Haptic feedback provides an essential sensory stimulus crucial for interaction and analyzing three-dimensional spatio-temporal phenomena on surface visualizations. Given its ability to provide enhanced spatial perception and scene maneuverability, virtual reality (VR) catalyzes haptic interactions on surface visualizations. Various interaction modes, encompassing both mid-air and on-surface interactions -- with or without the application of assisting force stimuli -- have been explored using haptic force feedback devices. In this paper, we evaluate the use of on-surface and assisted on-surface haptic modes of interaction compared to a no-haptic interaction mode. A force-based haptic stylus is used for all three modalities; the on-surface mode uses collision based forces, whereas the assisted on-surface mode is accompanied by an additional snapping force. We conducted a within-subjects user study involving fundamental interaction tasks performed on surface visualizations. Keeping a consistent visual design across all three modes, our study incorporates tasks that require the localization of the highest, lowest, and random points on surfaces; and tasks that focus on brushing curves on surfaces with varying complexity and occlusion levels. Our findings show that participants took almost the same time to brush curves using all the interaction modes. They could draw smoother curves using the on-surface interaction modes compared to the no-haptic mode. However, the assisted on-surface mode provided better accuracy than the on-surface mode. The on-surface mode was slower in point localization, but the accuracy depended on the visual cues and occlusions associated with the tasks. Finally, we discuss participant feedback on using haptic force feedback as a tangible input modality and share takeaways to aid the design of haptics-based tangible interactions for surface visualizations.

翻译：触觉反馈为表面可视化中的交互与分析三维时空现象提供了至关重要的感官刺激。鉴于虚拟现实（VR）在增强空间感知和场景操控性方面的能力，它促进了表面可视化中的触觉交互。通过使用触觉力反馈设备，研究者已探索了多种交互模式，包括空中交互与表面交互——无论是否施加辅助力刺激。本文评估了表面交互模式与辅助表面交互模式相对于无触觉交互模式的使用效果。所有三种模式均采用基于力的触觉手写笔实现：表面交互模式采用基于碰撞的力反馈，而辅助表面交互模式则额外附加了吸附力。我们开展了一项被试内用户研究，涉及在表面可视化上执行的基础交互任务。在保持三种模式视觉设计一致的前提下，研究包含以下任务：定位表面最高点、最低点及随机点；以及在具有不同复杂度和遮挡程度的表面上绘制曲线。研究结果表明，参与者使用所有交互模式绘制曲线所需时间几乎相同。与无触觉模式相比，使用表面交互模式能够绘制更平滑的曲线。然而，辅助表面交互模式比普通表面交互模式具有更高的精度。表面交互模式在点定位任务中速度较慢，但其精度取决于任务相关的视觉线索与遮挡程度。最后，我们讨论了参与者对使用触觉力反馈作为实体输入模态的反馈，并分享了有助于设计基于触觉的表面可视化实体交互的要点。