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.

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