# Haptixel: Encoding Data through Cutaneous Force-based Encountered-Type Fingertip Haptics

Elodie Bouzbib, Louis Badr, Claudio Pacchierotti, Anatole Lécuyer, Arnaud Prouzeau

## ► To cite this version:

Elodie Bouzbib, Louis Badr, Claudio Pacchierotti, Anatole Lécuyer, Arnaud Prouzeau. Haptixel: Encoding Data through Cutaneous Force-based Encountered-Type Fingertip Haptics. CHI 2026 - ACM Conference on Human Factors in Computing Systems, Apr 2026, Barcelona, Spain. 10.1145/3772318.3791027. hal-05533544

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# Haptixel: Encoding Data through Cutaneous Force-based Encountered-Type Fingertip Haptics

Elodie Bouzbib

UpnaLab

Universidad Pública de Navarra

Pamplona, Spain

elodie.bouzbib@unavarra.es

Louis Badr

Institute for Future Technologies

De Vinci Higher Education, Research

Center

Courbevoie, France

louis.badr@devinci.fr

Claudio Pacchierotti

IRISA

CNRS

Rennes, France

claudio.pacchierotti@irisa.fr

Anatole Lécuyer

Inria

Rennes, France

anatole.lecuyer@inria.fr

Arnaud Prouzeau

Université Paris-Saclay, Inria, CNRS

Paris, France

arnaud.prouzeau@inria.fr

## Abstract

Data visualization benefits from non-visual cues to enable people to understand information by engaging with it through multimodality, yet most approaches rely on cumbersome technologies or large scale artifacts, making them difficult to adapt to dynamic or complex datasets. In this paper, we explore the use of cutaneous haptics as a lightweight quantitative channel for visualization tasks, allowing users to feel data and interact with it dynamically. We present Haptixel, an open-source DIY encountered-type wearable providing force-feedback on the users' fingertips' pulp. We propose an interaction framework illustrating how Haptixel can be used to complement visualization tasks through combinations of force levels and contact types. We evaluate our approach in a pixel-art-like VR user study (n=16) where pixels color/height are associated to forces as a univariate value mapping. Results show that participants can retrieve information with Haptixel, and significantly discriminate 3D-data with at least four levels of forces; suggesting that cutaneous force-feedback can function for quantitative distinctions in visualization tasks.

## CCS Concepts

* Human-centered computing → Visualization systems and tools; Haptic devices; Empirical studies in HCI.

## Keywords

Wearable haptics, Cutaneous feedback, Data visualization, Data encoding, Virtual reality, Haptics, Encountered-type haptics

## ACM Reference Format:

Elodie Bouzbib, Louis Badr, Claudio Pacchierotti, Anatole Lécuyer, and Arnaud Prouzeau. 2026. Haptixel: Encoding Data through Cutaneous Force-based Encountered-Type Fingertip Haptics. In *Proceedings of the 2026 CHI Conference on Human Factors in Computing Systems (CHI '26)*, April 13-17, 2026, Barcelona, Spain. ACM, New York, NY, USA, 15 pages. https://doi.org/10.1145/3772318.3791027

<figure><img src="image_2.png" /></figure>

This work is licensed under a Creative Commons Attribution 4.0 International License. CHI '26, Barcelona, Spain

© 2026 Copyright held by the owner/author(s). ACM ISBN 979-8-4007-2278-3/26/04 https://doi.org/10.1145/3772318.3791027

<figure><img src="image_3.png" /><figcaption>**Figure 1:** (Left) Haptixel consists in a lightweight DIY wearable unit, (A) leaving the fingertip free and (B) encountering the users fingertip pulp to provide low, or (C) high levels of forces (and vibrations); with proximity and force sensing. Its concept relies on cutaneous force discrimination and allows to perform quantitative distinctions, treating force as univariate value mapping. Its capabilities allow (Right) to physically encode data values to complement visual encoding, or to convey additional dimensions to substitute it.</figcaption></figure>

## 1 Introduction

The use of non-visual modalities has been shown to effectively complement visual encoding. Work on multimodal and haptic interaction demonstrates that additional perceptual channels, such as sound or tactile cues, can support low-level analytical tasks by distributing perceptual load or enabling peripheral awareness [6, 69]. In parallel, data physicalization, with its tangible representations of data, has highlighted how physical properties can enrich the interpretation of quantitative information [6, 38]. Inspired by these directions, we explore in this paper the use of fingertip cutaneous force-feedback [55], a modality that remains under-examined in visualization. Largely explored in the haptics community through wearable haptic devices [57], cutaneous feedback through contact and skin deformation on the fingertip enables fine-grained discrimination [55, 77]; suggesting that a potential force-based cue supporting quantitative distinctions could allow for discrimination or comparison tasks in visualization contexts.

To investigate this potential, we designed Haptixel, a lightweight, DIY, and open-source fingertip-wearable interface that provides
cutaneous force feedback [61] by initiating contact with the finger pad (see Figure 1 - Left, A), encountering it (see Figure 1 - Left, B) and deforming it (see Figure 1 - Left, C). Haptixel was developed as an accessible platform to study how fingertip haptics can be used to encode a value in space to a specific force level, thus allowing the user to feel a different force depending on a data point value (see Figure 1 - Right). The device is self-contained and integrates compact force actuation and sensing while remaining unobtrusive enough to be used alongside VR/AR hand-tracking systems and simply sliding on the fingertip. As the finger pad deformation is shown to alter the perception of softness [74] or compliance [51] under constraints, we first proposed to explore the effect of Haptixel's finger pad support material (rigid, flexible) on the users' force perception. We evaluated how it influences discriminability, yielding a Just-Noticeable Difference (JND) of approximately 0.6 N.

We then empirically assessed whether Haptixel can support the perception of data values in the absence of visual encoding. Participants interacted with a blank pixel grid, conceptually similar to a coarse heatmap or heightmap, in which each cell conveyed a different data value through force feedback, effectively treating force as a univariate value mapping. Their task was to reconstruct the underlying pattern using only the force cues. Participants successfully reproduced these patterns, and results indicate that they could reliably distinguish at least four discrete value levels with Haptixel, suggesting that fingertip force can function as a quantitative channel for visualization tasks. This opens promising opportunities for integrating cutaneous feedback into future multimodal visualizations, where force cues may augment visual perception or provide a lightweight alternative when visual attention is limited.

Our main contributions are:

* A lightweight, open-source fingertip haptic device designed as an accessible platform for studying force-based scalar cues in visualization;

* An empirical quantification of cutaneous force-discrimination thresholds on the fingertip, including the effect of support material on users' JNDs;

* Empirical results demonstrating that discrete force levels can support simple quantitative distinctions, enabling users to reproduce coarse scalar patterns without visual feedback.

# 2 Related Work

In this section, we first describe how data visualization often relies on other cues then vision, for instance through tangible interaction with physical interfaces. Then, we show how haptics can be leveraged to enrich data visualization, and suggest how wearable cutaneous force-feedback can be used as an alternative to traditional vibrotactile devices. Finally, as an inspiration, we describe the different actuation types and perceived stimuli that have been used in wearable haptic devices in more general contexts than data visualization.

## 2.1 Data Visualization through Non-Visual Cues

Data visualization has been widely explored through non-visual cues; for instance through tangible interaction with physical artefact, referred to as *data physicalization*. Jansen et al. define it as "physical artefact whose geometry encode data" [38] (see Bae et al.

[6] for a review); and includes both static physical representations (e.g., 3D printed data [32]) or dynamic actuated ones (e.g., 2.5D tabletops [2, 26, 71], strings [23], fluids [36]). Beyond geometry, physical artefact can encode more dimensions through their inherent properties such as their roughness, as proposed by Du et al. [22], their colors or their movements [34]. In these approaches, the artefact is the representation: users extract information by physically exploring an object whose shape embodies the data, thus needing the physical presence of the external physical artefact. In contrast, multimodal visualization engages additional perceptual channels, such as touch, sound, or speech, to convey information, shifting from touching a shaped representation to receiving haptic or auditory cues about a representation.

Accordingly, prior work has explored touch and speech [44], auditory [81, 86] and/or haptic cues [58]. This latter, sometimes referred to as *haptization* [35], or *visuo-haptic visualization* [24], complements visual cues or provides additional non-visual dimensions, for instance through force, stiffness or friction [5]. Studies show that pairing haptics with visualizations can improve task performance and user preference, for example in localization tasks [49]. The use of kinesthetic haptic devices, such as the PHANTOM interface [48], a pantograph or more accessible and replicable open-source hardware, such as the HapKit [1], demonstrate that such feedback can complement or substitute vision for exploring data.

However, these haptic systems typically require external, grounded devices. The integration of active, on-body haptics that encode data through cutaneous skin-deformation, thus providing haptic cues without relying on a physical artefact, remains comparatively under-explored. In this work, we investigate how fingertip skin-deformation cues can serve as a lightweight, body-worn mechanism for representing quantitative data.

## 2.2 Data Visualization through Cutaneous Feedback

Cutaneous haptic stimuli can be embedded with the users, for instance using controllers - common in immersive environments; or onto them, using wearable technologies. In immersive analytics, Prouzeau et al. demonstrated with *Scaptics* [62] that vibrotactile feedback through a controller can provide efficiency and accuracy when exploring 3D scatter plots representations. Similarly, Bastidas et al. [8] embedded vibration motors onto their participants' fingers to provide a haptics pixelization of low-resolution images; and reported as qualitative feedback that participants could perceive "heights or quantities", and agreed that "vibration could encode a novel dimension" to visualized data. This exploration effectiveness was also demonstrated with electrotactile feedback (e.g., an electric stimulation under the skin), whether for perceiving scatterplots [29], in comparison tasks [4] or as a sensory substitution for accessibility purposes [39].

However, when interacting in the real world, most of our haptic rendering consists in contact perception (e.g. touching a table), and pressure applied onto the finger pad, perceived through glabrous skin deformation (e.g. writing on a keyboard, grabbing an object, pushing on a button). On the contrary, vibrations are not inherent from our daily interactions, and can tend to dissipate throughout the skin, providing a tactile satiety or a shift of sensitivity over
time [47, 80]. While many wearable haptics rely on electrotactile and vibrational feedback to provide information [79], we believe that a cutaneous force-feedback through skin deformation could provide a more realistic interaction with the environment [31] and hence offer a more straight-forward stimulus interpretation, with relatable haptic feedback [65]. Moreover, as demonstrated by Shorr et al, such cutaneous force-feedback through skin deformation can be used for stiffness [64] or weight [63] discrimination, making it a potentially good candidate to interpret scalar cues in visualization.

## 2.3 Wearable Haptic Devices

Although only a few studies have explored cutaneous haptics for data visualization, wearable haptic devices have been extensively investigated in broader interaction contexts. Wearable haptic devices are defined by Pacchierotti et al. as haptic "interfaces capable of communicating with the human wearers during their interaction with the environment they share" [57]. There exists an infinity of wearable haptic devices and designs, stimulating either kinesthetic cues (muscles spindles, tendons) [25], cutaneous and tactile cues (skin stimuli, e.g., stretch, deformation etc.) [56]; or both [17]. Each device is designed with respect to the body part it will stimulate (e.g., head [40], back [30], hands [59] etc.) and its context-of-use; whether for accessibility [21, 67], rehabilitation [82], teleoperation [77] and human-robot interaction [53], VR/AR exploration of objects [46, 70] or navigation guidance [12].

Specific to the hand, wearable haptic devices can come as exoskeletons or rigid wearable devices, constraining the fingers into a given position and providing kinesthetic feedback, or finger devices, usually cutaneous and stimulating the skin by vibrating, stretching or deforming it [57]. Kinesthetic devices generally provide physically stronger force interactions, for instance Ma et al. demonstrated they can provide up to 7 N forces with five distinguishable levels of stiffness perception [45]. They however tend to be bulkier and more cumbersome to wear; while cutaneous devices offer lighter, more seamless contact and pressure cues, with potentially similar perceptual performances. Contact and pressure can be provided through the lateral stretching of the finger skin [56], or directly be applied to the finger pad with external actuators, such as magnets [19], or internal actuators, such as lever mechanisms [28, 41]. Such cutaneous force-feedback was demonstrated to perform as well as kinesthetic feedback to discriminate surface stiffness [65] or even to outperform visual feedback [61].

In this paper, we investigate to what extent cutaneous force-feedback can be discriminated, to explore and leverage its benefits for complementing the visual channel for data explorations.

# 3 Haptixel

To design Haptixel, we considered multiple criteria from Pacchierotti et al. [57]: weight, form factor, wearability; and focused on providing relatively strong feedback with low inertia, high haptic transparency, in a low cost and DIY open-source self-contained interface.

Its main difference from the literature does not rely on its actuation nor its mechanism, but rather on its form-factor, which (a) enables the users to wear it over the tip of their fingers, without further attachments (e.g., no strap or other rigid parts over the finger); and, (b) enables the use of classic tracking methods (Meta Quest,

Mediapipe) without occlusion; and its interaction framework (see Section 3.4). Also, Haptixel does not only initiate contact with the user's finger to provide vibration [41] or surface information [28], (c) it leverages skin deformation and pushes through the fingertip to provide cutaneous force-feedback.

## 3.1 Design Choices

As we aimed to leverage finger pad contact and deformation to encode data, we thus wanted Haptixel to benefit from the "encountered-type haptic device" concept [11, 50]: letting the users' fingertips unencumbered when no interaction is required, and encountering it when needed. This concept has been integrated with controllers [20, 42] or exoskeletons [14]; but can also be miniaturized in fingertip devices. This can be performed by either rolling around the user's finger to provide contact [75], by *auto-gripping* the user's fingertip when required using proximity sensing [7], or using levers and mechanical crank-rod designs [28, 41].

We used an iterative design process and evaluated different lever mechanisms (e.g., 3DoF platform with 3 servomotors [16], single servomotor with PLA printed crank-rod; DC motor entangling two strings [76]), and chose the mechanism that provided the highest force-feedback with the least simplicity, for replicability purposes. We also tested different shapes and designs, and aimed to have the final device as compact and light as possible, to avoid occlusion with hand tracking methods [56]. We did not consider other actuators (solenoids, Haptuator [72]) for size and price purposes, to keep Haptixel replicable and affordable.

<figure><img src="image_4.png" /><figcaption>**Figure 2: Schematic of Haptixel's mechanism: the device consists in a crank-rod mechanism integrated into a small lightweight wearable unit. Haptixel's actuation brings a lever to encounter the user's fingertip pulp. It contains a servomotor, a 3D printed crank-rod mechanism; attached in a self-contained device. It can be attached to the finger using a finger support, that slides in the self-contained device. Call-out shows Haptixel's end-effector: a proxy sensor, on top of a force sensor, on top of a vibration motor, that comes in contact with the user's finger (represented by an arrow).**</figcaption></figure>
## 3.2 Hardware

3.2.1 Form-Factor. Haptixel consists in a 3D printed crank-rod mechanism (see Figure 2), encountering the fingertip pulp. Haptixel's weighs 19.8 g and measures 40 × 40 × 45mm³. Haptixel's design is open-source and available on the following<fnref n="1" />. Its printed parts weigh 9g in total, and it can be printed in its entirety in 1h50 minutes with an Ender 3 Pro. As mentioned previously, occlusion with traditional tracking devices or interferences with dexterity is now at the center of wearable haptic interfaces design [7, 57], as it is primordial to know one's position or movements to provide personalized haptic rendering. In this respect, all the studies in this paper were done using the Meta Quest and its hand tracking capabilities, while participants were wearing Haptixel. This feature is important and demonstrates how Haptixel can just be slipped on one's finger pad to render force at the fingertip scale for a given participant. It is indeed primordial to know one's finger position and dynamic displacements to provide personalized haptic rendering.

3.2.2 Actuation. Haptixel is actuated through a Feetech FS90 servomotor, with a weight of 9 g and a torque of 1.5kg.cm⁻<fnref n="1" />. Globally, Haptixel has a 70° stroke, which can therefore interpenetrate the fingertip's pulp with a high force. Apart from its lever concept and for versatility purposes, Haptixel's end-effector also contains a mini vibration motor (see Figure 2 - Callout), which we choose not to use in this paper as our scope focuses on cutaneous force-feedback, but which can be driven through PWM using an Arduino board. The servomotor is controlled using a Pololu Micro Maestro board, enabling an easy access to its speed and acceleration (see Figure 3 - Physical world.

3.2.3 Sensing. On top of its vibration motor, we integrated a 189-5556 FSR force sensor (see Figure 2 - Callout) into Haptixel's end-effector - which we plugged as a voltage divider in series with a 10kΩ resistor and a 5V input; and a capacitive sensing sheet (see Figure 2 - Callout) - which we plugged as a voltage divider in series with a 1MΩ resistor and a 5V input. The two sensors are then plugged into an Arduino Uno (see Figure 3 - Physical world).

3.2.4 Hand attachment. Haptixel is dependent of the finger pad deformation as it aims to provide force feedback to the fingertip pulp [74, 75]. The more constrained is the finger pad, its skin stretch and deformation, the higher its stiffness and therefore, the higher is the perceived force - with the same device mechanism. We designed a fingertip support and 3D printed it with different materials. The aim was for Haptixel to be maintained over the users' fingertip without additional attachments (e.g., strips), while allowing various sizes of fingertips; especially as it can alter the perception using a same device [84]. When the support was 3D printed as a TPU-95A part (Thermoplastic polyurethane 95A, soft flexible printing), it therefore did allow for less constrained finger pad, with a maximum applied force around 3 N. When the support was 3D printed as a PLA part (Polylactic acid, rigid solid printing), it could provide up to 5 N force feedback as the finger pad skin deformation was highly constrained (as a reference, cutaneous wearable devices provide usually around 1.5 N force-feedback [60]). When printing

with more flexible materials, the device would tend to slip during hovering movements; and enable lower force levels. They were thus discarded in our iterative design process. We conducted a psychophysical experiment to evaluate the JND (Just-Noticeable Differences) of both PLA and TPU-95A supports (see Section 4) to quantify the material effect on force perception.

## 3.3 Software

We chose to servo Haptixel in force and to control it in speed, while instantiating the god-object principle [54]. All the implementation is realized on Unity3D engine; and the scripts and scenes to control Haptixel are open-source.

<figure><img src="image_5.png" /><figcaption>Figure 3: Diagram of Haptixel. Digital world: software and motor control scheme using virtual springs and god-object principle. Physical world: Haptixel's circuit diagram to (a) the Pololu Maestro board, providing target speed and reading current speed; (b) the Arduino Uno, reading contact (capacitive sensor) and force. Haptixel's lever is controlled in speed and servoed in force: when the target force is reached, then Haptixel's speed is null and its servo stops moving. finger pad: Haptixel provides a finger pad scale pixel as force. Stimulus Interpretation: the perceived force is then transmitted to the brain and interpreted by its user.</figcaption></figure>

3.3.1 Haptixel motor control. We created a virtual spring between Haptixel's end-effector and a virtual proxy, so Haptixel's speed is proportional to the difference in position between its lever actual position and the proxy position (see Equation 1). This proxy is itself attached to a target position with a spring damper mechanism (Equation 2), and the target position is found as proportional to the error in force (Equation 3) (see Figure 3 - Digital world):

$$ \vec{v}_{Haptixel} = -K_p \times \vec{HP} \qquad (1) $$

where $\vec{HP}$ is the position vector from Haptixel to the proxy; $k_p$ the coupling stiffness. $k_p$ is chosen empirically as to minimise the following error between Haptixel and the proxy.

$$ \vec{F}_{proxy} = K_f \times \vec{TP} - K_d \times \vec{v}_{proxy} \qquad (2) $$

<footnote n="1">¹Haptixel's Git repository. Design, 3D parts, scripts and control of Haptixel are all included; with both force-serving, motor scheme with control in speed, and inclusion of the vibration motor if required.</footnote>
where $\vec{TP}$ is the position vector from the proxy to the target position and $v_{proxy}$ is the proxy velocity.

$$T_{x,y} = T_{x,y} + K_m \times \epsilon(\text{Force}) \quad (3)$$

where with $\epsilon = (\text{Force}_{command} - \text{Force}_{current})$, $T_{x,y}$ is the unknown target position, and $K_m$ is a proportional gain.

### 3.3.2 Digital/Virtual coupling.
Haptixel is coupled to digital and/or virtual environments using Unity3D engine. It can be attached to any object to provide contact information (by encountering the fingertip pulp). Each digital/virtual unit can be perceived as a fingertip scale **pixel** - which Haptixel physically embodies through force-based haptics. Haptixel instantiates the god-object principle, where a virtual spring is attached between the users' real fingers and the virtual objects boundaries [54]. Therefore, the mechanical displacement of the lever within the users' fingertip pulp is proportional to the users' virtual fingers displacements within virtual objects in direct interaction. In indirect interaction, and to perceive a chosen pixel, users can hover on top of a given visualization (allowed as Haptixel does not cause occlusion with traditional tracking systems); and as a mouse on a screen, can select which data value to perceive (see Figure 1 - Right). To gain more granularity, users can scale their visualization up or down, to adjust its level of detail. Haptixel could also benefit from being coupled to visual illusions and pseudo-haptic effects such as [13, 18], to increase deformation or compliance perception.

### 3.3.3 Accuracy and Latency.
We conducted 20 cycles of Haptixel getting from 0 N to force levels of {1.0, 1.5, 2.0, 2.5}N - then being stable for at least a second, and going back to 0 N; and measured the global accuracy (in N) and latency. We measured an accuracy below 0.07 N (95-CI = 0.04 N) for all force levels; and a latency in average of 1.4 s (1.04 s for 1.0 N, 95-CI = 0.31 s; 1.50 s for 2.5 N, 95-CI = 0.50 s), going from "no force/contact" (as per Figure 1 - Left, A) to the target force. This latency decreases when starting from another value than "no force/contact", for instance to go from 1 N to 1.5 N.

## 3.4 Haptixel: Interaction Framework

Haptixel's interaction framework consists of three complementary components: how it supports visual contexts, the range of force levels it can render, and the types of contact it can produce (see Figure 4).

### 3.4.1 Visual Support.
Haptixel provides physical feedback that can be perceived even without visual support. It can be used without visuals to enable physical depth or with displays (2D, 3D, AR, VR) to add a tangible dimension to visual content. With immersive environments, it can be coupled with tracking systems to enable users to freely hover on top of their chosen visualizations. In 2D environments, it can be coupled to a mouse displacement, as per Bastidas et al. [8], to provide feedback on the values it hovers on. As Haptixel is designed at the fingertip-scale, the granularity of the pixel it encodes should be changed on the visual side, by adjusting levels of details.

### 3.4.2 Force Levels.
We designed Haptixel as an encountered-type haptic device, as an "on-demand" wearable interface [11, 50]; it has the ability to let the user fingertip's unencumbered from a

<figure><img src="image_6.png" /><figcaption>Figure 4: Haptixel's interaction framework, through 3 dimensions: Visual Support, Force Levels, Contact Type.</figcaption></figure>

continuous force-feedback; **without force nor physical contact**. This is illustrated in Figure 1 - Left, A; where Haptixel's lever is not touching the user's finger pad. When touching the fingertip, Haptixel can provide a simple **contact without force**: it senses the fingertip proximity and can adjust according to it to clutch itself [7] and provide the user with a light touch. Finally, Haptixel also provides **low to high forces**, either caressing, touching or pushing on the user's fingertip.

### 3.4.3 Contact Type.
Users' perception depends on the contact type Haptixel provides. As an encountered-type device, and for the "physical presence" perception, it relies on a **discrete contact type**, like a stroke (on/off). On the opposite, it can also provide **continuous contact**: either a constant force, or a varying one. A **constant force** provides an absolute or a stationary information, and can be used to perceive a set of spatial data. Continuous **varying force** rendering would be ascending or descending, indicating more relative information (e.g. stronger, weaker). It can be used to indicate varying levels or intensities in a comparison task, or, represent temporal data, such as trends.

## 3.5 Opportunities for Data Visualization

While vibrations are commonly used for notifications or coarse encodings [8, 75], combining force levels with different contact types offers a richer haptic channel that can encode additional data dimensions. Haptixel supports a variety of low-level data interactions, following Munzner's consume-search-query categories [52] and existing task taxonomies [3, 15, 37]. To do so, it provides force-based scalar cues that act as univariate value mappings.

Supporting visualization tasks goes through a combination of both technical and perceptual requirements. To illustrate it, Haptixel **technically** requires (1) accuracy and precision when providing feedback; (2) a wide range of forces to be mapped; (3) acceptable
latency between "No Force" and "Force" levels; and, (4) a low "Just-Noticeable Difference" (JND), multiplying the users' discriminative levels. While the three first features are quantified in Section 3.3.3, we will conduct a preliminary study to quantify Haptixel's JND (see Section 4).

Perceptually, we will conduct a user study to illustrate whether Haptixel enables: (1) the discrimination of different force levels (e.g., discovery); (2) high accuracy in absolute force recognition (e.g., information retrieval), (3) high accuracy in relative force recognition (e.g. sorting, comparison, cluster); as well as (4) a low spread of variance and deviation per user within data ranges (e.g., range estimation, cluster, correlation) (see Section 5).

# 4 Preliminary Study

As mentioned in Section 3, we propose to characterize users' Just Noticeable Difference (JND) - as a function of Haptixel's finger support material (rigid or flexible). This JND will also inform us of the theoretical amount of discrete force levels Haptixel can provide.

Pressure can be induced through skin deformation; therefore depending on the finger support we use in Haptixel, force perception and discrimination can be altered. A more solid finger support can provide higher levels of force, though we do not know whether the JND (Just Noticeable Difference) is similar with both materials, or whether these higher levels of forces are proportional to the respective JNDs per material. In this preliminary study, we propose a psychophysical experiment, to quantify the JNDs per finger support material.

## 4.1 Participants & Procedure

We recruited 8 participants (3F; 5M; self-declared) aged from 23 to 34 (average = 25.6, std = 4.0) from our institution. One participant was left-handed. No gratification was provided for the experience and all participants self-volunteered after a call for participation through e-mail. Participants were asked to wear Haptixel on their dominant hand, then to compare various stimuli. We proposed a Latin-square design for both material and order in which stimuli were presented first (e.g. an ascending order, where the comparison stimulus is lower than the reference one; or a descending order, where the comparison stimulus is higher than the reference one).

## 4.2 Design, Task & Stimuli

To define the JND, we used the method from Frediani et al. [27], inspired from the methods of limits: we defined a series of forces to evaluate {0.5, 1.0, 1.5, 2, 2.5} N; which we used as both reference stimulus and comparison stimuli. We generated all combinations (e.g., with 1.0 N as a reference, we consider {0.5,1.5, 2, 2.5} N as comparisons; and so on), and the presented stimuli were then chosen randomly, as a succession of "Ascending" and "Descending" orders. For each set of stimuli, participants were stimulated with the Reference stimulus (RS), then with the Comparison stimulus (CS), and then answered the following: *The Comparison stimulus is Higher than (resp. Lower than) or Equal to the Reference stimulus.* As long as the comparison was perceived as higher (resp. lower), other sets of stimulus were generated - with the same Reference

and a novel comparison stimulus being:

$$CS_i = \frac{RS - CS_{i-1}}{2} \qquad (4)$$

Once the Reference and Comparison stimuli were eventually perceived as equal, we recorded the value for JND as the previous iteration stimulus (e.g. if $CS_i$ is considered as equal, the JND value is $CS_{i-1}$). The duration of the experiment was therefore not fixed - as it was dependent on the user's performances to discriminate stimuli. The visuals only consisted of the above question, with no other distraction; and participants answered using the keyboard. We used a within-subject design, and the experimental design was: 5 REFERENCE STIMULI × 4 COMPARISON STIMULI per MATERIAL; i.e., 8 PARTICIPANTS × 40 TASKS = 320 TRIALS, each with various amounts of comparisons.

## 4.3 Results

We computed a 2-Way ANOVA and verified that assumptions were not violated (Levene's test, QQ-plot).

JND. There was a significant effect on the chosen Material ($F_{(1,7)} = 6.03, p \le 0.05, \eta_p^2 = 0.04$). Globally, the JND was significantly smaller for TPU (0.6 N in average) than for PLA (0.73 N) for every tested force. Though, and, as per Figure 5, the results for the 0.5 N reference stimulus were quite high; as for the other values, the JND did grow with the stimulus [83], providing a constant Weber fraction ($Weber = \frac{CS_{JND}}{RS}$, 0.36 for TPU, std = 0.12; 0.41 for PLA, std = 0.09).

*Duration.* The experiment duration was longer for TPU (35 minutes, std = 8 minutes) than for the PLA (28 minutes, std = 5 minutes). This is due to participants including more steps in their force discrimination process before affirming the stimuli were equal using the TPU finger support. Consequently, this finding indicates a finer JND using the TPU finger support.

*Ascending vs. Descending.* We also studied whether the stimuli order (ascending vs. descending) affected the force discrimination in the JND characterization. There was also a noticeable significant effect on the order in which stimuli were provided ($F_{(1,7)} = 11.4, p \le 0.001, \eta_p^2 = 0.02$). When the stimuli was ascending (CS lower than RS, and therefore *ascending* to RS), the JNDs as Weber fractions were constant with a really low deviation ($Weber_{TPU-AS} = 0.33, std = 0.04; Weber_{PLA-AS} = 0.40, std = 7e^{-3}$); and showing better results than the global results. The JNDs when the stimuli was descending is significantly higher ($Weber_{TPU-De} = 0.49, std = 0.04; Weber_{PLA-De} = 0.70, std = 0.7$).

## 4.4 Discussion

In this study, we showed that the finger support material does impact the discrimination level for cutaneous force-feedback through skin deformation. Results suggest that a flexible finger support (here, TPU 95A) provides a significantly lower JND than a rigid finger support (here, PLA). In Tao et al. [74], authors had demonstrated that the same rigid object could be perceived with different softness, when the finger pad is under constraints. In this study, we validate
<figure><img src="image_7.png" /><figcaption>Figure 5: JND as a function of the Reference Stimulus (N), expressed both in Newtons and in Weber Fraction; for both PLA (rigid) and TPU-95A (flexible) finger supports. Error bars indicate 95-CI.</figcaption></figure>

that the skin deformation also influences the force-feedback discrimination levels; suggesting that flexible finger support would allow for a refined value mapping when it comes to data visualization.

The maximum tested force in this study was fixed at 2.5 N. We previously mentioned in the Implementation section (Section 3) that a force of 5 N could be reached using the rigid finger support. However, such high forces on the fingertip can be perceived as somewhat uncomfortable and oppressive, thus we decided to maintain lower forces. More materials, allowing higher forces and discrimination levels while remaining comfortable, or attachments methods, limiting this finger pad restriction in deformation, will be investigated as future work.

We note that the stroke of the servomotor is smaller with the rigid finger support than with the flexible one for the same force magnitude. Future work includes integrating alternative cutaneous force-feedback methods, such as electroosmotic pumps, to complement the lever mechanism stroke and provide a skin deformation from the lever geometry (e.g., inflating); and improve the JND results while providing a comfortable stimulus.

Reaching a JND of 0.6 N with a 2.5 N maximum force (0.36 in Weber fraction) already allows for at least four discrimination levels (e.g., one more than with vibrations [62]), which could be increased depending on the context-of-use; for instance in a task recognition rather than in an absolute recognition; or more importantly, with visual supports. As visuals dominates our haptic perception (for instance leveraged with pseudo-haptic illusions [43, 78], Haptixel could be used to encode more than four levels of forces when coupled with visual encoding. This JND of 0.6 N also is twice as high as the discrimination levels in AirPush [45], where participants performed a force magnitude recognition task with respective forces of 1.2 N apart from each other using kinesthetic feedback. This suggests that cutaneous force-feedback, with its lesser force feedback magnitude, is worth being explored for visualization tasks

against stronger kinesthetic feedback, as it demonstrates finer discrimination levels. It is important to note that this study does not strictly restrict Haptixel to four discrimination levels, that can be considered as Haptixel's absolute force levels. Haptixel can also be used to encode continuous or relative information.

# 5 User Experiment

We conducted a user experiment to demonstrate whether (a) discrete force levels can support simple quantitative distinctions; and, (b) be retrieved accurately even without visual feedback, substituting visual encoding.

## 5.1 Experiment Design

We designed a VR pixel-art like application where participants manually explored 3D patterns (similar to 3D bar charts) which they could not visually see, and physically retrieve through Haptixel. Conceptually similar to a coarse heatmap or heatmap, we mapped color/heights and forces together. Each cell conveyed a different data value through force feedback, treating force as a univariate value mapping, and participants were asked to retrieve its color/height (force → color/height, see Figure 6). When they were finished, they could perceive the force they associated (color/height → force) and confirm it or correct it. The task was thus a combination of Discovering, Retrieving values, Estimating ranges and Comparing.

5.1.1 Participants. We recruited 16 participants (7F, 9M, self-declared), aged from 23 to 38 (average = 26.9, std = 4.0) among staff and students from the university; all outside our research team, unaware of Haptixel's implementation and without participation to our first study (exclusion criteria). We made an informal call for participation at the cafeteria of the university. No gratification was provided. Three participants (19%) were novice in VR, 6 (38%) had already experienced VR (between 2 and 5 times), 5 (31%) were intermediate (between 5 and 10 times) and 2 (12%) were experts. Ten of them (62%) had already tried haptics experiences (ultrasound, pseudo-haptics), but none of them had experienced wearable haptics; and three of them (19%) were never involved in haptic experiences. Thirteen of them (81%) declared themselves as right-handed, while the rest were left-handed.

5.1.2 Procedure & Apparatus. Participants entered the room and were explained the aim of the study: treating force as a univariate value mapping, they had to reconstruct underlying patterns of blank canvases using only the force cues, and to express it through colors/heights as a force-based scalar. Five different color levels were represented as a continuous map, representing the Force Levels from Haptixel's interaction framework (Section 3.4): grey (no contact), white (contact but almost no force, = 0.1N), yellow (low force, = 1.3N), orange (medium force, = 1.9N) and red (high force, = 2.5N). Each color is associated to the cube's height as well (the more force, the redder and the higher; e.g., 2.5 N ⇐⇒ 15 cm). Each pixel (e.g. cube) originally measured 5 × 5 × 5 cm³ and were 2 mm away from each other, to ensure a continuous perception of force when hovering on top of them. We proposed four PATTERNS (cross, triangle, circles, and a random heat map pattern). We chose the random pattern to remove the a priori bias participants might have from drawing known shapes and trying to complete it in a
<figure><img src="image_8.png" /><figcaption>**Figure 6:** User experience example: (Before Drawing) The user hovers on top of a blank canvas with their dominant hand, and a white sphere is projected from their finger. They target their pixels through it. When hovering, they perceive (A) nothing; (B) low force; (C) high force. The user then assigns colors according to their perception. They can refer to the Calibration Cube, shown in the right bottom corner; and interact with the scene using the virtual keyboard (physically mapped with a real one, as per *Substitutional Reality* [68], using their non-dominant hand (here, left hand). Using the keyboard L/R keys (-/+), they modify the colors/heights of their canvases pixels. (After Drawing): (A) Still no contact; (B) Yellow color for low force; (C) Red for high force. We note that the user avatar hand in VR is tracked without occlusion from Haptixel; moreover, we have not represented Haptixel's presence in the virtual environment.</figcaption></figure>

"consistent" way. We controlled the number of force sub-levels to discriminate - cross: 1, triangle: 2, random: 3, circles: 4 (see Figure 6 - After Drawing); and participants all performed the four patterns in the same order, to get an ascending difficulty. The discrimination level was indeed increasing, from 2.0 N difference at Level 0 to 0.6 N at Level 3 (see Table 1). After understanding the tasks, participants were asked to wear Haptixel on their dominant index, and the MetaQuest 2 headset. Based on the preliminary study (Section 4), we used the TPU flexible finger support - to provide better levels of discrimination. The average duration was 45 minutes (std = 10 minutes).

5.1.3 *Task & Stimuli.* The virtual scene was designed on Unity3D.

<table><caption>**Table 1:** Levels (Difficulty), Pattern and Force Sub-Levels to Find. Each cell shows the provided forces per sub-level, and its associated color. For instance, Level 0 is a combination of Grey cubes - showing no contact, and of orange cubes, encoding a 2.0 N force.</caption><thead><tr><th>Difficulty</th><th>Pattern</th><th></th><th>Force Sub-Levels To Find</th></tr></thead><tbody><tr><td>Level 0</td><td>Cross</td><td>No Contact</td><td>2.0 N</td></tr><tr><td>Level 1</td><td>Triangles</td><td>No Contact</td><td>1.0 N</td></tr><tr><td>Level 2</td><td>Random</td><td>No Contact</td><td>0.6 N</td></tr><tr><td>Level 3</td><td>Circles</td><td>No Contact</td><td>0.5 N</td></tr></tbody></table>

The tasks were split between a first introduction “Calibration” scene and the global 4-c anvases to fill. Figure 6 can be used as reference to understand the presence of the Calibration cube, the finger cursor pointing at a pixel when hovering, or the virtual keyboard participants interact with (physically mapped with a real keyboard, as per Simeone et al.’s *Substitutional Reality* [68]), mentioned in the next paragraphs.

*Calibration.* Participants see a first cube: it is the Calibration cube. Whenever they hover on top of it, a cursor coming out of their hand selects it (see Figure 6). They adjust color and height with a virtual keyboard using +/- with the non-dominant hand. Simultaneously, they feel the corresponding force on their dominant fingertip (like a “force heat map”). Once they are familiar with the association color/force, they press “Continue” and see three **grey** cubes. They can feel that each of this cube has an **inner force**; and then modify their height and color by associating them to the force they perceived; still using the virtual keyboard with their non-dominant hand. Once they are confident about their associations force → color/height, they press on “Continue”. They then can feel what they have drawn: when hovering over the cubes, they perceive the force **they** previously associated (color/height → force). If they are satisfied, they confirm and press “Continue”; if not they reiterate until satisfied.

*Canvases.* They then see a 5x5 grey pixel art canvas: the game is starting; using the same process (see Figure 6). They explore, feel different force levels, draw (associate force perception → color/heights), verify (color/height → force). When they are done exploring and painting their four pixel-art canvases, the game is over.

5.1.4 *Design.* All participants drew all four patterns, and had a 5-minute break between patterns 2 and 3, to get some rest and free their fingertip from being stimulated. In summary, the experimental design is: 4 PATTERNS × 5x5 PIXELS = 100 force discrimination TASKS per participant; thus leading to a total of 16 PARTICIPANTS × 100 TASKS = 1600 TRIALS.

5.1.5 *Measures.* We measure the users' assigned forces (e.g. *not the cube inherent ones*), and their respective color coding.

## 5.2 Results

We define here the Absolute results as being the Absolute average force assigned by participants and its associated absolute error (assigned force vs. expected force); and Relative results as the sub-levels discrimination accuracy, the force difference between levels, and the spread of data for a given sub-level (e.g. an absolute offset can occur within the JND, as it should be felt as “non-noticeable”;
<figure><img src="image_9.png" /><figcaption>Figure 7: User Experience average absolute results: Each Level/Pattern to Find is represented with its associated force, and its corresponding Participant average drawing counterpart is indicated. Each pattern was accurately drawn; and each color level was represented in the same range of colors. These results indicate that Haptixel can therefore be used to discriminate at least 4 levels of force (+ no contact level).</figcaption></figure>

though if the whole level has the same offset and thus a low spread, this provides more information regarding participants' clustering and correlation performances using Haptixel beyond JNDs. We removed 14 values (0.88% of data) as they were considered as outliers (over 3 standard deviations in the pixel value analysis) and performed our analysis over 1586 pixels.

### 5.2.1 Force vs. No Force (Figure 4 - Force Levels)
Haptixel relies on an on-demand mechanism to either leave the fingertip unencumbered ("no force", see Figure 1 - Left, A) or to provide contact and force ("force, physical contact", see Figure 1 - Left, C). In total, 98.9% of the cubes (1568/1586) were correctly assigned (grey for "no force nor contact" cubes; and colors for "contact and force" ones). Only one cube was assigned a low value with color (0.04 N) instead of 0 N (grey); and 17 cubes were not assigned a force and left as grey.

### 5.2.2 Absolute Results.

**Global Results.** We measured the absolute forces that were assigned per PATTERN, per pixel and per Sub-level of force (see Table 1 for sub-level references). In Figure 7, each PATTERN is represented as "Pattern To Find" (left) with its respective Average participant drawing counterpart (right, showing the average assigned force and standard deviation). The colors in the heatmap is associated to the continuous color bar indicated on top of the figure. We can therefore notice that each PATTERN was correctly drawn; and, that each sub-level of force was indeed correctly represented per PATTERN, even though some low offset can be noted (e.g. in Random Pattern, Level 2). This will be discussed further in the Relative results section.

The global average error overall ($\epsilon = |pixel_{tofind} - pixel_{user}|$) is **0.19 N**; and, the average error in the discrimination tasks (e.g. removing all the grey/0 N cubes) is **0.34 N**.

**Absolute Error per Sub-Level of Force.** The absolute error per force sub-level is shown in Table 2. In the Triangle and Circle PATTERNS, the error is lower for higher forces (≈ 0.2 N for a 2.5 N expected force) than for the other ones (≈ 0.35 N). These errors levels do fall into the previously quantified JND - and therefore demonstrate that absolute forces could be discriminated adequately.

<table><caption>Table 2: Absolute error in N (std, in N) per Force Sub-Level. Each cell represents the user's average error in retrieving forces, per sub-level. For instance, while Level 0 showed an original orange 2.0 N, users retrieved it with a 0.34 N error (assigned vs. expected).</caption><thead><tr><th>Difficulty</th><th>Pattern</th><th>Average Error (N) Per Sub-Level of Force (std, in N)</th></tr></thead><tbody><tr><td>Level 0</td><td>Cross</td><td>0.34 (0.14)</td></tr><tr><td>Level 1</td><td>Triangles</td><td>0.38 (0.30) 0.22 (0.22)</td></tr><tr><td>Level 2</td><td>Random</td><td>0.38 (0.30) 0.42 (0.22) 0.38 (0.36)</td></tr><tr><td>Level 3</td><td>Circles</td><td>0.31 (0.20) 0.41 (0.26) 0.30 (0.24) 0.16 (0.31)</td></tr></tbody></table>

### 5.2.3 Relative Results.
As we see in Figure 7 - Level 1 (Triangle Pattern) or Level 2 (Random Pattern), the average colors users drew are not exactly matching the expected red pixels. Though, the difference between the different sub-levels can still be perceived. Indeed, even though participants have offsets in their assigned forces, they still perceived the relative differences of forces (e.g. stronger, lower) and/or the pixels that belong to the same force
sub-level, like clusters of sub-levels. Note that no indication that pixels were assigned per sub-level nor the number of sub-level was indicated to the participants. In this subsection, we therefore analyse the relative results, with the relative force discrimination and user data spread.

*Relative Difference per Level.* We had designed the Pattern difficulty according to the force difference between sub-levels. In the Triangle pattern, a difference of 1.5 N was expected between the two sub-levels (1.0 and 2.5 N): in average, we report a 1.13 N average difference among all users drawing. In the Random pattern, the difference between each sub-level was around 1.0 N; we report a 0.59 and 0.65 N difference between the sub-levels. In the Circle pattern, the difference between all the sub-levels was around 0.7N; we report relative differences of 0.45 N for the [2.5, 1.9N] sub-level, and 0.57 N for the [1.9, 1.2]N and [1.2, 0.5]N sub-levels.

*Spread of Data.* As illustrated in Figure 7 - Level 1 (Triangle Pattern) - we note that the expected force sub-level is not reached; though the whole set of red-ish pixels share the same color. To quantify it, we calculated the 95-confidence interval per sub-level **per user** to represent the spread of data within a force sub-level and to indicate whether participants did recognize which pixel provided the same levels of forces. We averaged it out for each Pattern's force sub-level, and results are displayed in Table 3: the more the expected force, the lower the spread of data (from ≤ 0.3 N to ≤ 0.1 N). These results therefore indicate participants were confident pixels were associated among one sub-level.

<table><caption>**Table 3: Average User 95-Confidence Interval per Pattern's Force Sub-Level.** These results for instance indicate that in average, all participants considered all of the Triangle Pattern red pixels to be equal, with 95% of the data included in a +/-0.05N range.</caption><thead><tr><th rowspan="2">Difficulty</th><th rowspan="2">Pattern</th><th colspan="4">Average User 95-CI (N), Per Sub-Level of Force</th></tr><tr><th>Cross</th><th>0.06</th><th>0.05</th><th>0.20</th><th>0.00</th></tr></thead><tbody><tr><td>Level 0</td><td>Cross</td><td>0.06</td><td></td><td></td><td></td><td></td></tr><tr><td>Level 1</td><td>Triangles</td><td>0.33</td><td>0.05</td><td></td><td></td><td></td></tr><tr><td>Level 2</td><td>Random</td><td>0.20</td><td>0.28</td><td>0.20</td><td></td><td></td></tr><tr><td>Level 3</td><td>Circles</td><td>0.28</td><td>0.14</td><td>0.10</td><td>0.0</td><td></td></tr></tbody></table>

*Cube Discrimination in Level 3 (Circle PATTERN).* We analysed Haptixel's ability to provide different levels of force by conducting a one-way ANOVA. We first verified ANOVA's assumptions (normality, equal variances) and none were violated. There was a significant effect on the sub-levels ($F_{(3,27)} = 96.3, p < 0.001, \eta_p^2 = 0.53$). Standard HSD post-hoc tests with Bonferroni-corrected p-values were then calculated, and significant effects were found between all the different sub-levels, with p-values < 0.001) (see Figure 8). These significance levels confirm that relative forces are correctly differentiated, beyond their absolute retrieved values.

### 5.2.4 User Observations and Qualitative Feedback.
Most of the users revealed that it was easier to draw the patterns by relying on relative force perception. The “calibration cube” was helping defining a first reference color, but as the distance between this latter and the canvas was over 7 cm, they had to focus and play on their own pressure/force memory to get an adequate color matching. They were then using their relative perception of forces from one

<figure><img src="image_10.png" /><figcaption>**Figure 8: Boxplot of participants' absolute assigned forces per sub-level in Level 3; significance reveals that sub-levels were indeed discriminated accurately.** Green triangles indicate average assigned forces. We can note that levels were retrieved without overlapping with each other, with high significance. This validates that participants can discover and retrieve, cluster, sort, or compare values with a high accuracy using Haptixel; and confirms our JND study results.</figcaption></figure>

cube to another, and then validated using the calibration cube once a first drawing was done. The “validation” phase, where they could perceive the drawing they had drawn, usually helped to detect a global offset of the whole pattern (e.g., when all assigned values were under- or over-estimated). One participant mentioned it was fun to focus on pressure memory, as it is a quite unusual task - compared to shape memory for instance. All participants mentioned the experiment was fun and original, and were surprised by the (large) force magnitude Haptixel provided.

## 5.3 Discussion

From the study results, we highlight five key findings:

1. Participants perceived the difference between “No force” and “Force” with a 99% accuracy;

2. Participants differentiated relative force levels, and actually used it as a strategy to retrieve absolute values;

3. Participants significantly differentiated four absolute force levels (low: 0.6 N) to high (2.5 N);

4. Participants retrieved absolute force as a univariate value mapping with a high accuracy (0.34 N);

5. Participants clustered data points with a low deviation of data.

We now discuss these findings implications with respect to visualization tasks; and compare it with existing literature.

### 5.3.1 Force vs. No force.
Differentiating when the fingertip is free from interaction and without any force shows that participants can freely discover values in visualization tasks. When aiming for
void zones in a graph, they will thus remain without any feedback. Perceiving a force will thus be correlated with encountering a data point, and perceiving its value.

### 5.3.2 Relative force levels.
Participants mentioned that their main strategy to retrieve values was to first identify a pixel, correlate it to the Calibration cube, and then define its vicinity using relative forces; as it was faster than going back to the Calibration cube, which force/color combination they would then have to remember (e.g., when leaving the calibration cube, Haptixel navigates between cubes, and thus goes to the "No force", out of the fingertip reach). This findings reflects on a combination of visualization tasks: while we aimed for users to "retrieve value" and "correlate" them with the Calibration cube, they intuitively chose to sort, estimate ranges and cluster them using relative forces felt on their finger pad. This also means that continuous force values can be felt and interpreted as a mapping while exploring data. As relative forces are distinguished quite accurately, these results can be extrapolated for dynamic uses of Haptixel, in temporal exploration for instance (e.g., hand remains static): where they could be interpreted as patterns or trends (see Section 6).

### 5.3.3 Force Levels Discrimination.
With respect to the previous JND study, where the discrimination level was estimated to 0.6 N (0.36 in Weber fraction), we validate that participants can indeed discriminate at least four absolute force levels with a maximum force of 2.5 N (e.g., separated from ≈ 0.7 N). We note that these absolute force levels were retrieved without overlapping with each other (see Figure 8), with an accuracy below Haptixel's JND. This suggests that other force levels could potentially be discriminated too, using the same setup and maximum force. Using other study designs, such as recognition tasks, or coupling cutaneous cues with visuals, this threshold also can be refined. This finding also confirms the variety of force levels from Haptixel's interaction framework (see Figure 4), as participants assessed how some pixels were surprisingly strong (e.g., 1.9 to 2.5 N), especially as opposed to others (0.6 to 1.2 N, or no force).

*Cutaneous force as an alternative to kinesthetic cues.* Kinesthetic feedback, while displaying stronger force magnitudes, was showed to enable five discrimination levels in a recognition task using a forced-choice design [45], with a difference in force between levels of 1.2 N. In this study, we show that cutaneous force can be considered as a finer alternative to kinesthetic feedback, as users can discriminate quantitative levels using only this cue.

*Cutaneous force as an alternative to vibration cues.* Vibrations were investigated as an additional cue to visual encoding in visualization contexts; and demonstrated as efficient to retrieve densities in 3D scatter plots, identify void regions and clusters; only using three discriminative levels (with a JND study). Our study results suggest that cutaneous force feedback can outperform vibrations, with an additional discriminative level; but more importantly, that it can too support "clustering" tasks.

*Improving the force levels discrimination.* A promising follow-up study would include the investigation of vibrations and cutaneous forces coupled together. Implementation-wise, Haptixel already includes vibration hardware and the associated software to control

it. Visualization-wise, as per bubble plots, encoding 5D-information through 3D position, size and colors; vibrations and forces could be coupled to add two additional dimensions in visualization tasks.

### 5.3.4 High absolute accuracy.
Participants managed to retrieve the values of each cell quite accurately (0.34 N average with only colored pixels, 0.19 N overall), while only focusing on their cutaneous cue. This finding has two implications for visualization tasks: (1) Haptixel can be a lightweight alternative when visual attention is limited; (2) Haptixel can be used with all sorts of visual supports, as claimed in its interaction framework (see Figure 4). More importantly, participants were satisfied of their visuals/force mappings when verifying their patterns haptically; showing that this cutaneous force feedback can also complement visual encoding and strengthen the confidence in value retrieval tasks.

### 5.3.5 Low deviation in sub-clusters.
Participants discovered and intuitively correlated value points together, assigning similar colors and heights to the pixels sharing the same force properties. While it might seem trivial at first, we emphasize that participants had no clue that each canvas contained different sub-levels of forces (e.g., level 0: 1 force; level 3: 4 forces), nor how many there were; but still sub-clustered pixels accurately, with a really low deviation between values. This is even more impressive in the "Random" pattern; where the final visual encoding could not have been expected. This finding illustrates how Haptixel can support "clustering" or "correlation" tasks in more general visualization contexts-of-use.

### 5.3.6 Pixel size and Granularity.
While our results are promising to support visualization tasks using cutaneous force as a quantitative channel, it is important to acknowledge the current limitation regarding "haptic pixel" sizes, also experimented with vibrations [8]. Haptixel currently only enables to render one pixel at a given time at the fingertip scale. While granularity can be adjusted with the visual level-of-detail, Haptixel could benefit from more degrees of freedom [64, 85], enabling to rotate its lever to provide finer force-feedback at the fingertip scale (e.g., a tilted surface could provide high and low forces simultaneously on the finger pad). This will be discussed further in the Future work section (Section 7).

## 6 Illustrative Use-Cases

With respect to participants' performances in absolute data retrieval and relative data estimations, we envision a set of use-cases for Haptixel. We discuss two main exploration types (see Figure 9), that rely on various visual supports, contact types, and force levels. The first use-case, reflecting on **spatial exploration** (e.g., geographic data), illustrates how dimensions can be embodied through a combination of Discrete and Continuous constant forces, quantifying discrete data values. The second use-case, reflecting on **temporal exploration** (e.g., stock market trend evolution), leverages the Continuous various forces contact type from Haptixel's interaction framework; where continuous data and trends can be quantified, and conveyed to embody slopes, speeds, or accelerations.

### 6.1 Spatial Exploration: Geographic Data Visualization, Urban Planning

As demonstrated in the user study (Section 5), participants can discover, explore, perceive, retrieve and interpret spatial data. As
an illustrative use-case outside the traditional graph exploration, we propose Haptixel to survey geographic maps (see Figure 9 - A). Haptixel can convey topography information [8, 32] (forces ⇌ heights), can help track and follow river flows [49] (forces ⇌ intensity), check population density (forces ⇌ density) etc. Haptixel can be used to confirm and enrich visually available geographical data, or encode an additional dimension (e.g., with a 2D map, it could encode topography as an additional dimension; with a 3D map, the same dimension would be enriched).

This can also be used in Urban planning use-cases, where users could also perceive the city topology, its architecture, or perceive densities of traffic.

<figure><img src="image_11.png" /><figcaption>Figure 9: Example Use-Cases: (A) Geographic Data Physicalization; (B) Stock Market Trend Evolution: Haptixel replicates the trends movements using its *continuous varying contact type*.</figcaption></figure>

## 6.2 Temporal Exploration: Stock Market Trends

Participants in our study only perceived dynamic changes of forces when moving from a fingertip-scale pixel to another; and actually revealed heavily relying on these relative force changes. These results can be extended to temporal exploration and the perception of patterns using Haptixel. It can encode dynamic representations of derived data, for instance encoding data values over time, encoding slopes, speeds, accelerations. This is better illustrated for dynamic graph exploration: instead of hovering over a graph to perceive its changes, a user can hover on top of category and perceive its trend evolution, as a detail-on-demand visualization [9, 73]. We illustrate this temporal exploration for Stock market trend following (see Figure 9 - B), where the user selects which stock to follow and perceives its local trend over dynamic displacements and forces over their fingertip. Haptixel replicates the trends' slopes using its *continuous varying contact type* (dynamic patterns ⇌ trend evolution). Force levels can also be mapped to be around the dotted line (e.g., low forces above the line; high forces below). Finally, a timestep can be provided to change the level of detail of the rendering, and adjust the global duration of the curve force-encoding.

## 7 Limitations & Future Work

Our empirical results suggest that fingertip force can function as a quantitative channel for visualization tasks, and open promising opportunities for future multimodal visualizations. In this section, we discuss the current limitations for Haptixel, and the research questions it opens up.

## 7.1 Pixel size and Granularity

The most critical limitation at the moment remains the granularity of Haptixel which provides one haptic pixel at the fingertip scale. Many cutaneous wearable haptic devices include 3 degrees of freedom, using three servomotors for instance [16, 60, 65, 85], enabling the contact surface to orient itself. While they demonstrate lower force capabilities (e.g., 1.5 N) than Haptixel, are heavier and more cumbersome to wear (thus can cause occlusion); future work does include the investigation of more degrees of freedom through similar mechanisms, to eventually provide continuous pixel changes at the fingertip scale. In this configuration, the JND would have to be both in force, and degree orientation, to understand how many pixels can be perceived at the fingertip scale.

Another limitation that can alter Haptixel's granularity with visualization contexts is its maximum force Haptixel: the higher the force, the higher the granularity of a continuous value mapping. When tested with the rigid finger support, perceived forces could go up to 5 N. As its respective JND value was 0.73 N; it would have theoretically allowed for 7 levels of discriminable forces; but it was discarded as it felt quite uncomfortable, as if the fingertip was stuck and compressed in a really narrow area. Using the flexible support, even when reaching the maximum stroke of the servomotor, this comfort issue did not occur but the maximum force was lowered (3 N), thus enabling theoretically five force levels.

A potential solution of both these limitations (e.g., JND thresholds and maximum force) can be investigated with alternative designs to the crank-rod mechanism. Instead of actuating the rod differently, the lever's surface could be made more versatile, for instance using mini-electroosmotic pumps such as the ones in *Fluid Reality* [66]. These would enable to keep a compact design form-factor while perceiving pixels of different force magnitudes. If a pump inflates, it can provide higher forces in cutaneous force-feedback and a potentially improved JND. Also, if multiple pumps are integrated, multiple pixels could be perceived simultaneously.

## 7.2 Latency

Participants did not perceive latency between trials; whether in the preliminary or main user study. However, Haptixel could technically benefit from a lower latency; especially for potential finer-grained visualizations. Crossing Haptixel's software with a Jerk model [33] or a eye-hand coordination [10] algorithm will be investigated to predict the users' next point of interest when discovering data, and reducing this latency upon arrival.

## 7.3 Cognitive Load in Visualization tasks

We designed Haptixel to evaluate whether cutaneous force-feedback could be used to interpret scalar cues in visualization tasks; and showed how force cues may augment visual perception or provide a lightweight alternative when visual attention is limited. While our results are promising, future work includes the estimation of cognitive load changes when using non-visual cues in visualization contexts-of-use, and more specifically the impact of cutaneous force-feedback while discovering or retrieving data. This cognitive load should be estimated when (1) only visuals are involved; (2) only cutaneous cues are involved; (3) both visual and cutaneous
are complementing each other; (4) visual and cutaneous quantify different dimensions.

## 7.4 Coupling with Other Cutaneous Cues

In the same line of observations, other cutaneous cues could be integrated to complement visual encoding or extend Haptixel's current granularity. As previously mentioned, Haptixel already includes a vibration coin motor, which we do not use in this paper. We envision to quantify how the combination of force and vibration cues can leverage Haptixel's JND for visualization tasks. Different configurations and research questions are to investigate: (1) one level of force with multiple levels of vibrations (does it enable more vibration discrimination?); (2) multiple forces with one level of vibration (does it enable more force discrimination?); (3) forces and vibration proportionally mapping the same dimension (do they complement each other?); (4) multiple forces and multiple vibrations mapping different dimensions (does one take over the other?). It is not clear yet how these dimensions would enrich each other, and more specifically, how they would be interpreted and integrated on a cognitive side.

## 8 Conclusion

In this paper, we explored the use of cutaneous fingertip haptics as a lightweight and adaptable quantitative channel for visualization tasks, and found it to be a viable alternative to kinesthetic feedback or vibrations. To illustrate it, we proposed Haptixel, a lightweight, open-source fingertip haptic device designed as an accessible platform for studying force-based scalar cues in visualization, allowing users to feel data through skin deformation. We described Haptixel through (1) design choices, (2) hardware and software implementations, (3) an interaction framework, and (4) a non-exhaustive set of visualization opportunities it can support.

We then conducted a first preliminary study to define whether force discrimination can be performed through cutaneous force-feedback, and quantified the impact of finger support material on force perception. We demonstrated that flexible material allows for more skin deformation and thus lower JNDs (0.36 in Weber fraction), theoretically allowing four forces levels discrimination with a maximum force feedback of 2.5 N. These first results were promising to consider cutaneous forces as an alternative to existing kinesthetic or vibrotactile methods, more commonly used in visualizations.

We then empirically assessed whether Haptixel could support the perception of data values in the absence of visual encoding. Participants interacted with a blank pixel grid, conceptually similar to a coarse heatmap, in which each cell conveyed a different data value through force feedback and treating force as a univariate value mapping. Participants reconstructed the underlying pattern accurately while using only the force cues, and evoked having mostly relied on relative perception to retrieve values accurately.

Overall, we demonstrated that fingertip cutaneous force can indeed function as a quantitative channel for visualization tasks, opening up promising opportunities for integrating cutaneous feedback into future multimodal visualizations.

## Acknowledgments

Authors would like to thank G.Bailly for providing feedback on this paper; and the reviewers for their suggestions. This research was funded by the European Research Consortium under grant agreement No 101042702 Intevol-ERC2021-STG.

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