# 3D timelines in VR: Adaptive speed for 3D data navigation on a concave timeline

Gary Perelman, Marcos Serrano, Aurélien Marchal, Emmanuel Dubois

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Gary Perelman, Marcos Serrano, Aurélien Marchal, Emmanuel Dubois. 3D timelines in VR: Adaptive speed for 3D data navigation on a concave timeline. International Journal of Human-Computer Studies, 2025, 207, pp.103672. 10.1016/j.ijhcs.2025.103672. hal-05519735

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# 3D Timelines in VR: Adaptive Speed for 3D Data Navigation on a Concave Timeline

## Gary Perelman

Elipse - IRIT, University of Toulouse, France, gary.perelman@irit.fr

## Marcos Serrano

Elipse - IRIT, University of Toulouse, France, marcos.serrano@irit.fr

## Aurélien Marchal

Elipse - IRIT, University of Toulouse, France, aurelien.marchal@irit.fr

## Emmanuel Dubois

Elipse - IRIT, University of Toulouse, France, emmanuel.dubois@irit.fr

<figure><img src="image_2.png" /><figcaption>Figure 1. Overview of the concave 3D timeline (Left) and illustration of its manipulation with one of our adaptive speed navigation techniques (Right).</figcaption></figure>

Timelines involving 3D objects can be rendered in VR to facilitate their visualization and various forms of data analysis, such as object location or pattern detection. While different timeline shapes have been proposed in 3D, such as convex or linear, the input interaction is usually based on inherited UIs (e.g. sliders), leaving the rich VR controllers unexploited. Hence, there is still room for more efficient interaction with 3D timelines in VR. Our first contribution is the experimental comparison of a concave timeline shape against other existing shapes. We demonstrate that users prefer the concave shape, which allows for faster object selection and pattern detection. Our second contribution is the design of four controller-based navigation techniques using adaptive speed, i.e. allowing the users to instantly adjust the panning speed in the timeline. We experimentally compared their performance to two baselines: a slider widget and a dual-speed navigation technique. We demonstrate that users prefer the techniques based on adaptive speed, which allow for faster object selection and pattern detection. Finally, in a third experiment we assess the scalability of the best techniques with a timeline containing a large number of elements. Our results show that the adaptive speed technique remains the most efficient with timelines containing thousands of elements.
# 1 INTRODUCTION

Visualization and interaction with temporal data involving 3D objects are common in various contexts [48], for example, in biology and medicine to better understand the evolution of a system (e.g. a human cell) or to detect recurring patterns (e.g. cell division). Previous work has shown that a practical solution to this exploration is to display a succession of data objects on a timeline [1] in a large virtual reality (VR) environment. Displaying several objects side by side facilitates pattern detection [15, 26] and locating future or past object states [16, 27]. Furthermore, VR facilitates data visualization by offering a large display space, all around the user [4, 7, 10, 12, 22].

To better understand the benefits of 3D timelines in VR, previous work mainly focused on the output interaction, i.e. the visualization aspect. A recent work by Fouché et al. [1] proposed a design space describing how to display 3D temporal data in VR. While their design space includes a variety of 3D shapes for the timeline including concave, convex, flat and multiple planes, their studies only focused on convex 3D timelines (circular and helicoidal shapes, curved around the user's position). From the input interaction point of view, VR controllers offer a rich bimanual interaction vocabulary with several degrees of freedom (DoFs), which could facilitate interaction with the timeline and 3D manipulation of the data objects. However, their use for navigating 3D timelines remains under-explored, as prior work only explored basic interaction techniques in VR, such as sliders [12, 19], gaze&click [1] or point&click [34].

In this paper, we set out to identify the best visualization and interaction techniques for navigating timelines that display a collection of 3D objects (e.g. human cells) in VR, see Figure 1. We specifically focus on two common visualization tasks [1, 34] for the exploration of time-varying datasets: finding a given 3D object (Lookup) and finding a pattern (Explore), i.e. a set of 3 consecutive 3D objects sharing the same characteristics.

Regarding the timeline shape, we extend prior work by exploring the use of a concave 3D timeline, inspired by the well-known desktop visualization Perspective Wall [32]. Indeed, Fouché et al. [1] identified the benefits of concave timeline visualizations in 3D, showing that it emphasizes the local temporal context, frees the space around the user and decreases the density of information in their field of view. However they did not include such a visualization in their experimental protocol. We believe that the benefits provided by concave timelines, such as providing both a detailed and close view of the objects in front of the user, while maintaining an overview of the other objects on each side of the timeline, will allow for faster navigation, limit head movements and be preferred by users. In our first study, we assess the impact of the concave shape on the users' performance for visualizing 3D timelines. To do so, we compare their performances, in terms of time and error, to the best-performing (in terms of time and density of elements displayed) visualization identified by Fouché et al. [1] (convex timeline) [1] and to the baseline of Fouché's experiment. This baseline consists in a snapshot of a timeline (called NoTimeline in previous work [1]), displaying only one 3D element at a time (like an animation). In this first study, users employ a virtual slider, the state-of-the-art solution to navigate through the timeline. To further complement Fouché's experimental approach, we then compare, in a follow-up study, the concave timeline to a linear timeline displaying the same 3D elements.

Regarding the interaction with the 3D timeline, we explored the benefits of controller-based interaction techniques supporting adaptive speed, i.e. that can dynamically adapt the zoom level and, hence, the panning
speed on the timeline. Such an approach, inspired by the desktop scrolling technique OrthoZoom [2], should be especially helpful to reach distant elements faster. To this end, we systematically explored using the joystick and the mid-air capabilities of regular VR controllers. In our second study, we compared these techniques to the same virtual slider that was used in our first study and to a dual-speed navigation technique, i.e. a technique offering only two predefined panning speeds. Finally, to assess the scalability of our solutions, we performed a third study in which the timeline contains up to 10000 objects.

Our contributions are as follows: 1) an exploration of different 3D timeline shapes, revealing the advantages of a concave timeline, 2) the design and evaluation of VR controller-based input techniques supporting adaptive speed navigation to enhance the navigation on 3D timelines in VR, and 3) an assessment of the scalability of these techniques for very large timelines.

## 2 RELATED WORK

We first synthesize works related to timeline visualization before focusing on interaction with timelines and, more specifically, in AR/VR environments.

### 2.1 Timeline visualization

Timeline visualization has been extensively explored in desktop environments [11, 18, 33]. They are mainly used to represent a series of events linearly. For instance, they allow to summarize or plan events in calendars or to visualize the temporal evolution of a system. The usual interface consists of displaying a unique element at a specific timestamp, i.e. a snapshot of the timeline. Changing this timestamp, i.e. navigating through the timeline, updates the displayed element and relies on an interaction technique, typically a slider [12, 19]. However, displaying only one element at a time hinders pattern detection [15, 26] and locating future or past object states [16, 27]. To overcome these limitations, other works explored different visualization techniques. Among them, Bartolomeo et al. [3] have shown that the timeline shape has a significant impact on the completion time of several tasks such as reading information or finding an element. As an example, in this work, participant could retrieve information faster from a 2D linear timeline than from a circle timeline or a spiral.

To help reasoning about the multiple possibilities for designing a timeline, Brehmer et al. [5] proposed a design space of 2D timeline visualizations. They identified three dimensions: scale, layout and representation. Scale represents the relation between the displayed distance and the temporal distance (e.g. linear timeline, sequential scale, etc.). The layout describes how the timeline is partitioned on the display (e.g. segmented, unified or faceted). Finally, the representation describes the shape of the timeline (e.g. the curvature of the time axis: flat, convex, concave, etc.). For example, Kondo et al. [28] proposed a linear (scale), unified (display) and flat (representation) timeline to visualize the evolution of 2D data points. Similarly, Schwab et al. [46] used the abscissa of a 2D chart to represent timelines.

In spatiotemporal 3D data, also named S4D by Kim et al. [27], multiple timestamps called small multiple [21], can also be visualized side-by-side simultaneously to facilitate pattern detection [15, 26]. As an example, in BentoBox [26], multiple views of a dataset are displayed in VR in a grid in front of the user. To address these situations, Fouché et al. [1] proposed a design space to describe how S4D can be displayed in VR. They adapted previous work on 2D timelines [5] to better exploit the 3D rendering capabilities of VR devices. However, in their experimental studies, they only considered convex timeline shapes.
And yet, in their work, they envisioned that concave timeline shapes are interesting and promising solutions to explore a temporal dataset because concave shapes free radial space around the user and decrease the density of information in their field of view. Furthermore, authors mentioned that such shapes provide a focus area close to the user, supporting a detailed visualization of elements, and a context area, allowing the perception of distant points, thus facilitating the search for recurrent patterns of elements. The principle of concave timelines can be related to the Focus and Context or Overview+Detail paradigms, well known in the literature, which has been shown to enhance understanding and navigation in large datasets [5, 13, 20, 36, 44]. Furthermore, concave timelines such as the Perspective Wall [32] have already been explored on desktop environments and were shown to facilitate the interaction with a timeline. As a result, concave timelines allow finding elements in the timeline faster and require less head movements as distant element can be seen without requiring the user to look above or under, as in a helicoidal timeline shape, or far on the left or right, as in a linear timeline shape. Therefore, in this work, we compare the S4D visualizations explored by Fouché et al. to a novel concave timeline shape in VR. Beyond visualizing the dataset, navigating through timeline data is particularly challenging as it requires users to efficiently explore a large dataset of elements. We thus review, in the following sections, how existing works facilitate navigation in a timeline.

## 2.2 Interaction with a timeline

Interaction with 2D timelines has been widely explored in desktop and mobile environments [11, 18, 33, 45]. Well-known tools, such as the Windows-Tab command, use a navigation bar (or slider) to move inside a timeline: dragging the cursor of the slider translates the dataset according to a linear transfer function. In addition to the slider, a cursor displays the current position inside the timeline and two buttons (e.g. up/down arrows) control unitary movements of the cursor. To facilitate the timeline navigation, existing apps, such as Youtube [53], provide an additional interaction mechanism: sliding up on the slider cursor displays a set of adjacent frames providing the user with the surrounding video frames and hence facilitating precise navigation around the current timestamp. This approach has been extended by Swifter [33] which explores the use of a 2D grid to display surrounding video frames. Dragicevic et al. [18] proposed video browsing by directly manipulating video elements without using the navigation bar: when an element is selected, the user can navigate inside the timeline following the evolution of the selected element through time. A similar approach has been used in DimpVis [28]. These works show that precise vicinity exploration allows for faster navigation in a timeline. However, they do not facilitate the search of a distant element or distant pattern in the timeline.

To overcome this limitation, Schwab et al. [45] explored panning and zooming on desktop or mobile displays to facilitate fast navigation in a timeline. They compared several pan and zoom interaction techniques to the default slider-based interaction. Their results established that zoom techniques facilitate navigation inside large datasets. Pan and zoom techniques have also been applied to large document navigation. For instance, Igarashi et al. [25] proposed to facilitate document navigation using speed-dependent automatic zooming: the speed of the scrolling gesture (with the mouse wheel) controls the zooming level of a document or image gallery. Cockburn et al. [14] used the document length to define the panning speed. Finally, Orthozoom [2] uses a perpendicular gesture to adjust the zooming level inside a document, and thus, the panning speed. All these approaches dynamically modify the scroll transfer function to facilitate data navigation and offer different panning speeds to navigate inside the dataset. Such approaches allow the user to quickly navigate through the dataset/document and find
distant elements while still offering precise movements to explore the vicinity of an element. However, these
works focused on desktop environments with a mouse or regular mobile interaction with touch input.
And yet, VR is an interesting alternative to desktop and mobile computers as it offers a large display space,
reducing information clutter and facilitating 3D objects visualization [12, 22]. For instance, Millais et al. [34]
showed that VR performs better than desktop environments for displaying large datasets. However, VR
environments do not integrate regular desktop or mobile interaction. We therefore review the interaction
modalities explored in VR or AR to support navigation in a timeline.

## 2.3 Interaction with a timeline in AR or VR

Interacting with a timeline in VR/AR often rely on the use of a basic VR/AR GUIs [39, 52] to allow timeline navigation. For example, Okada et al. [41] developed a technique to navigate inside aggregated spatialized tweet data using 3D sliders; Vremiere [39] facilitated the navigation and edition inside a 3D video using a VR graphical user interface (i.e. 3D panels displaying buttons and sliders, such as desktop GUIs).

In contrast, the spatial location of the timeline events has also been explored in VR. ReLive [24] uses AR to display an in-situ view of the timeline as a 3D trajectory: users can physically explore the view and point and click events (rendered as cubic boxes around the 3D trajectory) to access the corresponding spatiotemporal data. In GhostAR [8] the temporal trajectory of a visitor can be explored in-situ: moving along this timeline requires that the user physically moves towards the recorded position of the visitor. Then, users can interact with the timeline using AR controllers to group data points, or explore details in a given time point using AR controllers as input modality. In ReLive and GhostAR, the users need to physically or virtually move along a trajectory inside the temporal dataset to navigate the temporal dimension, which can be tiring. Furthermore, they are limited to small datasets as larger datasets would induce visual clutter or require too much physical movement of the user.

Overall, VR offers dedicated input interaction modalities, but as for 2D contexts, an efficient navigation technique for timelines in VR should strike a balance between allowing fast navigation, thus easing access to distant elements, and supporting slow and precise exploration of the vicinity of an element. Using adaptive speed achieves both of these goals.

## 2.4 Summary

On a first hand, previous work found that the timeline shape is an important parameter to facilitate its exploration. As a result, design spaces have been defined for 2D [5] or 3D [1] timelines. Based on these, multiple timeline shapes have been analyzed and compared, including basic timeline visualizations (i.e. with only a snapshot visible at any given time) and convex ones. However, while concave timelines have been explored in 2D [32], such timeline representation has never been explored in a 3D context.

On a second hand, multiple interaction techniques have been designed to facilitate timeline exploration. In 2D, the basic interaction technique rely on the use of a slider [45] which can be enhanced by adding visualization or manipulation tools [18, 28]. Other works extended the basic slider by proposing particularly efficient navigation techniques, such as pan and zoom [2]. However, these works focused on the mouse and keyboard or tactile input, which are not appropriate to VR. Regarding 3D timelines, previous work also explored the use of slider-based interaction using mid-air gestures and VR controllers. Other works focused on spatial navigation through the user's physical movement around and inside the dataset [8, 24]. However, these techniques do not take advantage of the advancement in interaction technique design from 2D contexts.
In this paper we first extend previous works focusing on the shape of timelines visualization and explore the concave shape for 3D timelines. Then, we adopt an input interaction point of view on the design of the timeline to increase interaction efficiency. Inspired by encouraging results on 2D timelines in desktop contexts, we propose to study the benefits of continuously adjustable zoom techniques on 3D timelines. Finally, given the prevalence of VR controllers to interact in VR environments and the benefits of such environments for 3D objects visualization (i.e. large display area available all around the user and ease of changing a point of view on the scene [4, 7, 10, 12, 22]), this paper aims to assess the interest of mid-air and VR-controllers DoF to facilitate 3D timeline navigation in VR.

# 3 STUDY 1: COMPARING VISUALIZATIONS FOR 3D TIMELINES

The goal of this first study is to compare different visualization shapes for the 3D timeline. Inspired by several works [1, 11, 33, 45], we assess the usability of our timeline shapes by measuring the completion time and the number of errors. Furthermore, to assess the user's interactive experience with the timeline, we also measure head amplitude and collect qualitative feedback such as mental demand and physical demand through a NASA-TLX form. In this section, we first describe the shapes we considered and the ones we excluded before presenting the experimental protocol.

## 3.1 Design of the 3D Timeline shapes

We go beyond prior literature by studying and comparing a concave timeline shape, that we called Perspective, to other timeline shapes. In a first step, we study three conditions: Perspective, Helicoïd and a baseline condition where only one element is displayed at a time, called Snapshot. Both Helicoïd and Snapshot visualizations were explored by Fouché et al. [1]. In their work, they also mentioned concave timeline shape. However, in their experimental protocol, they only compared a convex timeline shape with a helicoid shape and a one element timeline as a baseline (called No Timeline). They found that the helicoid shape was the most adequate visualization for achieving lookup and explore tasks on the timeline. Therefore, in this work, we extend the exploration of 3D timeline shapes by comparing their helicoid version, i.e. the best timeline shape in their study, with a concave timeline shape and their baseline. In a follow-up study, we also compare a linear timeline to our concave shape.

**Perspective (concave shape):** As previously mentioned, our approach for concave shape is inspired by previous work on Focus+Context, and more specifically by the Perspective Wall technique [34]. Hence, with this visualization, the 3D objects in front of the user are closer while the objects in the left and right areas are displayed on linear vanishing lines. While curved vanishing lines have been envisioned by previous work [1], we chose to adopt straight vanishing lines as in the PerspectiveWall because we believe it prevents further distortion of the dataset which might impact tasks involving several adjacent 3D objects of the timeline (see the Explore task below). By displaying the elements in front of the user instead of all around, we minimize the required eye and head movements. We empirically chose to display five 3D elements side by side in the central panel (see Figure 2 - Top-Left). This number of elements allowed for easy gaze detection on the elements in front of the user.

**Helicoïd (convex shape):** The Helicoïd shape displays several elements on a vertical spiral around the user (see Figure 2 - Top-Right). A prior study comparing Helicoïd with a convex shape and with the NoTimeline (also named Snapshot) condition highlighted that the users preferred the Helicoïd shape and had the best performance
with it [1]. Fouché et al. envisioned that the helicoid timeline manipulation, such as changing the scale dimension, could facilitate the visualization and comparison of occurrences of a particular event.

**Snapshot (single item):** The Snapshot shape displays only one element at a time which is replaced by another when navigating through the temporal dataset (see Figure 2 - Bottom-Right). We study this condition as it is a common baseline in prior work.

**Linear (flat shape):** The Linear shape is a 3D version of the traditional 2D timeline visualization. A horizontal line is displayed in front of the user (see Figure 2 - Bottom-Left). We study this condition in a follow-up study as its 2D counterpart is a common baseline in 2D prior work.

<figure><img src="image_3.png" /><figcaption>Figure 2. 3D timeline shapes: Perspective(Top-Left), Helicoïd (Top-Right), Linear (Bottom-Left) and Snapshot (Bottom-Right).</figcaption></figure>

The interaction with all these conditions is based on a horizontal slider displayed in front of the user, below the 3D objects. This interaction technique is hereafter referred to as **Slider**. The scroll cursor can be dragged with a raycasting technique controlled with the VR controller and its trigger. The users can also click inside the scrollbar but outside the scroll cursor to trigger multiple cursor movements until the clicked location: this behaviour is equivalent to regular desktop scroll widgets. Finally, two buttons on the left ([-] button) and on the right (+) button) of the scrollbar allow the user to scroll to the previous/next element along the timeline. In the Helicoïd and Perspective conditions, users can also point to a distant 3D object using the VR controller's raycasting to teleport the pointed element in front of the user. This option was not available in the Snapshot condition as there were no other displayed elements that could be pointed at.

## 3.2 Dataset and task design

To ensure the external validity of our work and its comparison with prior work, our protocol is inspired by Fouché et al. [1]. Concretely, users were placed in front of a 3D timeline containing 200 elements. Each element was composed of six spheres, forming a 3D cross. Each sphere was colored according to four predefined colors: red, orange, light blue or dark blue. This design is inspired by previous work [1] to facilitate comparison with our results. By adopting a similar experimental framework, we build upon acquired findings and provide additional results within a coherent setup, thereby extending the knowledge established under similar conditions. Each element comprised the 3D object and its step number (ranging from 1 to 200), displayed in white text under the
spheres (see Figure X). Every ten steps, the number was displayed above the element with a bigger font to facilitate navigation.

In this experiment, users had to perform two tasks: **Lookup** and **Explore**. The **Lookup** task, defined by Brehmer et al. [6] as searching for a known reference target in a familiar environment, consists in reaching a specific element of the timeline, called the target and designated with its step number. The **Explore** task, defined by Brehmer et al. [6] as searching for characteristics without regard to the location of the items, consists in finding a specific pattern of three consecutive elements with specific colors. We did not consider the two other visualization tasks used in previous work [1] as they are similar to Lookup and Explore tasks: Counting corresponds to multiple Lookups, and Maximum corresponds to finding one pattern in the dataset.

Before each trial, a panel in front of the user displayed the task type, the timeline shape, the current trial number, the total trial number and a start button. To start a trial, participants had to select the start button using the VR controller. Once the button was selected, the panel disappeared and the trial started.

For the **Lookup** task, the instruction, i.e. the target to reach, was displayed after the trial started, above the elements, in front of the user. The starting position, i.e. the step number of the element directly in front of the user on the timeline, was chosen using a semi-random algorithm (ensuring the desired target would still be inside the 0-200 interval). The target could be placed on the left or right of the starting position at a distance of 44 or 88 elements, thus representing close and far targets. Users had to bring the desired target in front of them (or at +/- 2 elements in front of them in the Helicoïd and Perspective conditions). Then, a gaze was used to validate the target. After a dwell of 500ms, if the user gazed at the correct target, the trial ended and the panel was displayed. The dwell time was subtracted from the completion time measured for each trial.

For the **Explore** task, users had to find 1, 3 or 5 occurrences of a specific pattern composed of three consecutive elements with specific colours. The patterns were placed randomly on the timeline. When starting the trial, users did not know how many patterns were present in the dataset. We used two distinct patterns: one in which the top and bottom spheres are light blue and the four middle spheres are dark blue, thus forming a horizontal line; and a second in which the left and right spheres are light blue and the top, center and bottom spheres are dark blue, thus forming a vertical line. For each trial, only one type of pattern was used, i.e. the 1, 3 or 5 patterns to find in one trial were all of the same type (horizontal or vertical). For this task, the trial always started at the element numbered 0, i.e., at the timeline's start. As for the **Lookup** task, users had to bring the pattern in front of them and then gaze at it to select it. After a dwell of 500ms, the pattern was validated and turned green. To end the trial, users could click on a virtual button "End Trial" displayed under the scrollbar. They were told to only click on the button if they thought they had found all the patterns in the dataset. Otherwise, a timeout of 180 seconds automatically ended the trial.

## 3.3 Apparatus and implementation

Users were seated on a stool and wore an Oculus Meta Quest Pro headset [40]. The headset weights 722g and has a field of view of 106 degrees horizontally and 96 degrees vertically, with one LCD display of 1800x1920 pixels per eye and a refresh rate of 90 Hz. They also held a VR controller (Premium Touch Pro controller) in their dominant hand. The VR headset was connected to a computer using the Oculus quest link cable. The experimental app was running on the computer (Windows 11, Intel core i7-12850HX, Nvidia GeForce RTX 3080 Ti, SSD 2To, 16Go 4800Mz DDR5 RAM) using Unity [49] in C#.
## 3.4 Participants

We recruited 12 participants for the experiment at the local university, all with a background in computing science (25.5 years old, SD = 4.55), seven self-identified as men and five self-identified as women. We disinfected the VR headset and the controller between each use and applied all the necessary barrier gestures to comply with sanitary protocols at our university. We complied with the local ethical requirements of our university and asked each participant to fill out an informed consent form.

## 3.5 Experimental design and collected data

The experiment followed a within-subject design for each of the two tasks. For the **Lookup** task, the experiment followed a 3x2x2 design, with **shape** (Snapshot, Helicoïd, Perspective), **distance** (44, 88) and **direction** (left, right) as factors. For the **Explore** task, the experiment followed a 3x2x3 design with **shape** (Snapshot, Helicoïd, Perspective), **pattern type** (horizontal, vertical) and **number of patterns** (1, 3, 5) as factors. The study was divided into three blocks, each corresponding to one timeline shape. The order of timeline shape was counterbalanced across participants using a 3x3 Latin square. For each shape, participants always started with the **Lookup** task, followed by the **Explore** task. For the **Lookup** task, participants had to perform 4 training trials followed by 12 trials (3 repetitions x 2 distances x 2 directions). For the **Explore** task, participants had to perform 6 training trials followed by 12 trials (2 repetitions x 2 pattern types x 3 number of patterns). We collected 12 participants x 3 shapes x (3 x 2 x 2 + 2 x 2 x 3) = 864 trials for the experiment and 12 x 3 x (4 + 6) = 360 for the training. The experiment lasted, on average, 102 minutes.

## 3.6 Collected data and data analysis

We measured the trial completion time and the maximum head rotation, hereafter referred to as head movements, for each trial. After each combination of task and shape, users had to fill out an unweighted Nasa TLX [43]. They were also invited to provide informal feedback about the timeline shape. At the end of the experiment, users had to rank the shapes in terms of preference for each task.

We used repeated measures two-way ANOVA to analyze the results (F, p, η²). Post-hoc pairwise T-tests with Bonferroni correction were used when needed. When the normality assumption was violated (Shapiro-Wilk normality test), we transformed the data using a log function. If the normality assumption was still violated, we conducted a Friedman test (χ², p, n), followed by a pairwise Wilcoxon test with Bonferroni correction. All reported confidence intervals (Cis) are 95% BCa bootstrapped with 10000 replicates. Our bootstrap method uses a deterministic approach. Scripts used in this work are available online [not available for submission].

While the Lookup task can be considered as a pointing task in a timeline, and thus, analyzed using the Fitts law, we didn't do such analysis because the navigation techniques are not identical for every timeline shape: Snapshot does not allow for distant pointing to grab the elements and bring them in the focus area. Furthermore, as the user does not know the location of the targets in the Explore task, our results can't be analyzed using the Fitts law.

## 3.7 Results

For both tasks, we verified that there was no effect of the order of shape. We also verified that there was no learning effect between the task repetitions for each data visualization.
### 3.7.1 Completion time

**Lookup task:** We found a significant difference in completion time between the timeline shapes F(2, 429) = 13, p<0.0001. The effect size, eta squared (η²), was 0.06. A post-hoc test established a significant difference between Perspective and the two other shapes, Snapshot (p<0.01) and Helicoïd (p<0.01). Overall, performing the Lookup task requires less time using Perspective (6.39s, CI[6.06, 6.75]) than using Helicoïd (7.95s, CI[7.41, 8.59]) or Snapshot (7.72s, CI[7.34, 8.14]), as illustrated in Figure 3 - Top-Left. We found no effect of the target distance or direction on the completion time nor any interaction between the timeline shape and these factors.

<figure><img src="image_4.png" /><figcaption>Figure 3. Completion time (in seconds) for the Lookup (Top-Left) and Explore (Bottom-Left) tasks; head movement (in degrees) for the Lookup (Top-Right) and Explore (Bottom-Right) tasks (CI 95%).</figcaption></figure>

**Explore task:** We found a significant difference in completion time between the three timeline shapes χ²(2)=17.17, p<0.01, n=12. A post-hoc test established a significant difference between Perspective and the two other shapes, Snapshot (p<0.01), and Helicoïd (p<0.01), and between Snapshot and Helicoïd (p<0.01). Overall, performing the Explore task requires less time using Perspective (36.7s, CI[34.5, 39.0]) than using Helicoïd (43.7s, CI[41.2, 46.4]) which also requires less time than using Snapshot (51.1s, CI[48.3, 53.9]), as illustrated in Figure 3 - Bottom-Left. We did not find any effect of the pattern type on the completion time nor any interaction between the experiment factors (number of patterns or timeline shape).

Overall, using the Perspective shape required less time to complete both tasks than using Helicoïd or Snapshot. These results can be explained by the fact that users were able to select distant elements precisely (not possible using Snapshot, where only one element is displayed), without large head movements (required for Helicoïd, as elements are displayed all around the user), thus allowing to quickly access the desired target. This is confirmed by participants' comments: "[Using Snapshot,] I can only see one item at a time, which makes finding a pattern quite hard.", P4. "I need to be precise to get the correct target using this one [Snapshot] as there is only one which is displayed, on the two others, I had five targets that I could select, it was easier" P6.

### 3.7.2 Head movements

**Lookup task:** We found a significant difference in head movements between the timeline shapes F(2, 420) = 27.4, p<0.01. The effect size, eta squared (η²), was 0.11. A post-hoc test established a significant difference between Perspective and the two other shapes, Snapshot (p<0.01) and Helicoïd (p=0.01), and between Snapshot and Helicoïd (p<0.01). Overall, performing the Lookup task requires smaller head movements using Snapshot (14.26, CI[12.19, 16.81]) than using Perspective (16.3°, CI[15.0, 17.87]) which also requires smaller head movements than Helicoïd (24.75°, CI[21.77, 28.46]), as illustrated in Figure 3 - Top-Right. We did not find any effect of
distance or direction on the head movements nor any interaction between the experiment factors (distance, direction, timeline shape).

**Explore task:** We found a significant difference in head movements between the three timeline shapes F(2, 414) = 83.9, p<0.01. The effect size, eta squared (η²), was 0.29. A post-hoc test established a significant difference between Snapshot and the two other shapes, Perspective (p<0.01) and Helicoïd (p<0.01). Overall, performing the Explore task requires smaller head movements when using Snapshot (14.95°, CI[13.64, 16.42]) than when using Perspective (33.68°, CI[31.70, 36.0]) or Helicoïd (53.15°, CI[46.13, 61.15]), as illustrated in Figure 3 – Bottom-Right. We did not find any effect of number of patterns or pattern type nor any interaction between the experiment factors (number of pattern, pattern type, timeline shape).

Overall, we found that Helicoïd involved larger head movements than the two other timeline shapes. This is due to the elements being displayed all around the user, including above and under the user. These results are confirmed by user's comments: "This one [Perspective] is better than the Helicoïd because I don't have to move the head so much. Looking up or on the sides was tiring." P2. "With this visualization [Helicoïd], it is harder to find the target because there are so much 3D objects everywhere around me, I'm feeling lost." P10. We also found that Snapshot requires the lowest head movements, which is logical as there is only one element displayed in front of the user.

### 3.7.3 NasaTLX

**Lookup task:** We found that Perspective induces a smaller mental demand than Helicoïd (p<0.01) or Snapshot (p=0.01) (F(2, 33)=7.02, p<0.01, η²=0.30). We also found that Helicoïd induced a bigger physical demand than Perspective (p<0.01) or Snapshot (p=0.02) (F(2, 33)=6.46, p<0.01, η²=0.28). Results further established that Perspective induces a smaller temporal demand than Helicoïd (p=0.02, F(2.33)=4.74, p=0.01, η²=0.22). The analysis did not reveal differences in terms of performance. Regarding effort, Perspective requires less effort than Helicoïd (p<0.01) or Snapshot (p=0.02) (F(2, 33)=7.27, p<0.01, η²=0.31). Finally, we did not find any difference in terms of frustration between the three timeline shapes. These results are illustrated in Figure 4 – Top.

<figure><img src="image_5.png" /><figcaption>Figure 4. NASA TLX scores for the Loopkup (Top) and the Explore (Bottom) tasks (CI 95%).</figcaption></figure>

**Explore task:** We found that Perspective induces a smaller mental demand than Helicoïd (p<0.01) or Snapshot (p<0.01) (F(2, 33)=11.7, p<0.01, η²=0.42). We also found that Helicoïd induced a bigger physical demand than
Perspective (p<0.01) or Snapshot (p<0.01) (F(2, 33)=7.87, p<0.01, η²=0.32). We did not find any difference in terms of temporal demand. However, we found that Perspective was considered more performant that Snapshot (p<0.01) or Helicoïd (p<0.01) (F(2, 33)=7.96, p<0.01, η²=0.32). We also found that Perspective requires less effort than Helicoïd (p<0.01) or Snapshot (p<0.01) (F(2, 33)=17.55, p<0.01, η²=0.52). Finally, we found that Perspective induces less frustration than Snapshot (p=0.01) (F(2, 33)=4.52, p=0.02, η²=0.22). These results are illustrated in Figure 4 - Bottom.

To summarize, for both tasks, users had the lowest mental demand using Perspective and the highest physical demand using Helicoïd. They also felt that Perspective required less effort than the other timeline shapes. Results are more nuanced for the three other NasaTLX scores.

### 3.7.4 Ranking

**Lookup task:** Users ranked the Perspective ten times in first position and two times in second position, see Figure 5 - Top. Helicoïd was most often ranked in second position (seven times), and Snapshot in last position (nine times).

**Explore task:** Users ranked the Perspective eleven times in first position and one time in second position, see Figure 5 - Bottom. Here again, Helicoïd was most often ranked in second position (six times) and Snapshot in last position (seven times).

<figure><img src="image_6.png" /><figcaption>Figure 5. Ranking of the timeline shapes for the Lookup (Top) and Explore (Bottom) tasks (in number of participants).</figcaption></figure>

As a result, for both tasks users clearly selected Perspective as their preferred timeline shape, and Snapshot as the least appreciated one. These results are confirmed by participants comments: "I don't like this one [Snapshot]. It's harder to find patterns because I can only see one element at a time." P8.

### 3.7.5 Summary study 1

Overall, we found that Perspective requires less time than the two other shapes for both tasks. It also induces less mental demand and effort than the two other timeline shapes. Finally, this shape is preferred over the two others. This result is particularly interesting as, while Fouché et al. envisioned concave timelines, they did not study them in their experiment and thus could not conclude on their benefits. However, in our study we did not compare the Perspective timeline shape with a traditional timeline shape used in 2D environments: a linear timeline shape. Hence, we conducted a follow-up study to compare these two timeline shapes, which we present in the next section.
# 4 STUDY 1 FOLLOW-UP: COMPARING CONCAVE AND LINEAR 3D TIMELINES

In our first study, we showed that a concave timeline shape (called Perspective) outperforms two other 3D timeline visualizations, Helicoïd and Snapshot. We decided to further compare the Perspective timeline shape to a Linear timeline shape, which is the most common approach in 2D environments.

## 4.1 Similarities and differences with study 1 protocol

This experiment used the same dataset, task design, apparatus, implementation and data analysis protocol as our Study 1. However, for the **Lookup task**, we added two new distances, 22 and 66 to the previously considered distances (44 and 88). Also, for the **Explore task**, we reduced the number of patterns to find, to limit the experiment's total time: participants had to find either 1 or 5 patterns (we removed the condition with 3 patterns from the previous study).

## 4.2 Participants

We recruited 12 participants for the experiment at the local university, all with a background in computing science (21.2 years old, SD = 2.37), eight self-identified as men and four self-identified as women. We disinfected the VR headset and the controller between each use and applied all the necessary barrier gestures to comply with sanitary protocols at our university. We complied with the local ethical requirements of our university and asked each participant to fill out an informed consent form.

## 4.3 Experimental design and collected data

The experiment followed a within-subject design for each of the two tasks. For the **Lookup** task, the experiment followed a 2x4x2 design, with **shape** (Linear, Perspective), **distance** (22, 44, 66, 88) and **direction** (left, right) as factors. For the **Explore** task, the experiment followed a 2x2x2 design with **shape** (Linear, Perspective), **pattern type** (horizontal, vertical) and **number of patterns** (1, 5) as factors. The study was divided into two blocks, each corresponding to one timeline shape. The order of timeline shape was counterbalanced across participants using a 2x2 Latin square. For each shape, participants always started with the **Lookup** task, followed by the **Explore** task. For each task, trials were generated in a random order. For the **Lookup** task, participants had to perform 8 training trials followed by 12 trials (3 repetitions x 4 distances x 2 directions). For the **Explore** task, participants had to perform 4 training trials followed by 8 trials (2 repetitions x 2 pattern types x 2 number of patterns). We collected 12 participants x 2 shapes x (3 x 4 x 2 + 2 x 2x 2) = 768 trials for the experiment and 12 x 2 x (8 + 4) = 288 for the training. The experiment lasted, on average, 74 minutes.

## 4.4 Results

For both tasks, we verified that there was no effect of the order of shapes. We also verified that there was no learning effect between the task repetitions for each timeline visualization.

### 4.4.1 Completion time

**Lookup task:** We found a significant difference in completion time between the timeline shapes (F(1, 560) = 262.218, p<0.0001). The effect size, eta squared (η²), was 0.32. A post-hoc test established a significant difference between Perspective and Linear (p<0.0001). Overall, performing the Lookup task requires less time using Perspective (6.01s, CI[5.86, 6.17]) than using Linear (8.03s, CI[7.82, 8.26]), as illustrated in Figure 6 – Top-Left.
This result remain true for every distance considered independently (p<0.001). We also found an interaction between the visualization and the distance factors on completion time $F(3, 560) = 5.54$, p<0.001. The effect size ($\eta^2$) was 0.03. A post-hoc test established that significant differences can be found between the distances only for the Linear timeline shape and not for the perspective timeline shape. More precisely, the two longest distance, i.e. 66 and 88, take more time than the two smaller distances, i.e. 22 and 44 (p<0.001).

We found no effect of the target direction on the completion time nor any other interaction between the experimental factors.

<figure><img src="image_7.png" /><figcaption>Figure 6. Completion time (in seconds) for the Lookup (Top-Left) and Explore (Bottom-Left) tasks; head movement (in degrees) for the Lookup (Top-Right) and Explore (Bottom-Right) tasks (CI 95%).</figcaption></figure>

**Explore task:** We found a significant difference in completion time between the two timeline shapes $F(1, 184) = 134.783$. The effect size, eta squared ($\eta^2$), was 0.42. A post-hoc test established a significant difference between Perspective and Linear (p<0.0001). Overall, performing the Explore task requires less time using Perspective 18.24s, CI[17.41, 19.14]) than using Linear (26.88s, CI[25.38, 28.37]), as illustrated in Figure 6 - Bottom-Left. We did not find any effect of the pattern type on the completion time nor any interaction between the experiment factors (number of patterns, pattern type or timeline shape).

**Summary:** Overall, using the Perspective shape required significantly less time to complete both tasks than using Linear. Furthermore, the Perspective shape is more robust to high distances than the linear timeline shape. These results can be explained by the fact that the Perspective shape allows users to select distant elements with more precision than with the Linear shape thus allowing to quickly access the desired target. This is confirmed by participants' comments: "With Linear, *I have trouble selecting elements further than 20 [elements] from where I currently am*.", P2.

### 4.4.2 Head movements

**Lookup and Explore tasks:** We found a significant difference in head movements between the timeline shapes using a Wilcoxon test. Perspective induces less head movements than Linear (p<0.001 for both tasks). Overall, performing the Lookup task requires smaller head movements using Perspective (19.65°, CI[18.75, 20.57] for Lookup and 21.89°, CI[20.17, 23.51] for Explore) than using Linear (50.51°, CI[49.40, 51.60] for Lookup and 46.50°, CI[44.58, 48.44] for Explore), as illustrated in Figure 6 - Top-Right (resp. Bottom-Right). We did not find any effect of distance or direction on the head movements nor any interaction between the experiment factors (distance, direction, timeline shape).

**Summary:** Overall, we found that Linear involved larger head movements than Perspective. This is due to the elements being displayed far on the left and right side of the user. These results are confirmed by user's
comments: "Each time I want to see if there is another pattern, I have to look far on the right, then click to bring the pattern in front of me, then look at it and then look back far on the right, its tiring" P11.

### 4.4.3 NasaTLX

**Lookup task:** We found that Perspective induces a smaller physical demand than Linear (F(1, 22)=12.06, p<0.01, η²=0.35). We also found that Perspective requires less effort than Linear (F(1, 22)=5.47, p=0.029, η²=0.2). We did not find any difference in terms of mental demand, temporal demand, performance or frustration between the two timeline shapes. These results are illustrated in Figure 7 - Top.

<figure><img src="image_8.png" /><figcaption>Figure 7. NASA TLX scores for the Loopkup (Top) and the Explore (Bottom) tasks (CI 95%).</figcaption></figure>

**Explore task:** We found that Perspective induces a smaller physical demand than Linear (F(1, 22)=22.26, p<0.001, η²=0.5). We also found that Perspective induces a smaller temporal demand than Linear (F(1, 22)=13.32, p<0.001, η²=0.38). Finally, we found that Perspective incudes less effort than Linear (F(1, 22)=22.32, p<0.001, η²=0.5). We did not find any difference in terms of mental demand, performance or frustration between the two timeline shapes. These results are illustrated in Figure 7 - Bottom.

To summarize, for both tasks, users had the lowest physical demand using Perspective. They also felt that Perspective required less effort than Linear.

### 4.4.4 Ranking

**Lookup and Explore tasks:** Users ranked the Perspective nine times in first position for Lookup (resp. ten times for Explore), see Figure 8 - Top (resp. Bottom).
<figure><img src="image_9.png" /><figcaption>Figure 8. Ranking of the timeline shapes for the Lookup (Top) and Explore (Bottom) tasks (in number of participants).</figcaption></figure>

These results are confirmed by participant's comments: "I preferred the Perspective visualization because I can see far on each side without moving my head too much. Moving my head every time makes me feel a little sick." P1.

### 4.4.5 Summary of the follow-up study

Overall, we found that Perspective requires less time, is more robust to higher distances and induces a smaller maximum head amplitude than the Linear shape for both tasks. It also induces less physical demand and effort than Linear. Finally, this shape is preferred over Linear. To further take advantage of such a timeline shape, we explore, in the following sections, alternatives to the Slider interaction techniques (described in section 3.1) considered in this first study.

## 5 DESIGN OF 3D TIMELINE ADAPTIVE SPEED NAVIGATION TECHNIQUES

In the previous study, users could navigate the timeline using a slider interaction. To design the adaptive speed navigation techniques using the VR controller, we considered two design aspects: the navigation sub-tasks (zoom or pan) and the input modality. We detail these aspects below, before describing the resulting interaction techniques.

### 5.1 Adaptive speed interaction design

Adaptive speed techniques are intended to enhance timeline navigation by enabling users to dynamically adjust the panning speed in a continuous manner [2]. The speed at which the panning occurs in the timeline is often visually represented using a zoom: when the timeline elements are zoomed in, the panning speed is slow; when zoomed out, the panning speed is high. This approach allows the user to perform precise navigation, using a low panning speed, and fast or long-distance navigation, using a high panning speed. While a dual-speed approach provides only two predefined panning speed [42], adaptive speed allows the user to choose the desired panning speed, for instance, based on the target's distance. We identified two design aspects to define adaptive speed navigation techniques: the navigation sub-tasks and the input modalities.
### 5.1.1 Navigation sub-tasks

Adaptive speed navigation can be decomposed into two sub-tasks: **zooming** and **panning** [2, 45]. Zooming sets the panning speed and visually impacts the rendering size of the elements. Panning allows the user to navigate through the timeline based on the panning speed (defined in the first task: **zooming**).

<figure><img src="image_10.png" /><figcaption>Figure 9. Example of the zoom and Pan sub-tasks. The red arrow and red glow around the item were added on the image and were not present in the VR environment.</figcaption></figure>

### 5.1.2 Input modality

Different input modalities can be used to control each of the two identified sub-tasks. In this paper, we explore how to exploit VR controllers which offer multiple DoFs and are commonly used for interaction in VR environments. In this study, we chose to study both isometric and isotonic input modalities, respectively the joystick and the mid-air translation of the controller itself.

**Joystick (isometric input):** We use the joystick for rate-based control. We kept the standard behavior of the joystick: a small inclination induces a low rate-based action (zooming or panning) and a large inclination induces a high rate-based action (zooming or panning).

**Mid-air gesture (isotonic input):** We use the mid-air translation of the controller for position-based control. Position-based control is known to be accurate but requires clutching [9], which can partly be addressed through an appropriate transfer function. The transfer function used to map the user's input to the panning speed is inspired by previous work on distant pointing [37]. We used the following parameters to define the transfer function: CDmin = 100; CDMax = 800, Vmin = 0; Vmax = 1; Vinf = 0.5; λ = 10.4.

$$gain(x) = \frac{CDmax - CDmin}{1 + e^{-(\lambda(x-Vinf))}} + CDmin$$

## 5.2 Interaction techniques

By combining the two Input modalities (Joystick and Mid-Air) with the two Navigation sub-tasks (Zooming and Panning), we came up with four interaction techniques, adopting the following naming convention: <Zooming Modality> + <Panning Modality>. As an example, using the joystick to zoom and mid-air movements to pan is named Joystick+MidAir. In the following subsections, we describe the four interaction techniques derived from our design space.
<figure><img src="image_11.png" /><figcaption>Figure 10. Interaction techniques for zooming and panning on a timeline: MidAir+Joystick (Top-Left), MidAir+MidAir (Top-Right) Joystick+Joystick (Bottom-Left) and Joystick+MidAir (Bottom-Right).</figcaption></figure>

**MidAir+MidAir:** This interaction technique fully relies on mid-air interaction, see Figure 10 – Top-Left. It consists in using the front/back mid-air movement of the VR controller to change the panning speed and the left/right mid-air movements, in combination with the controller trigger (a button on the joystick), to pan left (respectively right). At the start of the trial, the current controller's position is used to initialize the technique. The panning speed is set to its minimum value. Holding the trigger while moving left or right allows to navigate in the timeline. When moving the controller forward (resp. backwards), the panning speed increases (resp. decreases). A visual feedback is displayed to show to the user the current panning speed: the elements move away from the user, and are thus displayed smaller to depict a higher panning speed.

**MidAir+Joystick:** This interaction technique uses a front/back mid-air gesture to adjust the panning speed while it uses a left/right joystick gesture to navigate the dataset, see Figure 10 – Top-Right.

**Joystick+MidAir:** This interaction technique uses the front/back joystick movement to adjust the panning speed and uses a left/right mid-air gesture (in addition to the trigger) to navigate the dataset, see Figure 10 – Bottom-Left.

**Joystick+Joystick:** This interaction technique uses the front/back joystick movement to adjust the panning speed and uses the left/right joystick movement to navigate the dataset, see Figure 10 – Bottom-Right. We implemented a minimum threshold for detecting joystick movement to limit involuntary movements in directions orthogonal to those desired, e.g. performing a small zoom when the user only wanted to pan left.

All these techniques behave similarly: a low panning speed allows for precise navigation while a high panning speed allows for coarse navigation.
While we fully explored the combinations of mid-air gestures and joystick for the pan and zoom gestures, we believe that some of these techniques might hinder the interaction with the timeline. Indeed, we believe that 1) combining two mid-air gestures might lead to involuntary modification of one navigation sub-task while performing the other because of the imprecision of mid-air gestures and that 2) using the joystick for panning will induce a higher completion time as rate-based control is known to be less efficient for navigating large distances. As a result, 3) the Joystick+MidAir technique should be the fastest and preferred technique over the four we designed. We compare their performance in a user study presented in the following section.

# 6 STUDY 2: GESTURE-BASED ADAPTIVE SPEED NAVIGATION

The goal of this second study is to compare the previously presented adaptive speed techniques with two baseline techniques (slider and dual-speed), presented hereafter, for navigating on a Perspective shape. This exploratory study will allow us to better understand which input modality (mid-air and joystick) is best suited for which navigation sub-task (pan and zoom).

## 6.1 Interaction techniques

In the previous section, we presented four interaction techniques based on our design space. We decided to first study only the three techniques involving mid-air gestures, to limit the length of our experiment. In a follow-up study, presented in section 6, we compare the best MidAir-based technique to the one using only the joystick (Joystick + Joystick). As a result, in this experiment we compared the three MidAir-based adaptive speed techniques (Joystick+MidAir, MidAir+MidAir and MidAir+Joystick) to two baselines: Slider and Dual-Speed.

The first baseline, Slider, corresponds to the Slider technique implemented in our first study: this technique is commonly used to manipulate sliders in VR.

Our second baseline, Dual-Speed, relies on mid-air movements for panning, and pressing the VR controller's buttons for adjusting the panning speed. It is, hence, based on a discrete zoom with two values: users can press the A button to decrease the panning speed, allowing for slow and precise panning in the timeline; pressing the B button increase the panning speed, allowing for fast and coarse navigation. Such an approach has been demonstrated to be relevant for pointing in large environments [42]. Our goal was to explore the impact of the zoom manipulation (i.e. continuous vs discrete) on the technique performance. Regarding the panning with Dual-Speed, we only considered left-right mid-air movements, as the joystick was already used for zooming, and since our goal was to evaluate the impact of discrete zooming compared to the other gesture-based techniques using continuous zooming.

## 6.2 Dataset, Tasks, Apparatus and implementation

We used the same dataset (200 elements, each element is a 3D cross composed of 6 colored spheres), the same two tasks (Lookup and Explore), the same Apparatus (Oculus Meta Quest Pro) and the same implementation (Unity using C#) as in the first study.

However, for the Explore task, we reduced the number of patterns to find, to limit the experiment's total time: participants had to find either 1 or 5 patterns (we removed the condition with 3 patterns from the previous study).
## 6.3 Participants

We recruited 15 participants for the experiment at the local university, all with a background in computing science (23.1 years old, SD = 3.87), seven self-identified as men and eight self-identified as women. We disinfected the VR headset and the controller between each use and applied all the necessary barrier gestures to comply with sanitary protocols at our university. We complied with the local ethical requirements of our university and asked each participant to fill out an informed consent form.

## 6.4 Experimental design and collected data

The experiment followed a within-subject design for each of the two tasks. For the **Lookup** task, the experiment followed a 5x2x2 design, with **Interaction Technique** (Slider, Dual-Speed, Joystick+MidAir, MidAir+Joystick and MidAir+MidAir), **Distance** (44, 88) and **Direction** (left, right) as factors. For the **Explore** task, the experiment followed a 5x2x2 design with **Interaction Technique** (Slider, Dual-Speed, Joystick+MidAir, MidAir+Joystick and MidAir+MidAir), **Pattern type** (horizontal, vertical) and **Number of patterns** (1, 5) as factors. The study was divided into five blocks, each corresponding to one navigation technique. The order of the blocks was counterbalanced across participants using a 5x5 Latin square. For each block, participants always started with the **Lookup** task, followed by the **Explore** task. For the **Lookup** task, participants performed four training trials followed by 12 trials (3 repetitions x 2 distances x 2 directions). For the **Explore** task, participants performed four training trials followed by 8 trials (2 repetitions x 2 number of patterns x 2 pattern types). We collected 15 participants x 5 interaction techniques x (3 x 2 x 2 + 2 x 2 x 2) = 1500 trials for the experiment and 15 x 5 x (4 + 4) = 600 for the training. The experiment lasted on average 118 minutes.

## 6.5 Collected data and data analysis

We measured the trial completion time and the head movements for each trial. After each block, users had to fill out an unweighted Nasa TLX form [43]. They were also invited to provide informal feedback about the navigation technique of the block. At the end of the experiment, users had to rank the techniques in terms of preference for each task.

We used the same statistical analysis method as in our first study. Scripts can be found here [not available for submission].

As for our first experiment, we did not analyze our results using the Fitts law. First, this analysis could not be applied to the Explore task as the user does not know where the target is. Second, for the Lookup task, depending on the usage of a joystick [38] or mid-air gesture [13, 51], different Fitts law variants may be used. We are not aware of an existing work that compared those different adaptations of the Fitts law, and which one is best suited in which conditions.

## 6.6 Results

For both tasks, we found no effect of the order of the interaction techniques. We did not find any learning effect between the repetitions for each technique and each task.

### 6.6.1 Completion time

**Lookup task:** Using ANOVA, we found an effect of the interaction technique on the completion time F(4,880) = 50.27, p<0.01, η² = 0.19. A post-hoc test showed that the least efficient technique for performing the Lookup task
is the Slider (6.65s, CI[6.39, 6.95]; p<0.01). The most efficient is the Joystick+MidAir (4.81s, CI[4.67, 4.97]; p<0.01) except when compared to MidAir+Joystick (5.18s, CI[5.01, 5.38]) with which no significant difference could be found. We found no difference between using Dual-Speed (5.42s, CI[5.24, 5.63]) and MidAir+MidAir (5.70s, CI[5.50, 5.92]). These results are illustrated in Figure 11 – Top-Left. Overall, using Joystick+MidAir requires from 7.1% to 15.6% less time than the other interaction techniques.

We did not find any effect of the target direction or distance on the completion time nor any interaction between the experiment factors (direction, distance, interaction technique).

<figure><img src="image_12.png" /><figcaption>Figure 11. Completion time (in seconds) for the Lookup (Top-Left) and Explore (Bottom-Left) tasks; Head movements (in degrees) for the Lookup (Top-Right) and Explore (Bottom-Right) tasks (CI 95%).</figcaption></figure>

**Explore task:** Using ANOVA, we found a significant difference in terms of completion time between the five techniques F(4,580) = 41.51, p=<0.01, η² = 0.22. A post-hoc test established that Slider requires more time than any other technique (21.88s, CI[20.75, 23.43], p<0.01), as illustrated in Figure 11 – Bottom-Left. Conversely, we found that Joystick+MidAir requires less time than any other technique (15.6s, CI[14.73, 16.53], p<0.01). Overall, performing the Explore task requires from 15.9% to 28.7 % less time when using Joystick+MidAir than the other techniques. We did not find any effect of pattern type and number of patterns on the completion time nor any interaction between the experiment factors (pattern type, number of patterns, interaction technique).

To summarize, we found that Slider requires more time to complete both tasks. This validates that adaptive speed is faster than the slider baseline. Except for MidAir+Joystick for which we found no difference, Joystick+MidAir requires less time than the other techniques for the Lookup task. We also found that Joystick+MidAir requires less time than any other technique for the Explore task. This shows that using the Joystick to configure panning speed and using a mid-air gesture to pan through the timeline is the most efficient solution in terms of time. This result is confirmed by participant's feedback: "I have more control on the timeline navigation when I use a gesture than with the joystick." P13. "When I zoom [using MidAir+MidAir], it sometimes also pans, which makes precise movements really hard to perform" P7. This also tends to establish that associating two different modalities for the two steps of an adaptive speed navigation (zoom, pan) is more efficient.
### 6.6.2 Head movements

**Lookup task:** Using ANOVA, we found a significant difference in terms of head movements between the five techniques F(4,880) = 4.34, p<0.01, η² = 0.019. A post-hoc test only established that MidAir+MidAir requires larger head movements than Joystick+MidAir (p=0.02) and Slider (p<0.01), as illustrated in Figure 11 - Top-Right. We did not find any effect of distance or direction on the head movements nor any interaction between the interaction factors (distance, direction, interaction technique).

**Explore task:** Using ANOVA, we found a significant difference in terms of head movements between the techniques F(4, 580) = 4.73, p<0.01, η²=0.03.

A post-hoc test only established that Slider requires larger head movements than Dual-Speed (p<0.01) and MidAir+MidAir (p=0.02), as illustrated in Figure 11 - Bottom-Right. We did not find any effect of pattern type or number of patterns on the head movements nor any interaction between the interaction factors (pattern type, number of patterns, interaction technique). The limited differences observed in terms of head movements among the experimental conditions were expectable as they rely on the same visualization.

### 6.6.3 NasaTLX

**Lookup task:** We found no difference in terms of mental demand between the five techniques. We found that MidAir+MidAir induced more physical demand than any other technique (p=0.04 for MidAir+Joystick and p<0.01 for the other techniques) (F(4, 70)=10.61, p<0.01, η²=0.38). MidAir+MidAir also induces higher temporal demand than MidAir+Joystick (p<0.01) (F(4,70)=2.79, p=0.03, η²=0.14). Users rated their performance worse (higher score in the corresponding NasaTLX scale) for MidAir+MidAir than for Joystick+MidAir (p<0.01) (F(4,70)=3.78, p<0.01, η²=0.18). Regarding effort, we found that MidAir+MidAir requires more effort than Dual-Speed (p<0.01), Joystick+MidAir (p<0.01) and Slider (p<0.01) (F(4,70)=7.38, p<0.01, η²=0.3). Finally, MidAir+MidAir induces more frustration than Dual-Speed (p=0.01) and Joystick+MidAir (p<0.01) (F(4,70)=3.96, p<0.01, η²=0.18). These results are illustrated in Figure 12 - Top.

<figure><img src="image_13.png" /><figcaption>Figure 12. NASA TLX scores for the Loopkup (Top) and the Explore (Bottom) tasks (CI 95%).</figcaption></figure>

**Explore task:** We found no difference in terms of mental demand or temporal demand. However, we found that MidAir+MidAir induces more physical demand than Dual-Speed (p<0.01), Joystick+MidAir (p<0.01) and Slider (p=0.01) (F(4, 70)=5.93, p<0.01, η²=0.25). We also found that Joystick+MidAir performs worse than
MidAir+MidAir ($p<0.01$) ($F(4, 70)=3.15$, $p=0.02$, $\eta^2=0.15$). MidAir+MidAir induces more effort and frustration than Dual-Speed ($p<0.01$) and Joystick+MidAir ($p<0.01$) ($F(4, 70)=6.37$, $p<0.01$, $\eta^2=0.27$ for effort and $F(4, 70)=4$, $p<0.01$, $\eta^2=0.19$ for frustration). These results are illustrated in Figure 12 - Bottom.

Overall, we found no difference in terms of mental demand between the five techniques in the two tasks. We found that MidAir+MidAir induces higher physical demand than three (or four) other techniques in the Lookup (resp. Explore) task. As this technique uses physical gestures both for zooming and panning, this result is not surprising. It is also confirmed by participants' feedback: *"Always moving the arm to navigate the timeline is tiring."* P11. We did not find consistent differences in terms of temporal demand between the techniques in both tasks. However, interestingly Joystick+MidAir is perceived to be more performant than MidAir+MidAir in both tasks. Finally, overall, scores of NasaTLX express a negative feeling of the participants with respect to the MidAir+MidAir technique for the Lookup and Explore Task. This is probably due to the physical movement required for this technique and reinforces the fact that associating two different modalities to the two sub-tasks of an adaptive speed navigation is more appropriate.

### 6.6.4 Ranking of techniques

**Lookup task:** Most users preferred the Joystick+MidAir technique, although it partly relies on a physical gesture which could be tiring, while the least preferred one is unanimously MidAir+MidAir. Dual-Speed is the second preferred technique while the others were closely rated. These results are illustrated in Figure 13 - Top.

<figure><img src="image_14.png" /><figcaption>Figure 13. Ranking of the navigation techniques for the Lookup (Top) and Explore (Bottom) tasks (in number of participants).</figcaption></figure>

**Explore task:** It appears that the most preferred technique is also Joystick+MidAir, while the least preferred one is still MidAir+MidAir. Dual-Speed is the second preferred technique while the others were closely rated. These results are illustrated in Figure 13 - Bottom.

Overall, we found that Joystick+MidAir is always the preferred technique in both tasks and that MidAir+MidAir is almost always ranked last in both tasks. Dual-Speed is placed in second place in both tasks, which is interesting: users prefer controlling the zoom with a joystick or reducing the freedom in the available panning speed than using a mid-air gesture.
6.6.5 Summary study 2

In this experiment, we found that using Joystick+MidAir requires less time than three other techniques for the Lookup task and than any other technique for the Explore task. It is also the preferred technique in terms of ranking. As a result, Joystick+MidAir is the best interaction technique to navigate in a timeline using adaptive speed. To further assess the interest of the Joystick+MidAir technique we performed a follow-up study to compare it with a technique that does not involve any mid-air gesture: the Joystick+Joystick interaction technique.

# 7 FOLLOW-UP STUDY: MIDAIR VS JOYSTICK-BASED PANNING

In this experiment, we compare the best midair-based technique from our previous study, i.e. Joystick+MidAir technique, to the Joystick+Joystick technique.

## 7.1 Dataset, tasks, apparatus and implementation

This study used the same dataset, tasks, apparatus and implementation as our previous study.

## 7.2 Participants

We recruited 12 participants for the experiment at the local university, all with a background in computing science (25.4 years old, SD = 4.08), six self-identified as men and six self-identified as women.

## 7.3 Experimental design and collected data

The experiment followed a within-subject design for each of the two tasks. For the **Lookup** task, the experiment followed a 2x2x2 design, with **Interaction Technique** (Joystick+MidAir, Joystick+Joystick), **Distance** (44, 88) and **Direction** (left, right) as factors. For the **Explore** task, the experiment followed a 2x2x2 design with **Interaction Technique** (Joystick+MidAir, Joystick+Joystick), **Pattern type** (horizontal, vertical) and **Number of patterns** (1, 5) as factors. The study was divided into two blocks, each corresponding to one navigation technique. The order of blocks was counterbalanced across participants using a 2x2 Latin square. For each block, participants always started with the **Lookup** task, followed by the **Explore** task. For the **Lookup** task, participants had to perform 4 training trials followed by 12 trials (3 repetitions x 2 distances x 2 directions). For the **Explore** task, participants had to perform 4 training trials followed by 8 trials (2 repetitions x 2 pattern types x 2 number of patterns). We collected 12 participants x 2 interaction techniques x (3 x 2 x 2 + 2 x 2 x 2) = 480 trials in total for the experiment and 12 x 2 x (4 + 4) = 192 trials for the training. The experiment lasted on average 36 minutes.

## 7.4 Results

For both tasks, we did not find any effect of the order of the interaction technique. We did not find any learning effect between the repetitions for each task or each navigation technique. Overall, we found no difference in terms of completion time, head movements or NASA TLX scores between the users who already performed the previous experiment and the other users.

### 7.4.1 Completion time

**Lookup & Explore tasks:** We did not find any effect of the direction, distance, pattern type, number of patterns or the interaction technique on completion time for the Lookup or the Explore tasks. Performing the Lookup task takes 6.19s (CI[5.90, 6.57]) using Joystick+MidAir and 6.43s (CI[6.06, 6.87]) using Joystick+Joystick. Performing
the Explore task requires 18.76s (CI[17.12, 20.63]) using Joystick+MidAir and 18.98s (CI[17.15, 21.18]) using Joystick+Joystick.

### 7.4.2 Head movements

**Lookup & Explore tasks:** We did not find any effect of the direction, distance, pattern type, number of patterns or the interaction technique on the completion time for the Lookup or the Explore tasks. Performing the Lookup task requires head movements of 21.23° (CI[19.83, 22.77]) using Joystick+MidAir and of 21.80° (CI[20.66, 23.15]) using Joystick+Joystick. Performing the Explore task requires head movements of 22.01° (CI[19.94, 24.59]) using Joystick+MidAir and of 23.52° (CI[21.58, 26.13]) using Joystick+Joystick.

### 7.4.3 Nasa TLX

**Lookup & Explore tasks:** For both tasks, the NASA TLX questionnaire only revealed a difference in the physical demand between the two techniques $F(1, 22)=11.26, p<0.01, \eta^2=0.34$ for Lookup and $F(1, 22)=8.70, p<0.01, \eta^2=0.28$ for Explore. For both tasks, Joystick+MidAir induces more fatigue than Joystick+Joystick (p<0.01), see Figure 14.

<figure><img src="image_15.png" /><figcaption>Figure 14. NASA TLX scores for the Loopkup (Top) and the Explore (Bottom) tasks (CI 95%).</figcaption></figure>

### 7.4.4 Ranking

**Lookup task:** Users ranked Joystick+MidAir nine times in first position and three times in second position, making Joystick+MidAir their favourite navigation technique, see Figure 15 - Top.

**Explore task:** Users ranked six times Joystick+MidAir in first position and six times in second position. Thus, there is no clear preference between the two, see Figure 15 - Bottom.
<figure><img src="image_16.png" /><figcaption>Figure 15. Ranking of the navigation techniques for the Lookup (Top) and Explore (Bottom) tasks (in number of participants).</figcaption></figure>

## 7.5 Conclusion

Overall, we found no difference in completion time or head movements between the technique combining a joystick with mid-air gestures, and the technique using a joystick only, partially confirming our hypothesis 3). Informal feedback confirmed our hypothesis 1) by stating that using the mid-air gesture for both navigation sub-tasks induces involuntary gestures and is thus not a pertinent interaction technique for navigation in a 3D timeline. Although the NasaTLX scores revealed a significant difference in terms of physical demand, which is higher for Joystick+MidAir than Joystick+Joystick, our results indicate that the users preferred Joystick+MidAir for the Lookup task while no clear consensus is established for the Explore task. For the Lookup task, the precision required is higher than for the other task, as only one target must be selected while any of the three elements composing the pattern can be selected in the Explore task. Furthermore, users felt that using a mid-air gesture was more precise than using the Joystick, thus explaining the preference expressed towards Joystick+MidAir for the Lookup task only. This is confirmed by participants' comments: "I feel like it is more precise to select a pattern than it is to select a single target. When I want to select a pattern, I only have to gaze at one of the three elements, which is easier because I don't have to place it specifically in front of me" P2.

While these results show that both techniques are equivalent in terms of performance, their panning sub-task manipulation differs greatly: one is performed using a mid-air gesture, in position control, while the other requires a joystick movement, using rate control. Previous work showed that both approaches (position or rate control) do not perform similarly in large datasets as rate control performances diminish with very large datasets. We thus decided to conduct a third experiment with larger datasets than the one we used so far to evaluate the impact on the dataset size on these two interaction techniques.

# 8 STUDY 3: IMPACT OF THE DATASET SIZE

The goal of this third study is to assess the impact of the dataset size on the performance of Joystick+MidAir and Joystick+Joystick techniques, the two equivalent and best-performing techniques in our previous studies.

## 8.1 Dataset, tasks, and apparatus

We explored three dataset sizes: 200 elements (as in our previous studies), 5000 elements and 10000 elements. Large datasets (up to 10000 elements) are often found in previous work dealing with timeline visualizations [17, 48]. As an example, previous work collected and analyzed accelerometer's data placed on sheep [48] or cows [17]. These data represent timelines of 7200 elements (fourty measures per second during three hours) and up to
144000 elements (fifty measures per second during two days). Regarding the tasks, we only considered the Lookup task in this experiment. Indeed, locating a single pattern on large datasets containing thousands of elements would be a particularly tedious task. To adjust the experimental protocol to the size of the dataset, we increased the value of the distance factor for the Lookup task and compared four distances: tiny (11% of the dataset size), short (22%), medium (33%) and large (44%). We used the same Apparatus (Oculus Meta Quest Pro) and the same implementation (Unity using C#) as in previous studies.

## 8.2 Participants

We recruited 12 participants for the experiment at the local university, all with a background in computing science (21.9 years old, SD = 2.33), eight self-identified as men and four self-identified as women. Three of the participants also performed one of the previous experiments. We complied to the same sanitary protocols and local ethical requirements as in our previous studies.

## 8.3 Experimental design

The experiment followed a 2x3 within-subjects design with **Interaction technique** (Joystick+MidAir and Joystick+Joystick) and **Dataset size** (200, 5000, 10000) as factors. The study was divided into two blocks, each corresponding to one navigation technique. The order of blocks was counterbalanced across participants using a 2x2 Latin square. For each block, participants always started with a **Dataset size** of 200, then 5000 and finally 10000. Participants had to perform 8 training trials followed by 24 trials (3 repetitions x 4 distances x 2 directions) for each dataset size. We collected 12 participants x 2 interaction techniques x 3 dataset sizes x 3 repetitions x 4 distances x 2 directions = 1728 trials for the experiment and 12 x 2 x 3 x 8 = 576 for the training.

The experiment lasted, on average, 57 minutes.

## 8.4 Collected data and data analysis

We measured the trial completion time and the head movements for each trial. After each combination of technique and dataset size, users had to fill out an unweighted Nasa TLX [43]. They were also invited to provide informal feedback about the navigation technique. At the end of the experiment, users had to rank the two techniques in terms of preference. We used the same statistical analysis method in this experiment as in our previous studies.

## 8.5 Results

We did not find any effect of the order of the techniques or learning effect.

### 8.5.1 Completion time

Using ANOVA, we found an interaction between the completion time and the dataset size $F(1, 2272) = 26.32, p<0.01$. The effect size, eta squared ($\eta^2$), was 0.01. A post-hoc test established that Joystick+Gesture (10.55s, CI[10.16, 11.36]) requires less time than Joystick+Joystick (12.0s, CI[11.55, 12.51]) when the dataset size is 10000 (p<0.01). We found no difference between the two techniques for the 200 or 5000 dataset sizes, as illustrated in Figure 16 - Left. This result is explained by the impact of the rate-based control of the joystick: previous work already showed that rate-based interaction is less resilient to large datasets than position control [9] as the user has to wait a longer time before approaching the target location. Indeed, with Joystick+Joystick, one joystick
controls the zoom level while the other controls the panning in the timeline in a rate-control mode. Meanwhile, with Joystick+Gesture, the user's gesture controls the position in the timeline in a position-control mode. Hence, when panning with a joystick in rate-control mode, the user has to wait that the target destination is reached before releasing the joystick (e.g. performing the 88 element distance with a panning speed of 10 elements per second would require between 8 and 9 seconds). Adopting a higher rate-control would reduce this time, but would make it impossible to accurately stop on the desired item. This is confirmed by participant's feedback: "I had to stay like three or four seconds just waiting for the target to appear, it felt so long." P1. We also found the expected effect of the distance on the completion time $F(1, 2272) = 48.03, \eta^2=0.06$.

We found no effect of the target direction on the completion time or any interaction between the interaction technique and the direction.

<figure><img src="image_17.png" /><figcaption>Figure 16. Completion time (in seconds) for the Lookup task (Left); Head movements (in degrees) for the Lookup task (Right) (CI 95%).</figcaption></figure>

### 8.5.2 Head movements

Using ANOVA, we found an effect of the interaction technique on the head movements $F(1, 2272) = 46.055, \eta^2=0.03$. A post-hoc test showed that using Joystick+MidAir (12.37°, CI[11.72, 13.08]) requires more ample head movements than using Joystick+Joystick (9.85°, CI[9.31, 10.38]), as illustrated in Figure 16 - Right. This result is due to the fact that users were waiting for the target to appear in front of them when using the Joystick+Joystick technique, whereas they were actively looking for the target at a distance when using the Joystick+MidAir technique. Participant's feedback confirms this explanation: "With this technique [Joystick+Joystick], I'm not doing anything. I press the joystick, wait for the correct number to appear, then I stop and I gaze to select the target." P4. We found no difference in terms of distance or dataset size and no interaction between the distance, the interaction technique and the dataset size.

### 8.5.3 NasaTLX

As in our previous study, we found that Joystick+MidAir induces a higher physical demand than Joystick+Joystick (p<0.01) ($F(1, 66)=7.11, p=0.01, \eta^2=0.10$). We also found that Joystick+MidAir requires more effort than Joystick+Joystick (p=0.02) ($F(1, 66)=5.83, p=0.02, \eta^2=0.08$). These results are explained by the fact that Joystick+MidAir requires mid-air manipulations of the VR controller, which induce more fatigue (and thus require
more effort) than using the joystick. However, we found no difference in Nasa TLX scores between the two techniques regarding mental demand, temporal demand, performance or frustration, as illustrated in Figure 17.

<figure><img src="image_18.png" /><figcaption>Figure 17. NASA TLX scores for the Loopkup task (CI 95%).</figcaption></figure>

### 8.5.4 Ranking

Users ranked Joystick+MidAir nine times in first place and three times in second place, as illustrated in Figure 18. They preferred Joystick+MidAir over Joystick+Joystick as they had more control over the movement to perform with a mid-air gesture than with the joystick, as confirmed by participant's feedback: "*When I move my hand, I feel more confident in the final position I will achieve. But with the joystick, I have to wait and when I want to stop, there is still a small movement because the joystick is not going instantly from max movement to zero.*" P11. These results are in line with the results of our follow-up study for the Explore task (section 7.4.4), proving that the dataset size does not impact the user preference for an interaction technique.

<figure><img src="image_19.png" /><figcaption>Figure 18. Ranking of the navigation techniques for the Lookup task (in number of participants).</figcaption></figure>

### 8.5.5 Summary study 3

Overall, we found that the Joystick+MidAir technique allows for faster navigation in a 3D timeline than the Joystick+Joystick technique when the timeline contains a very large dataset (10000 elements). This results confirms our hypothesis 2) and thus also confirms our hypothesis 3): using rate-based interaction for navigating long distances requires more time than using position-based interaction, thus making Joystick+MidAir the preferred and fastest techniques of the four techniques of our design space. This result is particularly interesting as it confirms that using position control on large datasets performs better than using rate-based control. Finally, while it induces more physical demand and requires more effort, users still prefer Joystick+MidAir over Joystick+Joystick: this shows that users value the perceived precision of the mid-air gesture over the physical discomfort associated with moving the arm in mid-air.

## 9 DISCUSSION

In this section, we first summarize the core results of our studies. We then present perspectives on how they could be extended in future work.
## 9.1 Summary of our results

Our work contributes with novel knowledge on input and output modalities for browsing 3D timelines in VR. We first established that using a concave shape to display a 3D timeline is more efficient (time, head movements) and preferred than using previously explored visualizations, such as Snapshot or Helicoid, the best identified convex shape. We attribute these findings to the enhanced visualization of distant elements facilitated by the concave shape: users benefit from an overview of distant elements and a focus area distinctly presenting elements in proximity to the current timestamp. This allows users to easily visualize a distant pattern or area of interest, navigate through the timeline to bring it to the focus area, and then select it with precision as the focus area is larger and closer to the user than the other sections of the timeline. Our work is the first investigation comparing such concave and convex visualizations for timelines in VR environments.

Secondly, our work established that using a VR controller combined with adaptive speed is an efficient solution to facilitate the search of an element (Lookup task) or a pattern of elements (Explore task). Indeed, adaptive speed allows the user to adjust the precision of the panning during the interaction: the user can define a panning speed that facilitates rapid navigation across extensive distances, before adjusting the panning speed for slower and more meticulous scrolling as necessary, and vice versa. Our work hence expands previous investigations of adaptive speed on desktop environments and demonstrates that they apply to VR environments and controllers.

We also showed that an adaptive speed performs better than a dual-speed solution, commonly used in previous works for pointing in large environments [37, 42]. This result shows that users prefer using a zoom adapted to their needs during the Lookup or Explore task instead of relying on predefined panning speeds. It additionally emphasizes that users are not hindered by the definition of the panning speed: we found no difference in mental demand between Dual-Speed and the adaptive speed techniques.

Furthermore, we showed that using Joystick+MidAir performs better than Joystick+Joystick for large datasets (10000 elements) in VR. This result is particularly interesting as it informs future designers on which modality to use for timeline navigation depending on the size of their dataset. We anticipate that the results concerning this first step in scalability could be questioned for even larger datasets in terms of efficiency and usability both from a rendering and an interaction point of view. From a rendering perspective, our solution does not display all elements simultaneously but only a subset at a time, meaning that performance would not be directly impacted by the total dataset size. From the input interaction perspective, our current implementation already incorporates adaptive visualizations, such as dynamically adjusting numeric scales above the elements depending on the zoom level: this ensures that an overview is provided regardless of dataset size. Nonetheless, it would likely be necessary to further adapt the zoom levels to allow efficient exploration of extremely vast datasets, especially the minimum and maximum values defining the possible zoom range. Therefore, future work should explore how our interaction techniques perform under such conditions to confirm our hypothesis.

Finally, we showed that, for the Lookup task, users preferred using the Joystick+MidAir technique over any other technique. This can be due to the direct manipulation offered by the mid-air gesture (i.e. the user is moving his arm on the timeline) over the indirect manipulation provided by the joystick manipulation.

## 9.2 Concrete application in the MorphoNet platform

MorphoNet is an interactive viewer dedicated to temporal series of 3D data [30]. Among the multiple datasets already available in the platform [35], we focused on a dataset representing the embryonic development of
Phallusia mammillata. This collection of 3D objects enables scientists to browse the different steps of the cell development in order to identify structural patterns, such as detecting cell divisions.

In such scenarios, the concave timeline visualization facilitates the exploration of long-term cell dynamics by simultaneously providing an overview of distant temporal events while maintaining a focus area for fine-grained inspection of critical time points. Moreover, the fast navigation techniques we propose, combining panning and adaptive zoom, allow researchers to efficiently shift between different temporal scales—quickly moving across hundreds or thousands of steps while retaining the ability to slow down and inspect subtle variations at a precise moment. Together, these features could substantially improve the efficiency and comfort of analyzing large temporal biomedical datasets.

<figure><img src="image_20.png" /><figcaption>Figure 19. Illustration of the concave timeline usage on a Phallusia mammillata's embryonic development dataset. A cell division is represented in yellow (Left).</figcaption></figure>

## 9.3 Limitations and Future work

In this section, we describe the limitations of our studies and how they could be addressed through future works. In our experiment, we designed one concave visualization inspired by the PerspectiveWall [32]. While we describe its design and factors, we did not explore all of the parameters of this visualization, which could impact the understanding and navigation capabilities of this timeline shape. First, we empirically decided to show five elements only in the focus area of the concave shape; it would be interesting to explore how many elements can be displayed in this area without losing the benefits of the concave shape. Furthermore, using a different angle for the context areas on the left and right of the focus area would allow to visualize and select distant elements more easily, or require less display space. Using a non-linear curve for the context area would also be particularly interesting as it would allow determining if the curvature has an impact on the distant selection process of the context elements. In addition, it could be relevant to verify if our results remain valid on different type of 3D elements, including more complex elements (e.g. higher definition, one element composed by multiple smaller elements, etc.). We believe that only the element recognition step would be impacted by such modification, which would have the same impact on all timeline shapes. Finally, another interesting perspective regarding the timeline shape would be to explore the interest of a multi-focus concave shape similar to Melange [20]. Allowing the user to define multiple focus views and configure their length and depth could be useful for easier navigation or for comparing multiple distant sections of the timeline [44].

Beyond the visualization aspect of our contribution, regarding the VR controller interaction, we could have explored other DoFs, such as the rotations of the VR controller, or the use of its multiple triggers. This could
further enlarge the interaction vocabulary, however at the cost of a higher memorization effort or discoverability issues that need to be explored. Alternatively, considering bimanual interaction techniques based on two VR controllers would also enrich the possibilities. A long-term study will be required to explore this opportunity.

The VR interaction can be limited by the well documented arm fatigue resulting from the mid-air gestures, in particular under the term "gorilla arm effect" [23, 50]. Prolonged use of such gestures can cause muscular discomfort and decrease performances. In our case, this issue is mitigated because our two best-performing solutions are either partially based on joystick input (Joystick+MidAir) or entirely joystick-based (Joystick+Joystick), thus avoiding continuous arm elevation. Moreover, our techniques already incorporate clutching, which has been shown to alleviate physical fatigue by allowing users to disengage and reset their arm posture [47]. In scenarios of prolonged use, we can envision additional strategies to further limit fatigue: for example, providing a hybrid version for panning so that the joystick can control ample panning actions, while mid-air gestures will be used for final adjustments only. In such hybrid panning conditions, avoiding unintentional combined inputs could rely on a quasimode or a dead zone on the joystick, clearly separating pan or zoom gestures on the joystick.

In addition, the design of our interaction techniques was studied exclusively on the concave timeline shape. Although the users were less efficient when using other timeline shapes with a slider input controller, it could be worth evaluating whether the performance and usability benefits of our techniques would hold with alternative shapes. These additional studies would further inform on the possible generalization of our results, i.e. state whether the advantages we observed are specific to the concave representation or also apply to convex or linear timelines, or even more complex shape such as multi-focus solutions mentioned above.

Finally, from an experimental point of view, we only had 12 (respectively 15 for our second experiment) participants from our local university, of similar age. It would be interesting to verify the consistency of our results with a larger and more diverse population. In addition, we plan to explore the long-term use of our visualization and techniques in a realistic use (for example, to visualize and explore medical data [29] or complex multi-scale data [30, 35]). Finally, while our work focuses on timeline in VR, we believe it could be extended to other usage contexts, such as navigating in VR environments, multiple VR tabs or GUI panels (e.g. the Windows+Tab command) or in VR documents by replacing the standard slider interaction common in those contexts.

## 10 CONCLUSION

In this paper, we focused on extending previous knowledge on 3D timeline navigation in VR. We focused on two tasks (finding a given 3D object and locating a temporal pattern) and investigated two key aspects: the timeline shape and the navigation technique. In a first study, we compared a concave timeline shape, inspired by the well-known perspective wall, to prior convex and linear timeline shapes. We showed that using a concave shape allows for faster navigation and is also preferred by users. Then, we designed four navigation techniques, based on adaptive speed, to optimize navigation on a VR timeline. In a second study, we compared their performance to two baselines: one state-of-the-art technique consisting of a slider widget and a dual-speed technique. Our results showed that techniques using adaptive speed allow for faster selection and pattern detection, and are preferred over the baseline interactions. Finally, we assessed the performance of the best technique, an adaptive speed technique combining joystick and mid-air gesture, when the timeline scales up to 10 000 elements. Our results showed that using a combination of a joystick, for zooming, and mid-air gesture, for panning, is more efficient
than using the joystick only to control both sub-tasks (zooming and panning) when the dataset contains large number of elements (10000).

## ACKNOWLEDGMENTS

This work was conducted as part of the INTERPLAY, MAchine LEarning in 3D - READYNOV and JCJC PERFIN projects. INTERPLAY (ANR-21-CE33-0022) and JCJC PERFIN (ANR-18-CE33-0009) were supported by the French National Research Agency (ANR). The READYNOV project (N°22000056) was supported by the Occitanie Region. This project also received support from the company Zebrys, publisher of the R++ software. The authors would like to thank Emmanuel Faure (LIRMM) for the insightful discussions that helped identify the needs related to the visualization of large-scale data, particularly in the context of the Morphonet project.

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