  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.
