部运动（图 5-顶部）。我们注意到，完整的手臂运动是我们观察到肩膀发生重大运动的运动，而其他关节也可能同时运动。手腕的运动对于"挥动“手势特别高，其在图 5-底部中呈现的计数中占主导地位。用户从字面上解释了他们行动中的“波浪”运动。

The majority of upper-limb motions involved Full Arm followed by Forearm and Hand. By joints, the shoulder medial/lateral rotation was more frequent. The joint motions in decreasing order of frequency are: 1) shoulder medial/lateral. 2) shoulder flexion/extension, 3) Wrist Flexion/Extension, 4) Elbow Flexion/Extension, 5) Wrist Deviation, 6) Shoulder Horizontal Abduction

We further examine joint motions across each of the postures assumed by the participants. We observed that vertical movements usually involved shoulder flexion/extension, which is a relatively strenuous joint motion. However, whenever the arm was rested at a high surface (e.g., backrest, armrest) shoulder medial/lateral rotation, a less demanding motion, prevailed. We also find that across all postures, elbow flexion-extension was involved, as well as shoulder medial/lateral rotation in all but one user posture. Horizontal movement was dominated by shoulder medial/lateral rotation for a majority of the participants. Some male participants also engaged in high-amplitude shoulder horizontal abduction/adduction, which is associated with high fatigue. Unlike female participants, who executed wrist motions more often than full arm movements.
我们进一步研究了参与者所采取的每个姿势的关节运动。我们观察到，垂直运动通常涉及肩关节屈曲/伸展，这是一个相对剧烈的关节运动。然而，每当手臂放在高表面时（例如，靠背、扶手）肩部内/外侧旋转，这是一种要求较低的运动，占主导地位。我们还发现，在所有姿势中，除了一个用户姿势外，所有姿势都涉及肘关节屈曲-伸展以及肩关节内侧/外侧旋转。对于大多数参与者来说，水平运动主要由肩部内侧/外侧旋转主导。一些男性参与者还进行了高幅度的肩部水平外展/内收，这与高度疲劳有关。与女性参与者不同，她们执行手腕动作的频率高于手臂动作。

We summarize our findings as a set of general observations from this study:
我们将我们的发现总结为本研究的一组一般观察结果：

• The majority of upper limb motions involved the full arm and the forearm. The hand was primarily used in the ‘Wave’ gesture, but otherwise mostly accompanied the above two actions.
  大多数上肢运动涉及整个手臂和前臂。这只手主要用于“挥手”的手势，但其他大多数都伴随着上述两个动作。
  
• When movement was annotated on joint, shoulder medial/lateral rotation (forearm) and shoulder flexion/extension (upper arm) were the most frequent.
  当运动被标注在关节上时，肩部内/外侧旋转（前臂）和肩部屈曲/伸展（上臂）是最常见的。
  
• All users engaged in shouldermedial/lateral rotation (forearm movement) at least once (or more) across all postures, making it a common motion to explore.
  所有用户在所有姿势中至少进行一次（或多次）肩内侧/外侧旋转（前臂运动），使其成为一种常见的探索运动。
  
• Male participants engaged in full arm motions whereas female participants executed smaller arm movements.
  男性参与者进行完整的手臂运动，而女性参与者进行较小的手臂运动。
  
• In the vertical direction, users primarily engaged in shoulder flexion/extension (upper arm), while in the horizontal direction, users engaged in shoulder medial/lateral rotation (forearm).
  在垂直方向上，用户主要从事肩部屈曲/伸展（上臂），而在水平方向上，用户从事肩部内侧/外侧旋转（前臂）。
  
• Posture alone is not a sufficient predictor for arm motion given a specific gesture. We observed variability in arm motion across participants that chose similar postures, which suggests personal preference is a major factor.
  在给定特定姿势的情况下，单独的姿势不是手臂运动的充分预测器。我们观察到选择相似姿势的参与者手臂运动的变化，这表明个人偏好是一个主要因素。
  

In contrast to full arm motions, we define elbow-anchored motions as those primarily involving the forearm (shoulder medial/lateral rotation and elbow flexion/extension) as seen from this study. We next explore the necessary parameters to characterize elbow-anchored motions (section 4 and section 5) and then investigate the throughput and induced fatigue for such type of mid-air input (section 6). Finally, we examine the potential for forearm motions across different seated postures.
与全臂运动相反，我们将肘部锚定运动定义为主要涉及前臂的运动（肩内侧/外侧旋转和肘部屈曲/伸展），正如本研究所见。接下来，我们将探索表征肘锚定运动的必要参数（第 4 节和第 5 节），然后研究此类半空输入的吞吐量和诱导疲劳（第 6 节）。最后，我们研究了不同坐姿下前臂运动的可能性。

Having established that the upper arm movement is more physically demanding than the forearm movement, we focus our design on the latter. Since the distance between the hand and the elbow joint is always the length of the forearm, the hand motion is defined by the sphere centered at the elbow joint O with radius the forearm (Figure 7).
在确定上臂运动比前臂运动对身体的要求更高之后，我们将设计重点放在后者上。由于手和手肘关节之间的距离始终是前臂的长度，因此手的运动由以手肘关节 O 为中心、半径为前臂的球体定义（图 7）。

A sphere is defined with the elbow at the center. Only a subsection of the sphere is accessible due to range of motion of the elbow joint. The figure illustrates that region as ’ABCPD’ on the sphere, described as ’blue outline’ in the text.

Not everywhere on the sphere surface is reachable by the hand. To describe regions on the sphere that are reachable (blue outline in Figure 7), we consider four planes: OTAD, OTBC, ODPC, and the plane that crosses A and B and is perpendicular to z. Without loss of generality, assuming the user is right handed, the plane OTAD corresponds to the rightmost limit the user is able to move the hand to, and the plane OTBC corresponds to leftmost limit the user is able to move the hand to. We observed that our study participants performed gestures with the hand raised above a certain level, which we approximate by the plane ODPC for consistency and simplicity. On a couch this plane may represent the level ofarmrest.
球面上并非所有地方都是手可以触及的。为了描述球面上可达的区域（图 7 中的蓝色轮廓），我们考虑四个平面：Oscillator、OTBC、ODPC 以及穿过 A 和 B 并垂直于 z 的平面。不失一般性，假设用户是右撇子，则平面 OTBC 对应于用户能够将手移动到的最右侧极限，并且平面 OTBC 对应于用户能够将手移动到的最左侧极限。我们观察到，我们的研究参与者执行手势的手提高到一定水平以上，我们近似的平面 ODPC 的一致性和简单性。在沙发上，这个平面可以代表扶手的高度。

In the previous section, we estimated the maximum angles for a person sitting straight and anchoring the elbow on an armrest. In this setting, the maximum angle range ∠DOC of the left-right forearm movement is around 100°, with points C and D being the bottom left and bottom right corners of the input space. The angle range ∠DOA, which is same as ∠COB, for the up-down movement is around 70°. The points A and B are, respectively, the top right and top left corners of the reachablespace. We set a coordinate system that aligns the x-axis with OP and z-axis with OT.
在上一节中，我们估计了一个人坐直并手肘固定在扶手上的最大角度。在此设置中，左右前臂移动的最大角度范围θ DOC 约为 100°，点 C 和 D 为输入空间的左下角和右下角。上下运动的角度范围为 70°左右，与θ COB 相同。点 A 和 B 分别是可达空间的右上角和左上角。我们设置一个坐标系，将 x 轴与 OP 对齐，将 z 轴与 OT 对齐。

As an example, we have angles ∠POD = −60°, ∠POC = 40°, and ∠DOA = ∠COB = 70°. This allows any point in the input space to be specified by two angles θ ∈ [ − 60°, 40°], and ϕ ∈ [0°, 70°], which we refer to as azimuth and inclination, analogous to the longitude-latitude geographic coordinate system on Earth.
例如，我们有角度θ POD = −60°，θ POC = 40°，θ DOA = θ COB = 70°。这允许输入空间中的任何点由两个角度θ ∈ [ − 60°，40°]和θ ∈ [0°，70°]指定，我们称之为方位角和倾角，类似于地球上的经纬度地理坐标系。

After defining the spherical input space, we need to define a mapping to the output space, which in this paper corresponds to a large 2D display. We know it is not possible to project a 3-dimensional spherical surface to a 2-dimensional display while perfectly preserving areas and shapes. This is akin to the problem of map projection. For example, the shape or the size of the polar regions of Earth are typically severely distorted in a 2D map comparing to that of the tropical regions. There are different ways to map the angles (θ, ϕ) to the display coordinates. We consider a linear mapping between spherical and Cartesian coordinates:
在定义球形输入空间之后，我们需要定义到输出空间的映射，在本文中，输出空间对应于大型 2D 显示器。我们知道不可能将三维球面投影到二维显示器上，同时完美地保留面积和形状。这类似于地图投影的问题。例如，与热带地区相比，地球极地地区的形状或大小在 2D 地图中通常严重扭曲。有不同的方法将角度（θ，θ）映射到显示坐标。我们考虑球面坐标和笛卡尔坐标之间的线性映射：

We use a single-factor, within-subjects design. Each participant experienced three types of input spaces: elbow-sphere, elbow-plane, and shoulder-plane. To collect meaningful fatigue data, we controlled the duration of a session instead of the number of targets. As a result, the number of targets selected in a session varied with participant performance; likewise, the number of observations for targets at the end of the study is not uniform. The input spaces are as follows:
我们采用单因素、受试者内设计。每个参与者都经历了三种类型的输入空间：肘球、肘平面和肩平面。为了收集有意义的疲劳数据，我们控制了会话的持续时间，而不是目标的数量。因此，在一次会议中选择的目标数量随参与者的表现而变化;同样，在研究结束时对目标的观察数量也不一致。输入空间如下：

Participants were exposed to a target selection task based on Fitt's Law. Participants’ movements were mapped to a green circular cursor. The targets, also circular, were displayed one-at-a-time and were white on black background; they turned red when the center of the cursor was within their boundaries. The index of difficulty (ID) of a target was randomly sampled from six preset values (from 1 to 5). Given an ID and the position of the previous target, the target position was determined randomly. Target size (circle diameter) was determined according to the Fitt's Law formula:
参与者被暴露在一个目标选择任务的基础上费特定律。参与者的运动被映射到一个绿色圆形光标。目标也是圆形的，每次显示一个，黑色背景上是白色;当光标的中心在它们的边界内时，它们变成红色。目标的难度指数（ID）从 6 个预设值（从 1 到 5）中随机抽取。给定 ID 和先前目标的位置，随机确定目标位置。根据费特定律公式确定靶尺寸（圆直径）：

This generation process was run once, and produced a single list of targets that were used across participants and conditions. We recorded (a) movement time as the time elapsed from the previous selection to the next, (b) correctness as to whether or not the center of the cursor was within the target at selection time, and (c) the BORG fatigue level at 30s intervals. Order was counterbalanced.
这个生成过程只运行一次，并生成一个跨参与者和条件使用的目标列表。我们记录了（a）移动时间，即从上一次选择到下一次选择所经过的时间，（B）选择时间时光标中心是否在目标内的正确性，以及（c）博格疲劳水平每 30 秒一次。秩序得到了平衡。

Figure 8. Fully described in text.

Participants were seated on a lounge chair positioned two meters away from a 85” TV. They were instructed to seat comfortably and place their dominant arm on the armrest. Participants’ movements were tracked with 10 Optitrack 17W cameras. We attached a small circular rigid body directly to elbow and large rigid body to the wrist with a glove.
参与者坐在距离 85 英寸电视两米远的躺椅上。他们被要求舒适地坐在座位上，并将他们的优势手臂放在扶手上。参与者的运动由 10 台 Optitrack 17 W 摄像机跟踪。我们将一个小的圆形刚体直接连接到肘部，大的刚体连接到手腕。

Before starting any tasks, we performed a calibration step to determine the range of motion of the participant's forearm in the rested position. During calibration, the maximum angles for the spherical input space were progressively reduced so that an on-screen cursor controlled by the participant could reach the four corners of the TV. We did not make a judgement of the difficulty of reaching these boundaries, as this information will be present in the selection data; as such, we merely ensured that the boundaries of the output space were reachable.
在开始任何任务之前，我们执行校准步骤以确定参与者前臂在休息位置的运动范围。在校准过程中，球形输入空间的最大角度逐渐减小，以便参与者控制的屏幕上光标可以到达电视的四个角。我们没有判断到达这些边界的难度，因为这些信息将存在于选择数据中;因此，我们只是确保输出空间的边界是可到达的。

Participants were introduced to the task and presented with practice runs before each set of trials (one set per condition). They practiced until they felt ready to begin the task. For each condition, participants were asked to select circular targets on-screen for 5 minutes or until they were too tired to continue. This led to some variability in the number of observations per participant but did not affect our analysis as it does not require balanced samples. At 30-second intervals, participants were prompted to rate their level of arm fatigue on a BORG scale. We delayed the BORG scale appearance until selection of the current target was completed, so in practice, the length of this interval varied slightly. The 5-minute threshold did not include the time taken to periodically rate arm fatigue. Participants were asked to rest as much as possible between each set of trials.
向参与者介绍任务，并在每组试验（每种条件一组）之前向他们介绍练习。他们练习，直到他们觉得准备好开始这项任务。对于每种情况，参与者被要求在屏幕上选择圆形目标 5 分钟或直到他们太累而无法继续。这导致每个参与者的观察数量存在一定的差异，但不影响我们的分析，因为它不需要平衡的样本。每隔 30 秒，参与者被提示在博格量表上评估他们的手臂疲劳程度。我们将博格量表的出现时间推迟到完成当前目标的选择，因此在实践中，该间隔的长度略有变化。5 分钟阈值不包括定期评定手臂疲劳所需的时间。参与者被要求在每组试验之间尽可能多地休息。

Selection was done with the non-dominant hand by pressing the buttons of a bluetooth mouse. While not realistic, this choice of selection adds minimal overhead, allowing us to clearly measure the effect of movement. This is important because we are interested in the relative differences between the input spaces rather than in a real-world measure of performance.
选择是用非惯用手通过按下蓝牙鼠标的按钮来完成的。虽然不现实，但这种选择增加了最小的开销，使我们能够清楚地测量移动的效果。这一点很重要，因为我们感兴趣的是输入空间之间的相对差异，而不是现实世界中的性能度量。

We recruited 9 participants (5 males) within our organization, aged 22 to 35 years old. All participants used their dominant hand.
我们招募了 9 名参与者（5 名男性），年龄在 22 至 35 岁之间。所有参与者都使用了他们的优势手。

Following, we present statistics and significance tests for fatigue, movement time, and throughput. We are interested in the effect of input space on these variables. We fit linear mixed models with random intercepts for participant, and test significance with Wald t-tests on the null hypothesis that the effect estimates are zero. We report coefficient estimates as β, along with their standard error, as well as t-values and p-values. Models were fit using the R package nlme [43].In total, we collected 3,332 target selection observations from 9 participants.
接下来，我们提出了疲劳，运动时间和吞吐量的统计和显著性检验。我们感兴趣的是输入空间对这些变量的影响。我们拟合线性混合模型与随机截距的参与者，并测试显着性与 Wald t 检验的零假设，效果估计为零。我们将系数估计值报告为β，沿着其标准误差以及 t 值和 p 值。使用 R 软件包 nlme [ 43]拟合模型。我们总共从 9 名参与者中收集了 3，332 个目标选择观察结果。

6.5.1 Fatigue. Figure 9 shows a pronounced difference between the fatigue curves of the elbow-anchored input spaces and that of Shoulder-plane. For all nine participants, the maximum level of fatigue was experienced in the Shoulder-plane condition. 4 out of 9 participants withdrew the Shoulder-plane block before having completed 5 minutes of task time due to extreme arm fatigue. We tested the significance of fatigue differences by fitting a linear model to the normalized BORG data, with input space (dummy-coded) and time as predictors. Table 1 features the parameters of this model, with Shoulder-plane as the baseline. The statistically significant coefficients for Elbow-plane and Elbow-sphere confirm that the Shoulder-plane input space is indeed more tiring. The interaction between input space and the effect of time was not significant.
6.5.1 疲劳图 9 显示了肘锚输入空间的疲劳曲线与肩平面的疲劳曲线之间的显著差异。对于所有 9 名参与者，在肩平面条件下经历了最大程度的疲劳。9 名参与者中有 4 名由于手臂极度疲劳在完成 5 分钟任务时间之前撤回肩平面阻滞。我们通过将线性模型拟合到标准化的博格数据来测试疲劳差异的显著性，输入空间（虚拟编码）和时间作为预测因子。表 1 列出了该模型的参数，以肩平面为基线。肘平面和肘球面的统计显著系数证实肩平面输入空间确实更累人。输入空间与时间的交互作用不显著。

Figure 9.(Top) shows an increase in movement time with increase in index of difficulty for different input spaces. No input space condition is better than other for movement time. Figure 9 (bottom) shows that elbow-anchored input spaces are significantly less-fatiguing than shoulder-plane condition.

Table 1: Linear model fit to fatigue data with baseline set to Shoulder-plane. The variable time is ordinal. The model reveals that elbow-anchored input spaces accounted for a statistically significant (p < .05) reduction in fatigue.
表 1：线性模型拟合疲劳数据，基线设置为肩平面。变量 time 是有序的。该模型显示，肘部锚定输入空间在统计学上显著（p <0.05）减少疲劳。

		Std.
	Estimate  估计	Error  误差	t value  t 值	p value  p 值
(Intercept)  （截距）	2.975	0.441	6.745	0.00
Elbow-plane  肘刨	-2.097	0.610	-3.435	0.00
Elbow-Sphere  肘关节球	-1.890	0.610	-3.096	0.00
time  时间	0.292	0.078	3.728	0.00
Interaction (w/ time)  相互作用（w/时间）
Elbow-plane  肘刨	-0.091	0.104	-0.877	0.38
Elbow-Sphere  肘关节球	-0.124	0.104	-1.187	0.24

6.5.3 Effective Throughput. Effective throughput is a performance measure that accounts for the time-accuracy trade-off and computed as:
6.5.3 有效吞吐量。有效吞吐量是一种性能度量，它考虑了时间与准确性的权衡，并计算为：

$$T_e=(\frac{I{D}_e}{MT}),$$
(2)

where ID_e is the Index of Difficulty calculated with the effective width W_e. For each of our circular targets, W_e = 4.133 × SD_d, where d is the Euclidean distance between the observed selection and the previous selection (amplitude). ID_e is computed for each target with data from all participants. Figure 10 shows the throughput means and 95% confidence intervals computed over the participant means for each input space condition. These measures were calculated following the method of Morey [35] for within-subject designs. We tested the effect of input space on throughput with a repeated-measures ANOVA, and found no statistically significant differences (F_{2, 16} = 0.663, p = 0.529).
其中 ID _e 是用有效宽度 W _e 计算的难度指数。对于我们的每一个圆形目标，W _e = 4.133 × SD _d ，其中 d 是观察到的选择和前一个选择之间的欧几里得距离（幅度）。使用来自所有参与者的数据为每个目标计算 ID _e 。图 10 显示了在每个输入空间条件下，通过参与者平均值计算的吞吐量平均值和 95%置信区间。按照 Morey [ 35]的方法计算受试者内设计的这些测量值。我们用重复测量 ANOVA 测试了输入空间对吞吐量的影响，没有发现统计学显著差异（F _{2, 16} = 0.663，p = 0.529）。

Figure 10 shows the means and confidence interval 95% for all the three input space conditions. The difference in three conditions is minimal.

6.5.4 2D Throughput. With participants seated comfortably on a lounge chair and having their arms rested, it is plausible that performance, as measured with throughput, is not distributed uniformly over the space. In order to examine this hypothesis, we fit linear models for each input space with throughput as a response variable and the x and y screen coordinates of the targets as predictors. We used these models to generate the fine-resolution heatmaps shown in Figure 11. The heatmaps reveal distinct patterns for each input space. In Shoulder-plane, the top part of the space has worse performance, probably for requiring more physical effort to reach. With Elbow-plane the throughput gradient flows from left to right. Notably, the spherical input space features a region with very low throughput in the top left corner, which indicates that participants had trouble reaching that region.
6.5.4 二维放油。当参与者舒适地坐在躺椅上，手臂休息时，用吞吐量来衡量的性能在空间上并不是均匀分布的，这是合理的。为了检验这一假设，我们为每个输入空间拟合线性模型，其中吞吐量作为响应变量，目标的 x 和 y 屏幕坐标作为预测变量。我们使用这些模型生成了图 11 所示的高分辨率热图。热图揭示了每个输入空间的不同模式。在肩平面中，空间的顶部表现较差，可能是因为需要更多的体力来达到。使用 Elbow-plane，吞吐量梯度从左向右流动。值得注意的是，球形输入空间在左上角有一个吞吐量非常低的区域，这表明参与者很难到达该区域。

Figure 11 shows a non-uniform performance for all the three input spaces using a gradient-heatmap. The top-left corner of Elbow-sphere shows worse performance. The gradient of shoulder-plane flows from bottom to up and left to right for elbow-plane condition.

Our results show a surprising lack of trade-off between performance and fatigue. The heightened fatigue of the Shoulder-plane condition did not translate to worse or better performance. Despite ensuring that users would not get over-fatigued using pilot studies (to be compliant with our research ethics), fatigue was high enough in that condition to motivate four participants to quit before the end of the 5-minute session.We believe performance time would begin degrading after such a threshold. This outcome is also not uncommon as earlier work points at, under some instances, increased fatigue without degrading performance times [19, 21, 23]. The dimensions and position of Elbow-plane and Elbow-sphere are similar, but these spaces constitute very different interaction models, due to the non-linear nature of the control-device ratio in Elbow-sphere; that is, regions at the top of the output space correspond to smaller regions of the input space. In practice, this leads to the cursor moving much faster in the top. Nevertheless, the overall performance of Elbow-plane was not significantly different than that of Elbow-sphere, which is consistent with previous findings [19]. Upon closer inspection we found that the performance of these spaces is distributed differently. In particular, we see a bottleneck in the top-left corner with Elbow-sphere. This issue can be attributed to a motor constraint: at high elevation angles, it is difficult to move the arm from right to left when the palm is facing the screen. While turning the hand sideways makes this movement easy, participants could have ignored this possibility under an assumption that the screen needs to see the palm.
我们的研究结果表明，一个令人惊讶的缺乏性能和疲劳之间的权衡。肩平面条件下的高度疲劳并没有转化为更差或更好的表现。尽管使用试点研究确保用户不会过度疲劳（以符合我们的研究伦理），但在这种情况下，疲劳程度足以促使四名参与者在 5 分钟的会议结束前退出。我们认为，在这样的阈值之后，表现时间将开始下降。这种结果也并不罕见，因为在某些情况下，较早的工作点会增加疲劳，而不会降低性能时间[ 19，21，23]。肘平面和肘球面的尺寸和位置是相似的，但是由于肘球面中的控制-设备比率的非线性性质，这些空间构成非常不同的交互模型;也就是说，输出空间顶部的区域对应于输入空间的较小区域。 实际上，这会导致光标在顶部移动得更快。然而，Elbow-plane 的总体性能与 Elbow-sphere 的总体性能没有显著差异，这与之前的发现一致[ 19]。经过仔细检查，我们发现这些空间的性能分布不同。特别是，我们在 Elbow-sphere 的左上角看到了一个瓶颈。这个问题可以归因于运动约束：在高仰角下，当手掌面向屏幕时，很难从右向左移动手臂。虽然将手转向侧面使这种运动变得容易，但参与者可能会忽略这种可能性，因为他们假设屏幕需要看到手掌。

The equivalent overall performance of Elbow-sphere and Elbow-plane suggests that Elbow-sphere compensates in other regions the poor of performance in the top-left corner, specially in the bottom-left corner. We consider this factor in our next study, exploring the impact of posture variances on anchored-elbow input.
Elbow-sphere 和 Elbow-plane 的等效整体性能表明 Elbow-sphere 在其他区域补偿了左上角的性能差，特别是在左下角。我们在下一个研究中考虑这个因素，探索姿势变化对肘关节输入的影响。

The spherical input space can be implemented with any wearable device that provides a rotation vector, such as a smartwatch. By comparison, planar input spaces would require an additional piece of information, the forearm length, for conversion between spherical coordinates to Cartesian coordinates. We developed a smartwatch application on Android that allows mid-air control of a remote cursor. On the host computer, a client establishes a TCP channel with the watch. The client listens for packets containing real-time azimuth and inclination values, which are used to move the cursor. On the smartwatch, the application is a Wear OS Watch Face, an always-on, readily accessible application responsible for displaying the clock. The app reads the Game Rotation Vector from the Android Sensors API. This vector contains rotation measurements relative to a fixed reference coordinate system that corresponds to the device's default orientation. With the smartwatch attached to the user's wrist, this vector gives us directly forearm azimuth and inclination; however, a calibration step is necessary to adjust the reference coordinate system. We added a calibration button to the watch face, which users press while holding the forearm at rested position, parallel to the ground and orthogonal to the torso. This method does not require the user to be facing the TV. For selection, we used mouse clicks with mouse controls in the hand opposite to the one with the smart watch, however, it could also be implemented using a rapid index to thumb pinch [17]. We used mouse device for selection in order to allow user to select even the smallest of the targets, measuring as small as 12 pixels, generated from higher difficulty levels. This prevents any possible confounding errors due to selections made from the same hand that is used for pointer control, thereby keeping the observations valid and also isolating the effect of movement from the selection method.
球形输入空间可以用提供旋转矢量的任何可穿戴设备（诸如智能手表）来实现。相比之下，平面输入空间需要额外的信息，前臂长度，用于球面坐标到笛卡尔坐标之间的转换。我们在 Android 上开发了一个智能手表应用程序，可以在空中控制远程光标。在主机计算机上，客户端与手表建立 TCP 通道。客户端侦听包含实时方位角和倾斜度值的数据包，这些值用于移动光标。在智能手表上，应用程序是 Wear OS Watch Face，这是一个始终在线，随时可访问的应用程序，负责显示时钟。应用程序从 Android Sensors API 读取游戏旋转向量。该向量包含相对于固定参考坐标系的旋转测量值，该坐标系对应于设备的默认方向。 当智能手表连接到用户的手腕上时，该矢量直接为我们提供前臂方位角和倾斜度;然而，需要校准步骤来调整参考坐标系。我们在表盘上添加了一个校准按钮，用户在前臂保持静止位置时按下该按钮，平行于地面并垂直于躯干。这种方法不需要用户面对电视。为了进行选择，我们使用鼠标点击，鼠标控制在与智能手表相反的手中，但是，它也可以使用快速食指拇指捏来实现[ 17]。我们使用鼠标设备进行选择，以便允许用户选择即使是最小的目标，测量小至 12 像素，从更高的难度水平产生。 这防止了由于从用于指针控制的同一只手进行选择而导致的任何可能的混淆错误，从而保持观察有效并且还将移动的影响与选择方法隔离。

We employ a target selection task to compare mid-air interaction under four body postures, using a spherical mapping between motor and display space. The study follows a 4 × 8 within-subject design, with posture and target position as factors. We define four index of difficulty (ID) levels (2, 3, 4, 5) and four postures (Figure 12):
我们采用目标选择任务比较四个身体姿势下的空中互动，使用电机和显示空间之间的球面映射。本研究采用 4 × 8 被试内设计，以姿势和靶位为因素。我们定义了四个难度指数（ID）级别（2，3，4，5）和四个姿势（图 12）：

The four postures were elbow rested high, elbow rested low, sideways seated and sideways lying.

• Elbow Rested High -Seated, elbow rested at shoulder level
  肘部高放-坐姿，肘部置于肩部水平
  
• Elbow Rested Low -Seated, elbow rested at waist level
  肘部休息低-坐着，肘部休息在腰部水平
  
• Sideways Seated -Seated sideways (lengthwise), elbow rested at waist level
  侧坐-侧坐（纵向），肘部放在腰部水平
  
• Sideways Lying -Lying sideways
  侧躺-侧躺
  

The postures are representative of most postures one can assume in a common couch and, with the exception of Sideways Lying , capture the patterns seen in our observational study. Each posture presents distinct motor constraints to the arm. People either sit or lie on the couch. When seated, they rest their feet on the floor or on the couch (in a sideways orientation relative to the display). In addition, people can rest their elbow on a lower surface (armrest or waist) or higher surface (backrest).
这些姿势代表了人们在普通沙发上可以采取的大多数姿势，除了侧身躺之外，这些姿势捕捉了我们观察研究中看到的模式。每种姿势都会对手臂的运动产生不同的限制。人们要么坐在沙发上，要么躺在沙发上。坐着时，他们将脚放在地板上或沙发上（相对于显示器处于侧向方向）。此外，人们可以将肘部放在较低的表面（扶手或腰部）或较高的表面（靠背）上。

The height at which the elbow is rested influences the range of motion. With the elbow rested low, an upward motion is achieved via elbow flexion, while with the elbow rested high (e.g., on the backrest) the same motion is achieved via shoulder lateral rotation. Likewise, horizontal motion can be achieved through shoulder medial/lateral rotation or elbow flexion depending on where the elbow is rested. Furthermore, with the elbow rested low the body becomes an obstacle. In the sideways postures, the couch backrest becomes an obstacle.
手肘的高度会影响活动范围。手肘低置的情况下，通过肘部屈曲实现向上运动，而在手肘高置的情况下（例如，在靠背上）通过肩部横向旋转实现相同的运动。同样，水平运动可以通过肩部内侧/外侧旋转或肘部屈曲来实现，这取决于手肘休息的位置。此外，手肘放低，身体成为障碍。在侧身姿势，沙发靠背成为一个障碍。

We used a Fitts Law-style target selection task where eight circular targets were arranged in a grid (Figure 13a). Each target was presented one at a time along with a reciprocal target (i.e. same size) located at the center of the screen (Figure 13b). The role of the reciprocal target was to establish a common origin for all target selectionsand to allow measurement of selection time for each target, uniformly. Each selection task started with a reciprocal target, highlighted through an accent filling color, to be selected. Once the reciprocal target was selected, the actual target to be selected next was highlighted and the user was required to make a selection again. This active state switching repeated 5 times for each target and until all targets were selected in an ID. We manipulated ID by varying target size. Note that targets with the same ID have different sizes if they are not equally distant from the center. As we collected 5 observations per target, a total of640 observations per participantwere generated (8 target positions × 5 repetitions × 4 ID × 4 postures).
我们使用了费茨定律式的目标选择任务，其中八个圆形目标排列在网格中（图 13a）。每个目标沿着呈现一个，相互对应的目标（即相同大小）位于屏幕中心（图 13 b）。互惠靶的作用是为所有靶选择建立一个共同的起源，并允许统一地测量每个靶的选择时间。每个选择任务都从一个相互的目标开始，通过强调填充颜色突出显示，以供选择。一旦选择了相互的目标，接下来要选择的实际目标就会被突出显示，并且用户需要再次进行选择。这种活动状态切换对每个目标重复 5 次，直到在 ID 中选择了所有目标。我们通过改变目标大小来操纵 ID。请注意，如果目标与中心的距离不等，则具有相同 ID 的目标具有不同的大小。 由于我们对每个目标收集了 5 个观察结果，因此每位参与者总共产生了 640 个观察结果（8 个目标位置× 5 次重复× 4 个 ID × 4 个姿势）。

Even the targets within same ID differ in size. The size depends upon the distance from the center. A bigger ID has relatively smaller target size as compared to a lower ID

Participants were instructed to sit on the couch in the first posture assigned to them. The order of postures was counterbalanced using a Latin square design for each participant. The experiment facilitator described the calibration procedure and the task, then instructed participants to perform calibration followed by a practice run of the task. Participants were instructed to “select targets as fast as possible while keeping the accuracy at a constant level” [7]. During the practice run, participants were instructed to recalibrate if necessary. This procedure was repeated for every posture. After the completion of the tasks for each posture, the facilitator administered the Raw NASA-TLX (RTLX) questionnaire [20] and enforced a 5-minute break. The tasks within a posture block were presented without interruptions, but participants were allowed to rest anytime. Upon completion of the whole experiment, participants filled a custom questionnaire.
参与者被指示以分配给他们的第一个姿势坐在沙发上。每个参与者的姿势顺序都使用拉丁方设计来平衡。实验主持人描述了校准程序和任务，然后指导参与者进行校准，然后进行任务的实践。参与者被要求“尽可能快地选择目标，同时保持准确性在一个恒定的水平”[ 7]。在练习过程中，参与者被指示在必要时重新校准。对每个姿势重复该过程。在完成每个姿势的任务后，主持人管理原始 NASA-TLX（RTLX）问卷[ 20]并强制休息 5 分钟。姿势块内的任务在没有中断的情况下呈现，但参与者被允许随时休息。在完成整个实验后，参与者填写了一份自定义问卷。

We ran the experiment with 8 participants (2 female) aged between 21 and 38 years old. We collected 5,120 observations (target selections) in sessions that averaged 1 hour and 46 minutes excluding the time needed for calibration. After removing outliers with the interquartile range method, 5,060 observations remained. We use repeated measures ANOVA for statistical tests, with Tukey's HSD for post-hoc analysis. Where appropriate, we plot means and 95% confidence intervals calculated with Morey's [35] method for within-subject designs.
我们对 8 名年龄在 21 岁至 38 岁之间的参与者（2 名女性）进行了实验。我们在平均 1 小时 46 分钟的会议中收集了 5，120 个观察结果（目标选择），不包括校准所需的时间。用四分位距法去除离群值后，仍保留 5，060 个观察值。我们使用重复测量 ANOVA 进行统计检验，Tukey 的 HSD 进行事后分析。在适当的情况下，我们绘制平均值和 95%置信区间，采用 Morey [ 35]方法计算受试者内设计。

Figure 15 shows the questionnaires responses.The spherical interaction with elbow rested high is associated with higher physical demand, effort, and frustration, while interaction in the seated sideways posture had the lowest physical demand and effort.

7.5.2 Questionnaires. The NASA TLX data (Figure 15, left) shows that the spherical interaction with elbow rested high was associated with higher physical demand, effort, and frustration, while interaction in the seated sideways posture had the lowest physical demand and effort. Curiously, the 95% confidence intervals show that participants’ perception of their own performance in each postures was not systematically affected by their perception of effort. Our second questionnaire asked participants to provide two rankings of the postures: one where they weigh the postures according to their experience in the study, and another where they disregard the experience in the study. Generally, the results show that posture preference in the study was well aligned with participant's prior preferences. This is a positive result for the spherical interaction, as it did not seem to affect participants’ postural preferences. Despite this general pattern, one participant stated that mid-air interaction would motivate them to change posture: “I do sit in what I ranked as 1 and 4 (when TV is in front of me) and 2 and find those comfortable but if I needed to use a smartwatch to control the screen I would sit up most likely and not be lying down.” A second participant reported neck and shoulder discomfort in postures 1 and 4: “In general, the calibration and the cursor works well, although posture 1 (elbow rested low) and 4 (sideways lying) cause the tiredness for my neck and shoulder. The final level is difficult and tricky to do accurately”. Only one participant reported not using any of the study postures routinely; most participants reported frequently being on the couch in at least one of the postures.
7.5.2 附件。NASA TLX 数据（图 15，左）显示，肘部高放的球形互动与更高的身体需求、努力和挫折有关，而坐在侧面的互动具有最低的身体需求和努力。奇怪的是，95%的置信区间表明，参与者对自己在每个姿势中表现的感知并没有受到他们对努力的感知的系统性影响。我们的第二份问卷要求参与者提供两种姿势排名：一种是根据他们在研究中的经验来衡量姿势，另一种是忽略研究中的经验。一般来说，结果表明，在研究中的姿势偏好与参与者的先前偏好是一致的。这对于球形交互来说是一个积极的结果，因为它似乎没有影响参与者的姿势偏好。 尽管有这种一般模式，一位参与者表示，空中互动会激励他们改变姿势：“我确实坐在我排名为 1 和 4（当电视在我面前时）和 2 的位置，并且发现这些位置很舒服，但如果我需要使用智能手表来控制屏幕，我很可能会坐起来，而不是躺下。”第二位参与者报告了姿势 1 和 4 的颈部和肩部不适：“一般来说，校准和光标工作良好，尽管姿势 1（肘部放低）和 4（侧卧）导致我的颈部和肩部疲劳。最后一关很难准确完成”。只有一名参与者报告说没有经常使用任何研究姿势;大多数参与者报告说经常以至少一种姿势躺在沙发上。

Differences in performance due to postures were relatively small and dependent on target location. Our results point to difficulties with straight vertical movements towards the edges of the display. This problem may stem from a potential asymmetry in the calibration of input spaces; that is, the central axis of the space is not necessarily aligned with what participants identify as the central position of their forearm. Consider the case where the elbow is rested on the armrest of an office chair: a user may think that the center of the space is aligned with the armrest, but depending on the calibration, it may be offset towards the torso, since the accessible area in front of the body is larger than the area on the other side of the armrest. While the cursor may have helped participants identify such central axis, the motion may not be intuitive.
由于姿势导致的性能差异相对较小，并且取决于目标位置。我们的研究结果指出，困难与直线垂直运动的边缘显示。这个问题可能源于输入空间的校准中的潜在不对称性;也就是说，空间的中心轴不一定与参与者识别为其前臂的中心位置对齐。考虑手肘搁在办公椅的扶手上的情况：用户可能认为空间的中心与扶手对齐，但取决于校准，它可能朝向躯干偏移，因为身体前方的可接近区域大于扶手另一侧的区域。虽然光标可以帮助参与者识别这样的中心轴，但运动可能不是直观的。

Posture 1 (elbow rested high) is unique in that shoulder medial/lateral rotation and elbow flexion control vertical and horizontal movements, respectively, while in the other postures it is the inverse mapping. In addition, the physical input space is much larger, as participants had access to the lower hemisphere. Curiously, this mapping was beneficial for targets in the North and West zones. This finding strengthens the central axis hypothesis (aforementioned), as in elbow rested high the horizontal range is mostly symmetrical. In fact, in this posture nearly the entire ranges for elbow flexion and shoulder medial/lateral rotation are available, which may explain the increased physical demand that participants reported.
姿势 1（肘部高放）的独特之处在于，肩部内侧/外侧旋转和肘部屈曲分别控制垂直和水平运动，而在其他姿势中，它是相反的映射。此外，物理输入空间要大得多，因为参与者可以进入下半球。奇怪的是，这种测绘对北部和西部地区的目标有利。这一发现加强了中轴假设（前面提到的），因为在肘部高休息时，水平范围大多是对称的。事实上，在这种姿势下，几乎可以获得肘关节屈曲和肩关节内侧/外侧旋转的整个范围，这可以解释参与者报告的身体需求增加。

One design consideration revolves around scaling the motor movement to larger or small displays. For example, if needing to interact with a large wall display, Elbow-Anchored motions would still support such environments without any changes to the mapping function form—the output dimensions are just a parameter of the mapping. The same applies to when we need to scale down to interacting with a smaller display, such as in an AutoUI. We are not advocating for the replacement of remote-controlled devices. Instead, Elbow-Anchored input, as other mid-air interactions, offers a viable alternative to the solution of seeking a lost remote, or having to sequentially interact with an interface, such as with a directional pad (DPAD). Future design iterations of our proposed layouts will be necessary to ensure cross compatibility with both restful and device-based interactions. Furthermore, additional consideration is needed to intelligently assume the user's posture and provide an interactive model without needing to calibrate for each posture. One approach might be to use the available cameras on such displays to interpret the posture and adjust the input model accordingly.
一个设计考虑围绕着将电机运动缩放到更大或更小的显示器。例如，如果需要与大型墙壁显示器交互，肘锚定运动仍将支持此类环境，而无需对映射函数表单进行任何更改-输出尺寸只是映射的一个参数。这同样适用于当我们需要缩小到与更小的显示器交互时，例如在 AutoUI 中。我们并不主张更换遥控设备。相反，肘部锚定输入，作为其他空中交互，提供了一个可行的替代方案，以寻找丢失的遥控器，或必须顺序地与接口交互，如与方向垫（DPAD）。我们提出的布局的未来设计迭代将是必要的，以确保与 REST 和基于设备的交互的交叉兼容性。 此外，需要额外的考虑来智能地假定用户的姿势并提供交互式模型，而不需要针对每个姿势进行校准。一种方法可能是使用这种显示器上的可用相机来解释姿势并相应地调整输入模型。

A number of applications, aside from our demonstration on SmartTV input, can benefit from Elbow-Anchored interactions. For example, mid-air text-entry keyboards [32] can be mapped to the movements we demonstrate. Our throughput results indicate regions to be avoided for placing characters, and instead could be used for presenting text or other feedback. While we currently use mouse click for selecting an item, when designed to operate using a smartwatch, additional approaches such as pinching the thumb and index [17] could instead be leveraged to make input efficient.
除了我们对 SmartTV 输入的演示之外，许多应用程序都可以从 Elbow-Anchored 交互中受益。例如，半空中的文本输入键盘[ 32]可以映射到我们演示的动作。我们的吞吐量结果表明，要避免放置字符的区域，而是可以用于呈现文本或其他反馈。虽然我们目前使用鼠标点击来选择项目，但当设计使用智能手表操作时，可以利用其他方法，例如捏拇指和食指[ 17]来提高输入效率。

As mid-air interactions gain prominence in Automotive UIs, we can imagine interacting with such systems using Elbow-Anchored input. In many cases, with the presence of an arm-rest, the user's elbow has an available support for enabling comfortable and potentially less fatiguing input, than if the arm was held in mid-air. However, for such UIs, additional consideration is needed for providing suitable feedback, such as relying on audio or mid-air haptics.
随着空中交互在汽车用户界面中越来越突出，我们可以想象使用 Elbow-Anchored 输入与此类系统进行交互。在许多情况下，在存在扶手的情况下，用户的肘部具有可用的支撑，用于实现舒适的并且可能比手臂保持在半空中更少疲劳的输入。然而，对于此类 UI，需要额外考虑以提供适当的反馈，例如依赖于音频或半空触觉。

Finally, emerging AR/VR platforms could benefit from such mid-air interaction capabilities, provided that a method for resolving depth ambiguity is applied, given that our mapping only supports 2D output spaces. Many video games are played in VR while sitting. As such, an available arm rest could be employed for lengthy interactions. We note from our results that there is no loss of performance in comparison to a shoulder-based mid-air input allowing gamers to reap the benefits from using an anchored elbow during long gaming sessions.
最后，新兴的 AR/VR 平台可以从这种空中交互功能中受益，前提是应用解决深度模糊的方法，因为我们的映射仅支持 2D 输出空间。许多视频游戏都是坐着玩的。因此，可用的扶手可以用于长时间的交互。我们从结果中注意到，与基于肩部的半空输入相比，性能没有损失，允许玩家在长时间游戏过程中从使用固定肘部中获得好处。

Our results were derived from mostly right-handed participants, and additional work is required to ensure that Elbow-Anchored input is agnostic to hand-specific operations. For the majority of cases, we can assume that range-of-motion, shoulder medial/lateral rotation and elbow flexion-extension, operate in a mirrored and symmetrical fashion [40]. Additional work is needed to ensure that all users can benefit from Elbow-Anchored input. We demonstrate that elbow-anchored input is possible under a variety of postures. However, such postures are not exhaustive. Additionally, as there was no significant performance difference between between the postures, these minor differences may not warrant a redesign of the input space or the UI. However, for VR interactions, it may be necessary to research for ways to mitigate the inefficiencies we found, as VR users would likely interact with systems for a longer period of time and with smaller targets.Furthermore, we use the couch as it constitutes a central furnishing in homes (in most cultures), however, elbow-anchored should also be examined for postures when seated on the floor or in alternative arrangements. Finally, the spherical mapping enables input using a self-contained system, such as when the user is wearing a smartwatch. However, additional work is needed to decouple the device from the user, and instead use more generic capture methods, such as cameras in cars or on smartTVs, to understand the user's postures and apply our input model accordingly.
我们的结果来自大多数右撇子参与者，需要额外的工作来确保肘锚输入对于特定于手的操作是不可知的。对于大多数情况，我们可以假设活动范围、肩关节内/外侧旋转和肘关节屈曲-伸展以镜像和对称的方式操作[ 40]。需要做更多的工作来确保所有用户都能从 Elbow-Anchored 输入中受益。我们证明了肘锚输入是可能的各种姿势下。然而，这些姿态并非详尽无遗。此外，由于姿势之间没有显著的性能差异，这些微小的差异可能不需要重新设计输入空间或 UI。 然而，对于 VR 交互，可能有必要研究如何减轻我们发现的低效率，因为 VR 用户可能会与系统进行更长时间的交互，并且目标较小。此外，我们使用沙发，因为它构成了家庭的中央装饰（在大多数文化中），但是，肘部锚定也应该检查坐在地板上或其他布置时的姿势。最后，球面映射使得能够使用自包含系统进行输入，例如当用户佩戴智能手表时。然而，需要额外的工作来将设备与用户解耦，而是使用更通用的捕获方法，例如汽车或智能电视上的摄像头，以了解用户的姿势并相应地应用我们的输入模型。