# Study on Hand-Eye Coordination Area with Bare-Hand Click Interaction in Virtual Reality
## 1 Introduction  
The virtual environment (VE) is a new HCI interface. Applying virtual reality technology to create 3D scene images, users can interact with VE through input/output devices [1]. Virtual reality technology has been introduced into an increasing number of fields, such as medical surgery [2], operation training [3], and flight simulation [4]. The existing commonly used virtual reality visual output device is a head-mounted display (HMD), which can provide high immersion at a low/medium price [5]. Supporting stereo vision, HMDs, such as Oculus Rift and HTC Vive, provide users with visual self-motion feedback based on head movement. The interaction method in a VE is quite different from the traditional interaction method. The traditional \"window, icon, menu, pointing device\" (WIMP) paradigm of the graphical user interface (GUI) is mostly used in the interaction with the two-dimensional interface [6]. A mouse and keyboard are widely used as input devices. The input side of the GUI of the WIMP paradigm supports accurate clicking with one pixel [7]. However, this kind of interaction is not suitable for virtual interactive objects with three-dimensional coordinates in the VE. The perceived degrees of freedom provided by the VR HMD include the position of x-, y-, and z-axis coordinates. The increased dimension of the depth display is the most essential difference between the 3D and 2D displays [8]. The interaction with the three-dimensional VE usually relies on bare-hand gesture recognition or the use of VR handle controllers [9]. The related research on user experience shows that, compared with the handle controller, users are more inclined to choose the method of bare-hand interaction in virtualspace [10]. Using input hardware such as handle controllers in a VE may reduce the naturalness of interaction [11] and increase the cognitive burden of users [12], resulting in the decline of interaction performance and user experience. Poorly designed hand-held input devices can increase the difficulty of use and lead to awkward postures due to a non-intuitive design (poor cognitive mapping) and even increase risks for musculoskeletal discomfort during VR interactions [13; 14]. A commonly used and maturely developed support device for bare-hand interaction is the Leap Motion Controller (LMC), which uses infrared technology for gesture recognition. LMC is a commonly used low-cost gesture capture device [15], providing access to a skeleton model of a tracked hand to realize hand recognition and tracking. LMC can be attached to head-mounted display (HMD) devices to map the user's hand to the virtual hand and achieve the real-time acquisition of the hand posture [16; 17]. Comparing the performance of bare-hand interaction and handle selection interaction based on LMC devices in virtual space, [PERSON] et al. (2018) reported that the handle required a longer time and produced a higher error rate [18]. Commonly used bare hand interaction includes virtual hand technology and ray technology [19]. [PERSON] et al. (2020) compared the interaction methods of bare-hand direct clicks and rays, and found that the movement time and click accuracy of using bare-hand gestures to directly click on targets are better than those found when using rays [20]. Effective interactions demand, among other things, accurate space perception. However, unlike the relatively accurate space perception in the physical world, compression has been reported in the majority of studies of stereoscopic environments [21; 22; 23]. Using direct interaction improves spatial judgment in stereoscopic displays and interaction performance [24]. Therefore, direct click interaction with a bare hand applied to the virtual space of an HMD demonstrates higher usability. The distribution position of the target object in the VE will affect the interactive performance. Studies have addressed the task of user selection of objects in different locations [25; 26; 27].