This paper presents the first investigation into using the goal-crossing paradigm for object selection with virtual reality (VR) head-mounted displays. Two experiments were carried out to evaluate ray-casting crossing tasks with target discs in 3D space and goal lines on 2D plane respectively in comparison to ray-casting pointing tasks. Five factors, i.e. task difficulty, the direction of movement constraint (collinear vs. orthogonal), the nature of the task (discrete vs. continuous), field of view of VR devices and target depth, were considered in both experiments. Our findings are: (1) crossing generally had shorter or no longer time, and higher or similar accuracy than pointing, indicating crossing can complement or substitute pointing; (2) crossing tasks can be well modelled with Fitts' Law; (3) crossing performance depended on target depth; (4) crossing target discs in 3D space differed from crossing goal lines on 2D plane in many aspects such as time and error performance, the effects of target depth and the parameters of Fitts' models. Based on these findings, we formulate a number of design recommendations for crossing-based interaction in VR.

Crossing is a fundamental paradigm for target selection in human-computer interaction systems. This paradigm was first introduced to virtual reality (VR) interactions by Tu et al., who investigated its performance in comparison to pointing, and concluded that crossing is generally no less effective than pointing and has unique advantages. However, owing to the characteristics of VR interactions, there are still many factors to consider when applying crossing to a VR environment. Thus, this review summarizes the main techniques for object selection in VR and crossing-related studies. Then, factors that may affect crossing interactions are analyzed from the perspectives of the input space and visual space. The aim of this study is to provide a reference for future studies on target selection based on the crossing paradigm in virtual reality.