**5.1.3 Design**

Participants were assigned in alternation to the vertical or horizontal coding condition. Following the practice of Durgin, Li and Hajnal (2010), half the participants gave verbal estimates relative to horizontal and half gave estimates relative to vertical so that spatial biases could be distinguished from verbal biases. In each condition the same set of 16 orientations from 0 to 90° (by 6° increments) were presented in random order in each of two blocks of trials for a total of 32 trials. Random orders were generated in advance for each participant.

#### **5.1.4 Procedure**

86 Haptics Rendering and Applications

The participants were 20 Swarthmore College undergraduate students (13 female) who participated in partial fulfilment of a course requirement. Half were assigned to the

The haptic surface was a varnished wooden board mounted on a mechanical adjustable slant device (see Li & Durgin, 2009). The center of the surface was about 113 cm from the floor. A metal ridge was attached to the surface perpendicular to the axis of rotation as a guide. Participants stood in front of the apparatus wearing a blindfold (a plush sleep mask)

Fig. 8. The experimental set up. The orientation of the board could be rapidly adjusted to

Participants were assigned in alternation to the vertical or horizontal coding condition. Following the practice of Durgin, Li and Hajnal (2010), half the participants gave verbal estimates relative to horizontal and half gave estimates relative to vertical so that spatial biases could be distinguished from verbal biases. In each condition the same set of 16 orientations from 0 to 90° (by 6° increments) were presented in random order in each of two blocks of trials for a total of 32 trials. Random orders were generated in advance for each

horizontal coding condition and half to the vertical coding condition.

throughout the experiment. The set-up is shown in Figure 8.

one of 16 orientations from 0° to 90°.

**5.1.3 Design** 

participant.

**5.1.1 Participants** 

**5.1.2 Apparatus** 

Participants were shown the apparatus with the surface in the horizontal position and the procedure was explained to them prior to signing an informed consent form. Participants were shown where to stand (directly in front of the apparatus) and then asked put on the blindfold. Before each trial, the surfaces were set to the intended orientation manually using pre-set positions by the experimenter who then told the participant to explore the surface. The participants were to run the tip of their right index finger alongside the elevated ridge formed by a wire attached to the surface. No time limit was specified for exploration. When satisfied with their haptic observation the participant was to indicate the orientation of the surface in deg. Half were instructed that vertical was 0° and horizontal was 90°. The other half were told to consider horizontal to be 0° and vertical to be 90°. Participants were encouraged to be as precise as possible in their estimates by estimating orientation to the nearest 1° (even with such instruction, there is a strong bias toward values divisible by 5).

Fig. 9. Mean haptic slant estimates by reference condition in Experiment 1 with error bars representing ± 1 SEM. Trend lines are best fitting cubic polynomials.

#### **5.2 Results**

Mean estimates were computed for each presented orientation by condition. Figure 9 shows the estimates for each condition. It can be seen that the spatial bias was in the same direction in each condition inasmuch as participants overestimated deviations from horizontal and underestimated deviations from vertical.

To represent the spatial bias function, we recalculated each estimate in the vertical referent condition with respect to horizontal and then averaged all estimates with respect to horizontal. The resulting function is plotted in Figure 10, superimposed on the similarlyderived spatial function for visual slant perception from Durgin, Li and Hajnal (2010, Experiment 1), plotted earlier in Figure 1. The functions are strikingly similar, as predicted

Spatial Biases and the Haptic Experience of Surface Orientation 89

The participants were 12 Swarthmore College undergraduate students who either

The apparatus was the same as in Experiment 1, except that a computer program was used to dynamically choose stimuli for presentation based on a staircase procedure designed to sample densely in the range surrounding each participant's subjective bisection point.

Each participant gave responses to individual stimuli selected from an up-down staircase procedure. There were 10 blocks of 6 trials each in which two trials from each of three staircases were randomly interleaved. The starting values for the three staircases were either approximately 12°, 42°, and 72° (N=6) or 18°, 48° and 78° (N=6). The step size of each staircase was 18°. That is, if the presented orientation was deemed closer to vertical, the next orientation presented by that staircase was 18° lower, and if the presented orientation was judged closer to horizontal, the next presented orientation was 18° higher. The three staircases together sampled orientation space with a resolution of 6° and approximated a

Participants were shown the apparatus with the surface in the horizontal position and the procedure was explained to them prior to signing an informed consent form. Participants were shown where to stand (directly in front of the apparatus) and then asked put on the blindfold. Before each trial, the surfaces were set to the required orientation manually by the experimenter according to a computer instruction. The participant then explored the surface as in Experiment 1. When the participant gave the forced choice response ("closer to vertical" or "closer to horizontal"), the experimenter pressed either the up-arrow key or the down arrow key on a keyboard, causing the computer to record the trial and update the staircase. The computer then gave instruction to the experimenter concerning the orientation

The responses for each participant were fitted with a logistic function and the subjective bisection point was calculated for each psychometric function as the point at which participants were equally likely to respond that the surface was closer to vertical and that it was closer to horizontal. The average subjective horizontal/vertical bisection point was 31.2° (SEM = 2.0°) from horizontal. Although numerically lower than the 34° average reported for visual slant by Durgin, Li and Hajnal (2010), this difference was not statistically reliable. The subjective bisection point did not differ reliably from 30°, *t*(11) < 1, but did

method of constant stimuli that was centered on the apparent bisection point.

participated in partial fulfilment of a course requirement or were paid to participate.

The haptic horizontal/vertical bisection point was measured.

**6.1 Method** 

**6.1.1 Participants** 

**6.1.2 Apparatus** 

**6.1.3 Design** 

**6.1.4 Procedure** 

of the next stimulus.

differ reliably from 45°, *t*(11) = 6.89, *p* < .0001.

**6.2 Results** 

by the calibration hypothesis. Both functions seem to reflect a common underlying spatial coding bias.

Fig. 10. Overall spatial bias in haptic perception of slant (Experiment 1) superimposed on the visual slant bias function from Durgin, Li and Hajnal (2010).

#### **5.3 Discussion**

Using real surfaces with a demarcated axis of haptic exploration, we sought to extend the methods used by Durgin, Li and Hajnal (2010) to the haptic domain. Our results indicate a close correspondence between visual and haptic spatial biases in the peception of orientation. Our results are somewhat at variance with those of Hajnal et al. (2011). Because Hajnal et al. did not constrain the path of digital exploration, it is possible that participants tended to explore their surfaces along a somewhat oblique (and therefore less steep) axis. Our data are consistent with the proposal that there is a trend for there to be calibration between visual and haptic representations of 3D surface orientation.
