# Rendering Strategy to Counter Mutual Masking Effect in Multiple Tactile Feedback
## 3 The Proposed Rendering Algorithm
### The Idea  
For example, let us suppose that we are planning to simultaneously render bumpy geometry by the EV and a uniform texture by the MV, as shown in Figure 4. The texture, which has constant intensity at all positions, can be rendered by the MV [18; 19; 20]. The geometry (bump), which has varying intensity depending on the position, can be rendered by modulating the intensity of the EV according to surface gradients [21; 22]. The horizontal axis in all graphs in Figure 4 represents the haptic interaction point  
\begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline  & **Target** & **Massing** & **Frequency** & \multicolumn{4}{c}{**Masker Intensity (dB SL)**} \\ \cline{4-9}  & **Stimulus** & **Stimulus** & **Frequency** & **of MV (Hz)** & **5** & **10** & **15** & **25** & **25** \\ \hline \multirow{3}{*}{Experiment I} & \multirow{3}{*}{EV} & \multirow{3}{*}{MV} & 120 & * 0.433 & * 0.322 & 2.992 & 7.265 & 10.107 \\  & & & 180 & * 0.771 & * 0.808 & 3.611 & 7.427 & 10.502 \\  & & & 270 & * 1.171 & 3.608 & 6.411 & 9.428 & 13.301 \\ \hline \multirow{3}{*}{Experiment II} & \multirow{3}{*}{MV} & \multirow{3}{*}{EV} & 120 & * 0.417 & 9.506 & 13.376 & 18.727 & 22.891 \\  & & & 180 & 6.118 & 12.158 & 18.015 & 22.278 & 27.612 \\  & & & 270 & 6.546 & 13.235 & 18.306 & 23.580 & 29.195 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Mean changes in the absolute threshold (AL) of electrovibration (EV) and mechanical vibration (MV) (in dB) at different frequency pairs, and under varying masker intensities. The frequency of EV was 270 Hz. The asterisks denote data that were not significantly different from 0 (i.e., no masking effect appeared).  
Figure 3: Masking functions of electrovibration (EV) and mechanical vibration (MV) fitted from the results in Table 2. AL, absolute threshold; SL, sensation level.  
(HIP) on the touch surface. The vertical axis is in units of \"dB SL\" and represents the input intensity, generated by the device (left), or the users' perceived intensity (right). In the left-side graphs, solid lines depict the input intensity of the MV (solid red) and EV (solid blue), whereas dashed lines depict the masked AL of the MV by the EV (dashed blue) and the masked AL of the EV by the MV (dashed red). In the right-side graphs, solid lines depict the users' actual perceived intensity, and the dashed lines depict the intended (or designed) perceived intensity. The perceived intensity can be expected to be the difference between the input intensity and the masked AL. Ideally, if there is no masking effect, the input intensity and the perceived intensity would be the same, as shown in Figure 4a. In practice, however, the masking effect may cause a significant distortion in the perceived intensity. That is, the intended stimulus intensity might not be conveyed to the users due to the masking effect, as shown in Figure 4b. In this case, the perceived intensity of the MV, designed to provide a constant intensity at all positions, changes in unintended ways. Besides, the EV would be perceived at an intensity lower than the desired perceived one. Specifically, the user might not perceive a stimulus lower than 0 dB SL (i.e., when a stimulus intensity is lower than the masked AL), which is marked as gray shading in the figure. Thus, it is necessary to apply a rendering strategy from a different viewpoint when the masking effect is present. Herein, we propose to adjust the input intensity in a way that would produce the desired perceived intensity. As shown in Figure 4c, the desired perceived intensity could be achieved by modulating the input intensity of the MV and EV accordingly.