## 2 Materials and Methods
The head was positioned directly forward with the feet aligned at the malleoli along a line at 0.95m from the wall, calculated so that the eccentricity of the peripheral targets was approximately 20\({}^{\circ}\) by reference to the central one. The board was placed on a wall at an adjustable height so that the eyes faced the central target. The baseline posture for each participant was recorded in this starting position, while they looked forward to the central target (three trials). Then, two separate movement tasks were examined. In the heading task, participants were instructed to turn their head towards and look at the designated target. In the pointing task, participants  
Figure 1: Experimental set-up. (**a**) Photo with the helmet (with head sensor) and targets, (**b**) schema of the reference frames. were instructed to indicate the designated target with their right index finger (no specific instruction was given on head posture). Upon each trial, the experimenter verbally designated the target by color. Participants were first required to focus upon the central target then, following a \"go\" signal from the experimenter, perform the required movement task. Posture in heading and pointing were maintained for 5s before returning to the starting position. Participants performed three blocks of nine movements for both the heading and pointing tasks. Task order and target sequence was randomized for each participant. All movements were recorded with a sampling frequency of 30 Hz. The duration of the experimental procedure was approximately 30 minutes. The STROBE checklist was used for the reporting [29]. Data analysis specifically examined the orientation of the trunk and the head. For each trial, data were extracted at two instants: movement initiation (initial posture prior to heading or pointing) and task completion (final posture characterized by the maximum rotation of the head or arm in heading or pointing tasks, respectively). The variables of interest were Euler angles (expressed in degrees) describing the orientation of the trunk and head in space and the head with respect to the trunk (head versus (vs.) trunk) at each time point (data presented in an Excel file \"experimental data\" in supplementary material). Mean and standard error (SEM) values were calculated for the three trials on each target in the respective movement tasks. Statistical analysis of Euler angles was firstly carried out using two-way repeated measures analysis of variance (ANOVA) considering movement task (heading, pointing) and target (8 levels) as independent factors. Subsequent post-hoc comparisons were carried out using \(t\)-tests. Further analysis of the effects of target direction was carried out using sinusoidal fitting. For this analysis, mean Euler angles of head orientation for the 10 participants were calculated for each target. Mean values were projected as a function of target trigonometric direction, and fitted on sinusoidal curves (Origin Software, Levenberg Marquardt algorithm). This process provides an equation for the variable \(y\) as a function of the direction of the target (Appendix A):  
\[y=y0+A\times\sin(\pi\times(\varphi-\varphi 0))\]  
with the following parameters: \(A\): amplitude; \(y0\): offset; \(w\): period; \(\varphi 0\): phase shift. According to this fitting process, the amplitude \(A\) specifies the amount of periodical variation of the angle with target direction; the offset \(y0\) specifies its constant deviation by reference to the baseline posture irrespective of target direction; and phase shift \(\varphi\) the target direction where the maximum rotation is observed. See Appendix A for mathematical examples demonstrating the effects of changes in parameters. The fitting process was performed separately for the three Euler angles measuring head orientation in both reference frames (head in space and head vs. trunk) in the two movement tasks (heading and pointing). Comparisons of parameters across each condition were carried out using paired \(t\)-tests.