Squishy, Yet Satisfying: Exploring Deformable Shapes' Cross-Modal Correspondences with Colours and Emotions

Surfaces with deformable and shape-changing properties seek to enhance and diversify tangible interactions with computing systems. However, we currently lack fundamental knowledge and user interface design principles that connect the inherent properties of deformable shapes with our human senses and cognitive associations. To address this knowledge gap, we systematically explored deformable shapes’ cross-modal correspondences (CC) with colours and emotions. In our CC study, 52 participants were presented with deformable shape stimuli that varied in stiffness and angularity. They were asked to associate these stimuli with colours and emotions under (i) visuo-tactile and; (ii) tactile-only conditions. For the first time, our findings reveal (1) how stiffness level primarily influences the CC associations and; (2) that stiffness and angularity play a significant role in CC associations over the visibility of the shapes. The results were distilled into design guidelines for future deformable, shape-changing interfaces that engage specific human senses and responses.

deformable shapes with our human senses and cognitive associations.To address this knowledge gap, we systematically explored deformable shapes' cross-modal correspondences (CC) with colours and emotions.In our CC study, 52 participants were presented with deformable shape stimuli that varied in stifness and angularity.They were asked to associate these stimuli with colours and emotions under (i) visuo-tactile and; (ii) tactile-only conditions.For the frst time, our fndings reveal (1) how stifness level primarily infuences the CC associations and; (2) that stifness and angularity play a signifcant role in CC associations over the visibility of the shapes.The results were distilled into design guidelines for future deformable, shape-changing interfaces that engage specifc human senses and responses.

INTRODUCTION
Shape-changing and deformable interfaces ofer the unique potential for physical manipulation as a communication medium [2,5,24,55].They can provide users with compliant screens that enable variations in stifness [31,75] and the ability to morph into diferent shapes for both dynamic physical feedback and dynamic afordances [48].Recent eforts in this space are largely technologyfocused, with researchers seeking to develop new construction approaches for deformable and shape-changing interfaces [2,5].However, as the feld matures, there is a growing need to develop fundamental design principles [2] on the user perception of these devices.This will enable designers to leverage deformation and shape to create intuitive mappings for interface signifers and multisensory experiences that combine visual and tactile modalities with user afect.
To address this need, we draw on the Crossmodal Correspondence (CC) phenomenon, and its role in understanding how the human brain integrates information from multiple senses [39].There is robust evidence, ranging from neuroscience [17,67] to psychology [6,51,63] and HCI [56], that multi-sensory harmony allows efcient processing [41].Research in cognitive science describes how external physical representations can aid in cognitive tasks such as encoding explicit information or coordinating thoughts [38].CCs stretch across cultures [13], and even across generations [46], and thus provide reliable, inclusive design solutions.This makes the study of CCs involving deformability and shapes a clear avenue to inform design guidelines of such novel interfaces.Emotional responses to interfaces are known to impact whether someone will buy a device or use it regularly, thus the links between the senses and afect are crucial design considerations [34].
Work has begun to map out these fundamental principles for shapes, particularly CC of tactile static shapes [40] and dynamic shapes [21] to colour and emotions.This work includes guidelines based on studying visual-tactile CCs across deformable surfaces and their correspondences with shapes and colour [65], providing insights into the interplay between fat deformable surfaces and visual interface elements.We advance this growing area of research by studying the combinations of deformable shapes and their correspondences to colours and emotions.We seek to answer the following questions: RQ1 How do people interact with, and assign emotions and colours to various deformable shapes of diferent stifness?
RQ2 Do emotions and colour associations difer based on whether deformable shapes are visible during tactile interaction?
We address our research questions through a within-participants user study with 52 participants.We used a set of shapes as stimuli (see Figure 1), of which we varied the shape (Curve, Sinuous, Emerge, and Porous), angularity (Bouba, Kiki), and stifness (softer than skin, equal to skin, harder than skin).For example, a hard Bouba-Curve represents a round cylindrical shape with little compliance, whereas a soft Kiki-Sinuous consists of multiple squishable spiky shapes (see Figures 2 & 3).The participants explored the diferent deformable shape stimuli and were subsequently tasked with associating them with emotions (Pleasure-Arousal-Dominance (PAD) Emotional-State Mode) and colours.These associations were performed in visuo-tactile and tactile-only conditions to investigate the infuence of visual context on participants' perceptions.
The results of our study identifed six key takeaways: (1) shape and stifness consistently infuence users' colour and emotional associations across both visuo-tactile and tactile-only modalities; (2) soft shapes are associated with cooler colours and harder shapes with warmer colours; (3) high brightness is associated with combinations of soft-rounded, or spiky shapes while darker colours are associated with harder-rounded shapes; (4) soft-rounded shapes are associated with pleasant feelings, while harder, spiky shapes tend to evoke unpleasantness; (5) spiky shapes are associated with excitement, while rounder shapes with calmer designs; and (6) rounder protruding shapes convey a sense of high control and making them softer can enhance this feeling.
These results have the potential for a lasting impact on the shapechange and deformable user interface feld through our synthesis of the results into implementable design implications.For example, we envision UI designers of variable stifness devices [28,76,80] can apply fnding (2) to set user expectations of the softness/stifness of a widget or surface before and interaction begins, resulting in more efcient and desirable interaction experiences.
Our study contributes evidence of cross-modal correspondences between the sensory haptics of physical shape and stifness, with colours and emotions.The fndings further advance the knowledge of designing efective afordances and signifers for physical interfaces, with particular implications for deformable and shapechanging interfaces, eyes-free interaction, and multi-sensory experiences in HCI.We make the following contributions: • Empirical evidence demonstrating how diferent shape features, stifnesses, and user-applied force interact to determine associations with colour and emotions during tactile exploration (see Figure 1).• We show that the visual modality has little infuence over user associations with colour and emotions when exploring deformable shapes.• Guidelines for the design of physical user interfaces that combine the visual-tactile modalities, as well as user afect.

RELATED WORK
We summarise related work on deformable and shape-changing interfaces and the use of Cross-modal correspondences in HCI.

Deformable & Shape-Changing Interfaces
Ishii et al. [29] outlines a defning vision for the future of physical interfaces with Radical Atoms.It envisions a world that goes beyond existing fat, static forms of interfaces and towards one with transformable materials.Since then, the way in which interfaces can change [2,55] and deform [5] has been explored in a multitude of approaches.
A wide range of research has explored how to develop deformable non-rigid User Interfaces (UIs) elements that incorporate dynamic stifness elements.Parkes and Ishii [52] demonstrate Bosu as a design tool for soft mechanics that can record and playback 3D motion.Similarly, Materiable imitates dynamic properties, such as fexibility, elasticity, and viscosity, again using 3D motion [49].Such prototypes enable a richer embodied interaction and perceptions of rendered materials.Dynamic stifness is also explored through pneumatics [28,76,80], including for tactile response related to levels of force input [76].
Smart materials and fuids ofer new routes for implementing haptic and deformable displays.Ferrofuids, triggered by magnetic felds, can set areas of 'hardness' that also allow users to push into the interface [31,32,74].Microfuidics presents an opportunity to down-scale the form factor of such devices [78].Miruchna et al. [47] introduces temperature-actuated hydrogels, which provide an alternative method for adding actuated deformable elements to touch surfaces.Due to this combination of actuation and deformability, it has also been used in the context of wearable technologies [33] and the simulation of the feeling of paints on mobile devices [66].
The space of the deformable surfaces has also seen fabric used in devices, for example, TableHop [60].Here, the fabric is used as a display alongside transparent electrodes to provide haptic feedback and deformable cues to the user [60].Other non-rigid deformable interfaces include examples of foldable displays [36], elastic displays [73], thin-flm touch-displays, and stretchable onbody displays [77].

The Human Side of Deformable & Shape-Changing Interfaces
While signifcant work has focused on technological advances in deformable and shape-changing interfaces, there is a need for a deeper understanding of user experiences with these novel devices [2].To advance this understanding, we can look at key framework papers in the feld.Morphees [59] presents a framework for the resolution of actuated mobiles; this framework was further evaluated and expanded by the authors in workshops that created taxonomies of everyday re-confgurable objects [37].Resolution change was then further explored by [53], but then in relation to people's feelings and perceptions via a large-scale video study where users watched handheld devices change shape.Similarly, the feelings and perceptions of users were studied in 'Imagined Physics' [45,50].This work reviewed examples of shape-changing interfaces and analysed human responses to the changes.Sturdee and Alexander [68] classifed diferent forms of shape change, this time on an application level, providing insights into end-use cases.We also see work focusing on understanding afordances and their role in shaping users' mental models [71].Similarly, Follmer et al. [24] outline frameworks for dynamic afordances and constraints, shedding light on the design possibilities in shapechanging interfaces.Extending this, other work has proposed a design space for shape-changing widget controls and applications in eyes-free scenarios again, focusing on shape resolutions [57].
We also see work that seeks to understand the impact of deformations on usability for force input tasks [25,61].Fan's JND (Just Noticeable Diference) study [19] explores the detection of surface shapes under varying stifness conditions, contributing to our understanding of deformable interactions with shape-changing displays.
Collectively, these studies showcase the diverse technical and interaction possibilities within the design space of deformable and shape-changing displays, emphasising the importance of understanding user experiences and perceptions when developing future prototypes and applications.Furthermore, there is a large body of work that explores the haptic perception of deformable material [3,10,14,64].This paper expands on these perception studies and framework papers by studying Crossmodal Correspondences (CC), and the pairing of deformation and shape.

Crossmodal Correspondences in HCI
Crossmodal correspondences (CC) pertain to the non-arbitrary perceptual mapping of stimulus features, both within and across diferent sensory modalities.One of the most widely-known CC phenomena is known as the "Bouba/Kiki" efect [54], which dates back to the 1970s.The results consistently demonstrated that the majority of participants associated the round shape with "baluma" and the angular shape with "takete" [39].Subsequent studies replaced these names with "bouba" and "kiki", yielding similar outcomes.This work demonstrated that our afective or emotional response to objects can impact our aesthetic experience of them and judgments of appreciation [34].
Human-Computer Interaction (HCI) inherently involves multiple sensory modalities [35].Common computer interfaces seamlessly integrate visual elements (e.g.monitors) with tactile components (e.g.touchscreens, keyboards, or mice).The use of CCs presents numerous advantages for novel HCI research, where the interplay between sensory modalities during presentation or input plays a central role.These benefts include gaining insights into which cues evoke specifc human responses, learning how to harness these cues efectively, and identifying those that should be avoided.An intriguing characteristic of CCs is their universal presence across various languages, cultures [12], and age groups, which underscores their potential to yield reliable and inclusive design [43,46].
As a result, there is a growing trend of incorporating CCs into HCI research and design [23,40,46].This trend encompasses investigations into colour associations with tangible objects [40], shapechanging [22], and deformable surfaces [65].Along with colour, Lin et al. [40] highlights the need to fll the gap in our understanding of how sensory modalities combine to convey and interpret emotional content.However, prior work that maps emotion associations to physical interface properties has so far only focused on haptics [79], solid, tangible shapes [40], or dynamic angularity change [22,70].Therefore, we contribute results on emotional associations for compliant shapes, combining shape and stifness factors.Our work extends this by studying the CCs of deformable shapes with colours and emotions in the context of HCI.To the best of our knowledge, our work is the frst to focus on cross-modal correspondence combinations of variable shape and stifness stimuli in the context of HCI.

METHODOLOGY
This study aims to understand the crossmodal correspondence between tangible, deformable shapes of diferent stifness, with colours, emotions, and user-applied force.These associations were measured in both visuo-tactile and tactile-only conditions.The study followed a within-subjects design.

Deformable Shape Stimuli
We developed a range of physical shapes, created with diferent Stifness levels and Angularity, as stimuli for the study.This section describes these materials, the measures used in the study, and the rationale behind our choices.We primarily focused on touch and fnger-based input scenarios when designing the stimuli.These encompassed activities such as pressing deformable buttons [1,28,62], applying pressure to various sections of the screen [31,75], and interacting with shape displays [24,30,48].
3.1.1Shapes.The variable properties for shapes are drawn from past literature on cross-modal correspondences [40,65] and shapechanging interfaces [59] research.They were chosen based on a subset of 3D shape features that showed cross-modal correspondence between 3D shapes and stifness [65].They are summarised in Figure 2 and documented below: Curve: A Morphees shape feature [59].The curvature is determined by calculating the angle between three successive control points, naturally defning the degree of roundness in the shape Sinuous: 3D versions of Bouba/Kiki shapes based on Lin et al. [40].Given their extensive background in cross-modal correspondence studies in psychology literature, these act as foundation shapes.
Emerge: Shapes based on pin array shape-changing interfaces [24,30,57].This shape acts as an inverse for porosity and incorporates elements of the amplitude Morphees feature [59].
Porous: Morphees shape feature porosity [59].Refers to the presence of discontinuities or perforations within a shape.Porosity quantifes the proportion of the perforated sections relative to the total area of the shape.
3.1.2Shape Angularity.The angularity for these stimuli was determined by the mathematical formulas successfully used in previous studies [40,42].For each shape feature, we designed a rounded "Bouba" version of the shapes, and a pointy "Kiki" version.The 3D shapes were designed via a combination of Fusion 360 for digital modelling and Python scripts to generate and calculate the exact curvature and angularity of the shapes.All shapes were modelled via the same process of 3D-printed moulds and pouring three different types of silicone to cast the stifness levels.For consistency, all shapes were modelled to a 20mm × 20mm × 20mm footprint and height.

Shape Stifness.
To investigate the impact of surface stifness on the cross-modal correspondences, each tactile shape stimulus was moulded at three distinct stifness levels (soft, medium, and hard).The decision to use three levels was informed by the stifnessto-shape correspondence results of Steer et al. [65].The stifness levels were selected based on past studies investigating the impact of stifness on user perceptions of deformation and shape [18,19].These are based on the reference point of the index fnger pad, and the three levels of stifness (See Figure 3) are as follows: Soft (Softer than a fnger pad): The softest level of stifness was designed to be softer than the typical index fnger pad, with a Shore hardness rating of 00-10.instead of its sharpness.

Medium
Soft Hard Medium (As soft as a fnger pad): This level of stifness was calibrated to be similar to the typical index fnger pad, with a Shore hardness rating of 00-50.Hard (Harder than a fnger pad): The hardest level of stifness was designed to be harder than the index fnger pad, with a Shore A-30 (approximately equivalent to Shore 00-80) hardness rating.
As is commonly used in other deformable perceptions studies, we used Ecofex Silicone 1 for the silicone [19,65].To reduce surface texture's impact, each of the stimuli was dusted in calcium carbonate (chalk) [19,26].This chalk was also available for participants to dust their fngers with throughout the study.

Measures
3.2.1 Colours.Participants were presented with 10 distinct colours to choose from.The colours and their presentation in the interfaces were chosen based on the approaches used in previous CC studies [15,40].Doing this allows us to maintain continuity for our results with passed colour-based CC studies.Participants could refne their selection via a brightness bar (see Figure 4).Alongside each colour, examples of the minimum and maximum brightness versions of that colour were presented.The 10 colours and corresponding hexadecimal codes were red (ED3020), yellow (FFFF55), blue (3A5AC2), pink (ED3269), grey (7F7F7F), orange (F06E2B), lime green (91FB4D), sky blue (6FFCFE), purple (6323F7), and brown (AF7B51).All of the colours were displayed on the tablet screen over the top of a neutral grey (BCBCBC) background.

Emotions.
To measure the emotions associated with the shapes, we used the Pleasure-Arousal-Dominance (PAD) Emotional-State Model [44], as this model is commonly used in CC studies within HCI [22,40].We asked participants to focus on subjectively experienced emotions induced by the sensory stimuli, rather than as a quality of the stimuli independent of an observer.In a similar manner to Lin et al. [40], we asked participants "feeling the object with my hands gives me a sense of" followed by three scales: pleasure (terms: Pleasant-Unpleasant), arousal (terms: Calm-Excited) and dominance (terms: Control-Lack of Control).Emotions were measured on an intuitive slider, which they dragged towards the word most ftting emotions on each of the scales of prevalence, arousal and dominance.E.g. sliding the cursor closer to pleasant compared to unpleasant for more pleasant associations.Because  there was no conceptual absolute 0, it was not intended for participants to quantify their emotion perception as a number, so they did not see any values on the slider when making their input.The slider produced scores between 0 and 100 for increased granularity in scores and statistical convenience.Such input was preferred to a self-assessment manikin, since the latter is typically employed for measuring emotion excitation, or what users actually feel [7,27], rather than just stimulus associations that are not meant to actually induce emotions.

User Force.
For both tasks, the amount of force the user applies is recorded during their exploration of the stimuli.We used a widely available Force-Sensitive Resistor (FSR)2 implemented with a Teensy43 microprocessor to read the sensor output, connected to serial and integrated with the study software.We followed other papers' hardware setup and calibration process using force sensors [19,25].Following this process ensured that we could map the voltage reading to grams and achieve nearly linear output.This involved amplifying the signal using the circuit seen in Figure 5. Right: Force Platform used for each shape, with a Curve Bouba shape on it.

Study Setup & Apparatus
Our study setup consisted of (1) a force-sensing platform to place the stimuli, and (2) a touch screen monitor used to input answers depending on the task.In the tactile-only condition, a box covered the force-sensing platform and stimuli (see Figure 6).The study area was carefully controlled to minimise strong colour infuences in the surrounding area of the participant's vision.Throughout the tasks, the participants sat on a chair at a desk and were told to rest their wrist on the table while touching the shapes.

Force-Sensor Platform.
To capture force input, we mounted a force sensor inside a 3D-printed platform (see Figure 5).The platform ensured consistent placement of the stimuli for force sensing.

Cover for Tactile-only Conditions.
A box was placed over the stimuli platform in the conditions where the shapes were hidden from view (See Figure 6).Participants used a single front opening to insert their hands to interact with the stimuli.The general placement and design allowed participants to rest their wrists fat on the table, as instructed by the researcher.

Selection Interface.
To the left of the stimuli, we placed a touchscreen monitor.This was used to record the study's stifness associations for colour and emotions.The system was coded using Java Processing 4 and integrated with the force sensor via serial communication (See Figure 6).

Procedure & Tasks
After obtaining participants' consent, they were asked to complete a demographic questionnaire.The experimental procedure comprised four main tasks: colour-tactile-only, colour-visuo-tactile, emotiontactile-only, and emotion-visuo-tactile.In all tasks, participants pressed and matched 24 tactile stimuli (shape-stifness) to either a colour or emotion scale (creating a total of 96 trials per participant).During these presses, the system recorded the force the participant's fnger applied.In the visuo-tactile tasks, participants saw the stimulus before pressing it, while in the tactile-only tasks, the stimuli were hidden from view.Throughout the tasks, participants were reminded that there were no right or wrong answers.The task sequences were counterbalanced, and the order of presented stimuli was randomised to avoid ordering efects.The study concluded with a semi-structured interview, where participants were queried about their underlying rationales and strategies for forming associations for colour, emotion, and applied force across seen and unseen conditions.Each session took approximately 50 minutes (of which approximately 45 minutes tasks, and 5 minutes interview).

Participants
We recruited 52 participants, 26 identifying as female and 26 as male (Aged 18-60 years, Mean: 31.8,SD: 11.9).During the study, participants used their dominant hand to touch the stifness stimuli.
Of the participants, four were left-handed.All participants had normal or corrected-to-normal visual acuity and normal colour vision.All participants were compensated with a £10 gift voucher.An ethics review committee gave a favourable ethical opinion for this research project.This process involved submitting the study documentation, including procedures, questionnaires, interview scripts, consent forms, and information sheets for ethical review by two expert reviewers.

RESULTS
To answer our research questions, we analysed which properties of the deformable shapes afected colour and emotion associations, investigated how people interacted with the shapes, analysed what efect seeing the shape had on these associations, and summarised qualitative responses to understand participants' approaches and rationale for selections.

Data Analysis
Quantitative data was collected from the touch interface and force sensor.We elicited a total of 4992 responses from our 52 participants.These responses associated our deformable shapes with colours and emotions in visuo-tactile and tactile-only conditions.The forces users applied during the exploration of the shapes were collected and post-processed via coveting the voltages to grams based on our force sensor calibration process as mentioned in the Methodology.We calculated the average force over time for each shape interaction under each task for each condition.
For the quantitative data, we ran repeated measures analyses of variance (ANOVAs) investigating the efects of Stifness (Soft, Medium, and Hard), Angularity (Bouba and Kiki), and Visibility (Visuo-Tactile and Tactile-Only) for each of the Shape's (Curve, Sinuous, Porous, and Emerge) associations with colour (Hue and Brightness) and emotion (Valence, Arousal, and Dominance).We used the same approach to test for efects on the force users applied during interaction.
Our analysis uses Holm-corrected post hoc pairwise comparisons where signifcant main efects and interactions were found.
The assumption of sphericity was checked where necessary using Mauchly's test, and in cases where it was violated, results were reported with Huynh-Feldt corrections.We mark p-values with * for signifcant results where < .05,* * for signifcance of < .01,and * * * for signifcance of < .001.We also report 2 efect size to show the magnitude of the observed diferences for main efects and Cohen's for post hoc tests.
Qualitative data was collected from the post-study interviews and audio-recorded with participants' consent.Recordings were transcribed, and 260 quotes were extracted.These were categorised through a deductive approach along three research themes: refections in relation to (i) emotion associations, (ii) colour associations, and (iii) the force applied to the stimuli.Per research theme, a subset of the quotes was analysed using inductive thematic analysis [8,9] to iteratively craft themes that comprised participants' most important refections, after which all quotes were categorised accordingly.

Colour Associations
Overall, we observed that stifness signifcantly afected colour associations for both Hue and Brightness across all Shape types.In most cases, this resulted in the softer version of the shapes being associated with lighter shades, and hues of yellows, greens, and blues (with exceptions for Porous shapes).A summary of colour selections is shown in Figure 7.In the remainder of this section, we provide a detailed analysis of the results.We used a repeated measures ANOVA followed by a post hoc pairwise comparison to investigate the efect of Stifness, Angularity, and Visibility for the associated colour scales of Brightness (See Table 1) and Hue (See Table 2).We introduce the results individually for each Shape.

Colour Associations Summary.
Our results show that stifness signifcantly afects colour associations for both Hue and Brightness, regardless of Shape.Softer versions of the shapes were usually associated with lighter shades, and hues of yellows, greens and blues.The exception was Porous shapes, whose softer versions were associated with dark shades (instead of light shades).In addition, harder Porous shapes were associated with even darker shades and mostly reds.Where Angularity had efects, Kiki shapes were more associated with high brightness.Visibility played little role in participants' shape-colour associations, the exceptions being the Brightness of Hard-Sinous shapes and Hue associations for Hard-Emerge shapes.

Emotion Associations
Overall, we observed Soft shapes were associated with higher pleasantness, while Hard shapes were associated with lower pleasantness.For arousal, Soft versions of Curve, Emerge, and Porous shapes were calmer and Hard Stifnesses were more exciting.Dominance measures were less well defned, with Bouba-Sinuous, Bouba-Curves, and Kiki-Emerge-Hard rated with higher control.Visibility only saw a few specifc instances of signifcant efect.A summary of the emotion associations is shown in Figure 8.
We used a repeated measures ANOVA followed by a post hoc pairwise comparison to investigate the efect of Stifness, Angularity, and Visibility for the associated emotion scales of Pleasure (See Table 3), Arousal (See Table 4), and Dominance (Table 5).The discuss the emotion results in more detail in the following sections.The Visibility post hoc analysis showed that Visuo-Tactile was associated with greater pleasantness than Tactile-Only ( (51) = −2.211,< .032* , = −.150).

Emotions Summary.
Overall we observed Soft shapes associated with higher levels of pleasantness, while Hard shapes were associated with lower levels of pleasantness.Specifcally for Curve and Sinuous shapes, Bouba Angularity contributed to higher pleasantness and Kiki to lower pleasantness.For arousal, the Soft Curve, Emerge, and Porous shapes were calmer and Hard Stifness more exciting.Additionally, Bouba versions of Curve and Sinuous shapes contributed to calmness and Kiki to more excitement.For dominance, both Bouba-Sinuous and Bouba-Curve were rated with higher control compared to Kiki.For Emerge shapes, Stifness played an additional role, where higher control was associated with harder shapes with Kiki Angularity.Finally, we only observed a few efects for Visibility.Visual-Tactile Soft-Emerge shapes were associated with more pleasantness and seeing Curves only infuenced higher diferences between Soft-Visuo-Tactile and Hard-Tactile-Only for arousal.

Force Applied during Interaction
Overall, Curve, Sinous, and Porous Shapes, yielded higher forces on Bouba Angularity and lower forces on the Kiki versions.In contrast, Emerge shapes yielded lower forces on Bouba Angularity and higher forces on the Kiki versions.A full overview of the average force applied in each colour and emotion task can be seen in Table 7 and 9, respectively.The remainder of this section analyses the forces applied during interaction more deeply.We used a repeated measures ANOVA followed by a post hoc pairwise comparison to investigate the efect of Stifness, Angularity, and Visibility for the force users applied during each the Colour Tasks (see Table 6) and Emotion Tasks (see Table 8).

Force Applied Summary.
Overall, the Shapes Curve, Sinous and Porous, yielded higher forces on Bouba Angularity and lower forces on the Kiki versions.In contrast, Emerge shapes yielded lower forces on Bouba Angularity and higher forces on the Kiki versions.Additionally, in colour tasks, Emerge, Porous and Sinuous Hard Stifnesses yielded higher forces, with lower forces on the Soft Stifness versions.For Visibility efects, we only saw diferent force interactions for Porous in colour tasks where higher forces were applied in the Tactile-Only condition.

Qualitative Results
In this section, we present participants' reasoning behind assigning colours and emotions to diferent stimuli, and whether their interactions with the objects changed across conditions.Throughout this section, participant refections will be in relation to the stimuli as shown in Figure 7 and Figure 8.

Colour Associations.
We observed a diversity of approaches when associating colours with shapes and stifnesses.These encompassed both rational refections grounded in the inherent properties of the stimuli and personal strategies unique to each individual.Participants articulated their associations through several similes and the use of positive and/or negative mappings.Finally, a minority of participants relied on the colours shown in the interface to inform their colour choices.
Rationale for Object-Colour Associations: When participants were asked about their rationale for associating colour with objects, more than half made specifc references to choosing colours based on both shape and stifness (n = 31).These participants confated the two concepts when describing their strategies (e.g.juxtaposing 'soft' with 'spiky' or 'sharp').For example, P46: "A pointy hard shape was a very cold colour.A soft rounded shape was a more warm colour".In contrast, some participants solely referenced shape (n = 11) or stifness (n = 9).For instance, a shape mapping by P48: "The [Kiki-Sinuous] ones, they kind of look like stars, so I picked yellow a couple of times" (see Figure 7).
Strategies for Colour Associations: Participants highlighted diferent overarching strategies for colour associations.First, 20 participants did not indicate a clear rationale for their colour choice, but described it as a decision based on their feelings or intuition (e.g.P37: "On the frst touch of something, a colour just sprung to mind from the palette available and for the softer squishier shapes I tended to go for brighter colours, dull or unresponsive shapes I went for more matte, less vibrant colours").Second, participants used their visual imagination (n = 19), such as P26: "When I couldn't see what they were, I kind of like imagined what they would be [...] I think [Porous] reminded me of cheese, which is why I put them as yellow" (see Figure 7).Third, participants commented specifcally on the tactile properties of the objects to determine colour (n = 18), such as P8: "The softer the object for me the more pleasant the sensation, so I went to brighter colours between green and yellow".Fourth, participants would refer to personal preferences (n = 9) such as their favourite colour for their mapping: "Anything that I didn't like, especially shapes with gaps or shapes that aren't uniform in a sense, I linked them to colours that I don't like, like orange and darker brown shades" (P21).Lastly, participants would describe their expectations regarding the visual and/or tactile properties of the object (n = 8), and choose a colour based on whether these expectations were met: "From looking at it I assumed how stif it was, and then based on how stif it actually was, I changed my mood about it.So if it looked like it was gonna be soft and it wasn't soft, I put a darker colour" (P1).
Use of Similes to Describe Colour Choices: More than half of the participants (n = 29) made use of similes when describing colour choices.The majority would compare the stimuli to everyday objects, such as buttons (Bouba-Curve), buildings (Emerge), brushes (Bouba-Emerge), game controllers (Bouba-Curve), pyramids (Kiki-Curve), Lego (Emerge), and keyboard keys (Porous); see Figure 7. Another common simile was nature and seasons, for instance, participants associated Kiki-Sinuous shapes with sea creatures, and Emerge shapes with seaweed or coral.Others would associate stifness with concepts such as moss, leaves fowers, or grass: "For [Bouba-Sinuous], if it was really sturdy, I went for a grey, like a stone.But if it was really soft, I chose green because it gave me ideas of leaves or moss or something like that" (P28).Participants would also reference food items to decide on colours, for instance, Bouba-Sinuous shapes were associated with blancmange or soft sweets (e.g.gummy bears).Comparisons to pop culture were made, such as Pokemon and Mario for Kiki-Sinuous shapes (Figure 7).At times the similes for a singular shape would be diferent across stifnesses, for instance, P30: "[Porous] kind of reminded me more of bricks, whereas some of the softer ones more of sponges".Others made positive and/or negative associations, either based on shape, such as P50: "The pointy shapes to me, they were always red because it signifed danger"; or stifness, such as P12: "The ones that are more spiky and hard to press are more like red so like danger, and then things that are more squidgy were safer".4.5.2Emotion Associations.We observed diferent approaches by participants when connecting emotions to shapes and stifness.These approaches involved rational refections rooted in the inherent properties of the stimuli, particularly the tactile interactions with them.Further, participants assigned emotions based on their immediate emotional response to the stimuli, and adjusted their emotional associations based on the visibility of the stimuli.
Rationale for Object-Emotion Associations: When participants were asked about their rationale for associating colour with pleasure, arousal, and dominance, the majority (n = 46) made specifc references to selecting emotions based on shape as well as stifness: "The softer it was the more control I felt, the softer it was the more pleasant it was, the spikier it was the more excitement or lack of calmness" (P31).
Emotions based on Tactile Feedback: Almost half of the participants (n = 25) based their emotions on the tactile feedback of the objects, for example, P6 describes the following for control: "The things that were like the grid type [Emerge], I felt particularly at the harder end of the spectrum [hard Emerge], I felt very in control with those.Whereas with the ones that are a bit like toothbrushes [soft Emerge], because they're kind of fopping around your fngers, they didn't feel so much like I was in control of them" (Figure 2).In contrast, only 8 participants described visual feedback to be of infuence.
Evoking Emotions: Some participants (n = 17) expressed feeling a particular emotion because of the stimuli, which could be either a positive experience, for example, P5 regarding the shape of the object: "I think when the shape looks extravagant, like a star [Kiki-Sinuous] or anything like that.When it's more complex, then obviously it's more exciting for me" (Figure 2).Additionally, it could also elicit negative emotions, especially in relation to the stifness of the stimuli: "Touching the soft ones was really gross, the stifer and spiky ones, I liked those more" (P29).
Revision of Emotions based on Visibility: Participants also expressed the change in feelings based on the visibility of the stimuli (n = 12), attributing more importance to diferent emotions: "I think when I couldn't see them, I was focusing more on control of being able to move them around.I instantly didn't like any of the spiky ones when I couldn't see them, they just creeped me out a little bit" (P7).Further, diferences in stifness of the stimuli became more prominent, as explained by P35: "Especially when I can't see it, the stifness level makes more diference.I would say just in general, that it's the softest touch and stifness that makes big diferences, rather than the shape, the visual".4.5.3Force Applied.More than half of the participants (n = 33) indicated that the visibility of the stimuli played a major role in the level of force they applied, two participants attributed it to stifness, only one to both visibility and stifness, and 16 did not indicate any infuence at all.More specifcally, 20 participants expressed pressing harder and/or for a more prolonged time when they could not see the stimuli, primarily to explore the shape.For instance, P9: "I think when you can't see it, it's weird.You have to kind of wiggle a bit harder.But when you can see it, you can gauge more what the texture is going to be like".In contrast, 9 participants would press harder when seeing the stimuli because of familiarity with the shapes or to explore the visual deformation: "When I could see them I pressed a bit harder maybe just because I could see it deforming under my touch.So I could also see the limit of the material" (P4).Two participants pressed more softly when they could not see the stimuli, as they wanted to be more careful or were apprehensive to touch them: "I did not like pressing the spiky ones when I couldn't see the objects, I have a bit of a fear of needles.So I think that was kind of playing into that" (P7).Finally, of the two participants who described the stifness of the stimuli as an infuence on their applied force, one expressed pressing harder when frm, whereas the other pressed harder when soft because of the physical deformation: "I probably ended up pressing frmer into the soft ones just because they were squidgy, it felt nice to press into (P1).4.5.4Summary.To summarize, our qualitative results provide further insights into how participants associate colour, emotions, and tactile experiences with shapes and stifness.When associating colour with shape and stifness, over half of the participants made specifc references to the stimuli's physical characteristics and used vivid similes to elucidate their choices.Additionally, they described a myriad of strategies, including intuition, visual imagination, tactile sensations, personal preferences, and expectations to support their colour associations.The majority of participants linked emotions to the stimuli's shape and stifness, drawing on tactile feedback and emotional responses evoked by the stimuli, and occasionally revised their associated emotions based on the stimulus' visibility.Furthermore, more than half of the participants acknowledged the substantial impact of stimulus visibility on their interactions, as they reported altering their engagement patterns, such as pressing harder or exploring the object more thoroughly when the stimulus was not visible.These fndings collectively illustrate the intricate interplay between sensory perceptions, cognitive strategies, and stimulus characteristics in shaping individuals' colour and emotion associations, as well as their tactile interactions.

DISCUSSION
This paper explored cross-modal correspondences of deformable shapes with colours and emotions.More specifcally, our RQs focused on investigating the possible relation between angularity and stifness for colour and emotion associations (RQ1), and the possible infuence of visibility on these associations (RQ2).The results of our study revealed (i) the cross-modal correspondences between angularity and stifness for colour and emotions, (ii) the diferences in applied and perceived force, and (iii) the lack of efect visibility has on tactile associations.Below, we discuss the trends and extrapolate their implications for the future design of physical user interfaces in more detail.

Colour Associations
We noticed distinctive trends in the relationships between brightness and hue for collections of shapes and stifnesses.The angularity of protruding shapes (Curve, Sinuous, and Emerge) compared to permeable ones interact with brightness, resulting in clear mapping of associations between brightness and stifness for protruding shapes, whereas permeable shapes show a non-linear mapping.We observed a pronounced infuence of stifness on hue, with stifness playing a more dominant role than angularity.Specifcally, harder shapes are predominantly associated with red, while softer shapes are yellows, blues, and greens (See Figure 7).5.1.1Brightness of Protruding Shapes.For Curve, Sinuous, and Emerge, softer shapes were more closely associated with higher brightness and harder shapes with lower brightness.In other words, for any of the protruding shapes, regardless of their Kiki or Bouba equivalent, the overall stifness seemed to be a stronger indicator for colour associations than angularity.Our fndings on stifness levels align with [65], where soft, fat surfaces were associated with higher brightness.However, we contrast with previous work where Bouba-Sinuous shapes were associated with a higher brightness level, and Kiki-Sinuous shapes with dark colours [40].This suggests that adding deformation to protruding shapes (Curve/Sinuous/Emerge) changes their cross-modal associations, even compared to studies exploring CCs with rigid shapes [40].This could be explained by the unique interplay of shape and stifness for determining colour.For our study conditions, whenever participants were asked to associate a colour, more than half of them referenced similes, and described the visible (angularity) and/or tangible (stifness) properties that motivated their choices.We observed that participants created concept pairings between hard and soft objects of the same shape type (e.g., sponge vs. brick for Porous, moss vs. stone for Sinuous), illustrating how diferent combinations of stifness and angularity result in diferent associations.

Brightness of Permeable Shapes.
In contrast to protruding shapes, the Porous soft shapes were associated with lower brightness, medium stifness with higher brightness, and hard stifness in between.Previous research [65] investigated associations between stifnesses and visual shapes.It found that high porosity was linked to soft surfaces, as well as a connection between high brightness and soft surfaces.However, our study suggests that examining these properties in isolation may not refect their combined efects, in this case, showing that porosity is associated with low brightness.Again, this could be explained by the unique interplay of shape and stifness when determining colour, but with the diference that the results for permeable shapes suggest that the relation between brightness and stifness is not a straightforward, linear one, but rather follows a more complex pattern than protruding shapes.5.1.3Hue for Sof and Hard Shapes.Our qualitative results highlighted the unique nature of hue associations, which can vary from person to person due to factors such as personal preferences, similes, and positive or negative associations.Regardless of that, we observed signifcant efects of stifness for hue, in which soft shapes were consistently associated with cold (blue/green) and warm colours (yellow), while hard shapes were predominantly linked to warm colours (shades of red).This connection between red and hardness aligns with our qualitative fndings, where participants associated Kiki-Curve and Kiki-Sinuous shapes with 'danger', hence signifying the colour red.This resonates with prior research on CC [40], which showed that Kiki shapes were associated with red and Bouba shapes with blue.However, our study introduces a novel perspective by incorporating stifness properties.We observed that in the context of stifness, the soft Sinuous-Bouba shape is associated with blue, while the hard Sinuous-Bouba is linked to red.This result suggests that when considering the interaction of stifness and angularity, stifness takes precedence over angularity in infuencing colour perception when the shapes become harder.

Emotion Associations
Overall, for aesthetic experience (e.g.pleasure, arousal), stifness played more of a role than for pragmatic experience (e.g.dominance).This showed a more intricate interplay between angularity and stifness, dependent on the shape.It became evident that the various emotional responses, both across and within diferent emotions, can be traced back to individual diferences among the participants.This diversity in emotional associations underscores the presence of unique mappings between emotions, stifness, and shape characteristics.For instance, our fndings reveal distinct mappings where stifness, coupled with specifc shapes (Emerge), infuences control perception, while angularity in conjunction with other shapes (Curve/Sinuous) is also linked to control perception.Further, we observed that these mappings can be inherently variable, with some individuals associating softness with pleasantness and others attributing softness to unpleasantness.In essence, our study highlights the nuanced nature of emotional and perceptual responses, suggesting that users' assessment of UIs encompasses both unique individual mappings and potentially opposing associations, as well as overarching properties that could strategically inform the elicitation of emotions when interacting with future UIs.

Dominance in Relation to
Angularity and Stifness.In general, it seems that participants assigned dominance to the perceived level of stability of the stimuli, which was intricately tied to the shared result of specifc characteristics of angularity and stifness within each shape.This resonates with the qualitative observation of emotions based on tactile feedback of the stimuli, as this can give more or less a sense of agency during interaction.For both Curve and Sinuous shapes, we observed a correlation between angularity and the perception of control.Hence, the Bouba shapes consistently instilled a heightened sense of control, while the Kiki shapes evoked feelings of less control.This observation can be attributed to the inherent disparities in the ease of manipulation between spikier and rounded shapes.For instance, attempting to press the pointed tip of a Kiki-Curve shape, in contrast to a Bouba-Curve, often led to greater instability, thus contributing to a reduced sense of control (See Figure 8).
In the case of Emerge shapes, angularity played a less prominent role in dominance.Instead, we identifed a correlation between stifness and the perception of control.Here, the harder variants consistently elicited an elevated sense of control, while the softer versions gave a perception of reduced control.In contrast to the Curve and Sinuous shapes, where angularity played an important role in shaping stability and control perceptions, for the Emerge shapes this was hinged on the stifness.For example, applying force to frmer pillars, whether cylindrical or square in shape, conveyed a heightened sense of control.In contrast, attempting to manipulate soft pillars, showed greater compliance and less predictability, thus diminishing the perceived sense of control.

5.2.2
Pleasure and Arousal in Relation to Stifness.Conversely, our fndings on the dimensions of arousal and pleasure show a more uniform trend.Across the majority of stimuli, stifness emerges as a key factor, where softer shapes are associated with higher levels of calmness and pleasantness, and harder shapes were more frequently linked to feelings of excitement and unpleasantness.This resonates with the qualitative insights on the elicitation of emotions when touching particular stimuli, either creating positive or negative reactions that contributed to participants' perception of aesthetic or hedonic properties.Specifcally, the Bouba versions of Curve, Sinuous, and Emerge shapes were associated with a higher degree of pleasantness, while the Kiki shapes elicited a greater sense of unpleasantness, which aligns with prior research [40].However, our results show a large efect size for the impact of stifness, highlighting that deformation elicits stronger associations to certain levels of pleasure (i.e., soft is more pleasant and hard is less pleasant).

Visibility & Force Applied
RQ2 investigated whether emotions and colour associations difer based on whether deformable shapes are visible during tactile interaction.Our analysis showed few signifcant diferences between the visual conditions for each shape type, highlighting that seeing the stimuli had little impact on the resulting associations.As these CCs demonstrate, stifness and shape design factors can be employed across visuo-tactile and tactile-only modalities for successful multi-sensory experiences.This implies that when touching interface elements, people's assigned qualities, such as emotions and colour, do not change based on whether they can see these interface elements or how their touch deforms them.In real-world applications, this would mean that interface elements will sustain their qualities (e.g. a calming button in a medical context), so a designer can implement these interface elements, knowing that a user will interact with it consistently across diferent visibility conditions and can switch between them.This provides further motivation for deploying deformable and shape-changing UIs in both eyes-free and eyes-on contexts [11,57,58].
Interestingly, the quantitative results only show a signifcant diference for Porous shapes across visibility conditions, whereas more than half of the participants expressed they altered their interactions based on whether they could see the stimuli.This implies that although the absolute forces applied are similar, people's perception of the amplitude and duration of applied force difers based on visibility.

DESIGN IMPLICATIONS
The successful design of multi-modal cues and signifers requires an understanding of their perception by users-our study provides this insight for deformable user interfaces.
This paper contributes towards a growing set of CC study results [22,40,46,65] that are building a picture of how people perceive and make associations with visual-haptic interface elements within HCI.This supports researchers and designers in the development of novel, but intuitive physical user interfaces.
Our fndings are a pathway towards creating diverse multisensory interaction opportunities that combine deformation, shapes, emotions, and colours.We distill our fndings into key design recommendations for creating diverse multi-sensory interactions, particularly for leveraging the haptic properties of deformation and shape in future physical UI design.
Our design implications support practitioners in navigating the broad range of shape and deformation possibilities [4,37,55,59], and by doing so we begin to address one of the grand challenges within the feld [2].
The guidelines are particularly relevant for physical UIs of personal devices (e.g., phones, smartwatches, tablets) and fnger-based interactions with UI elements.Our recommendations provide a new design space to inform the next generation of physical signifers (see Figure 9).We present our implications in three parts: implications for emotion associations, implications for colour associations, and implications for eyes-free interaction.

Implications for Emotion Association
Our recommendations related to emotions (Design Recommendations 1-3) are designed for creating interface elements that map to user associations with emotions of pleasantness, arousal, and dominance.Incorporating these recommendations into UI design can create interfaces that align with users' emotional expectationscreating a 'multimodal harmony'-and/or interfaces that target specifc emotions to direct user experience and interaction.
Design Recommendation 1: Soft rounded shapes are best for eliciting pleasant associations.Harder, spiky shapes will elicit more unpleasant associations.
The combination of shape and stifness can directly impact user feelings of pleasantness in future physical interfaces.For example, it could allow game designers to manipulate the shape and feel of deformable controllers based on interactions with the video game environment (e.g., an unpleasant spiky object in a horror game).Further, it could be an additional design factor when nudging particular user behaviours.For example, a phone display becoming stifer as a motivator to reduce social media time or a softening display to promote reading time.
Design Recommendation 2: Spiky shapes are best for excitement, while rounder shapes are for calmer contexts.
Shape is the dictating property when considering arousal levels for user associations.For example, round UI elements could be used in a meditation app to convey calming associations or spiky shapes for a text message notifcation from a close friend inviting another friend to a party.This resonates with examples from prior research on shape-changing interfaces that aimed to calm users through an infatable round (balloon-like) interface [20] or to visually alert people of phone notifcations through a variety of shape resolutions [53].
Design Recommendation 3: Rounder protruding shapes are associated with high control, whereas spiky shapes can be used to associate less control.Making rounder shapes softer can increase this factor of control.
The shape of an object plays a signifcant role in the associated sense of control.Softening controls based on round shapes can elevate this sense of control.Compliant and shape-changing displays (e.g.[24,48,69,75]) can modify their controls' shape and stifness dynamically exert greater control.For example, in a graphic design tool, softer and more rounded controls could support the fne manipulation of graphics (and the opposite for courser, larger objects).
Figure 9: Visual overview of the design implications of using shape (exemplifed by a Kiki and Bouba shape) and stifness (soft, hard, or any stifness) for association with emotion and colour.For example, (1) indicates soft rounded shapes (white Bouba) are best for eliciting pleasant associations (left), whereas harder spiky shapes (black Kiki) with more unpleasant associations (right).Design recommendation (6) demonstrates that associations and recommendations (1)-( 5) can be used identically in eyes-free and eyes-on contexts.
This would enhance the sense of control, potentially leading to a more efcient user experience.
This recommendation could also be applied to interactions that extend beyond a display, where there are limited visual channels for emotional signifers.For example, when a drone is gradually fying out of signal range of its controller, the joystick area can become spiky to create an intuitive haptic mapping to notify the user of a lack of control, which they can experience irrespective their eyes' position (on or of the controller).

Implications for Colour Association
Hue and brightness can be used together, or individually, to complement shape-changing and/or deformable properties on a physical UI.Design Recommendations 4 & 5 explain how to use colours in physical UI design to ensure intuitive visual and tactile mapping.When users see colours in conjunction with haptic sensations from the interface elements, colour can reinforce stifness and shape signifers, either confrming something previously felt or providing feedforward on what to expect to feel.
Design Recommendation 4: Soft shapes should be used in conjunction with cooler colours (e.g.green and blue).While harder shapes should be used with warmer colours (e.g., red).
Design Recommendation 5: Soft-rounded or spiky shapes should be used in conjunction with high brightness.While harderrounded shapes should be used with darker colours.
When a UI designer has freedom of colour choice, they can use a specifc colour to signify stifness and shape and create sensory harmony (for example, a red button to indicate hardness), extending the work by Steer et al. [65] on colour and stifness associations.Conversely, they can subvert expectations by choosing opposing combinations (e.g. a soft red button).However, not all interfaces have the freedom to pick any colour, as there may be specifc requirements for branding, aesthetics, or application (e.g.simulating mixing of paint colours on a deformable display [66]).In such cases, designers can use brightness to associate diferent shapes and stifnesses.Prior work on confgurable platforms implementing shape-change and force [16,48] often utilise projection or LED technologies to convey colour (e.g. on a pin-based grid or deformable LED spheres), and can therefore make use of these recommendations to match colours for a variety of applications.

Implications for Eyes-Free Interactions
In scenarios where users are switching between eyes-on and eyesfree, designers can maintain the continuity of the signifer.Regardless of whether someone is looking at their device (e.g.phone, tablet), the stifness of the device can be associated with specifc emotions and colours.
Design Recommendation 6: Properties of shape and stifness can be used identically in both eyes-free and eyes-on contexts -users will make the same colour and emotional associations.
For example, recognising incoming phone calls from colleagues outside regular work hours becomes instinctive as the phone responds with a more pronounced spikiness upon being grasped, regardless of whether it is visible or in a pocket.This is particularly relevant to the feld as several works have highlighted the benefts of using tangibility for eyes-free interactions [11,57,58].

Summary
Our design recommendations contribute to actionable knowledge of how people perceive and associate visual-haptic interface elements.As we add our fndings to the growing repository of cross-modal study results, we pave the way for researchers and designers to develop multi-sensory interactions for shape-change and deformable interfaces confdently.By distilling our discoveries into actionable design recommendations, we envision a future where diverse tactile experiences, encompassing deformation, shapes, emotions, and colours, foster intuitive physical interfaces.Our work addresses grand challenges within the feld and provides fndings for shaping the next generation of physical signifers.We envision these principles being utilised across conventional UI components like buttons and innovative applications of deformable surfaces, including video games and entertainment experiences.

LIMITATIONS & FUTURE WORK
This study continues the investigation of CCs in physical user interfaces.In this work, we did not intentionally elicit emotions in the participants through the stimuli.We focused on the associations of deformable shapes with emotions (e.g.'this shape is pleasant)'.However, during interviews, some participants described experiencing emotions as well (e.g.'this shape makes me feel pleasant').
In future research, it may be valuable to incorporate bio-measures to understand better whether this study's results align with direct emotional elicitation.Further, while our study collected qualitative data on participant association strategies, future studies could focus on people's expectations based on how the stimuli looked.This would provide insight into how associations with colour and emotion relate to current fndings [65] when people could only see the stimuli.This would build a better understanding of user anticipations and expectations before interaction occurs, similar to work on shape-changing afordances from Tiab and Hornbaek [72].The next logical step in our research trajectory involves the exploration of dynamic shapes and dynamic stifnesses.Dynamicity may shed light on the evolving nature of cross-modal correspondences, providing insights into how users perceive and respond to changing shapes and stifness levels over time.Additionally, delving into dynamic shapes and stifness could have practical implications for developing interactive technologies, such as deformable interfaces in gaming, virtual reality, and other interactive applications.The shapes, and resulting design recommendations, have not yet been employed within "real-world" scenarios.It is therefore important for future work to investigate how this controlled understanding of shapes applies in real-world contexts to assess the ecological validity of the results, practical implications, and potential benefts and drawbacks.

CONCLUSION
This paper advanced our understanding of cross-modal correspondences for deformable shape interactions.More specifcally, it explored CCs between physical shape, stifness, colours, and emotions.Our research outcomes uncover a series of key takeaways: (1) shape and stifness properties consistently infuence users' colour and emotional associations across both visuo-tactile and tactile-only modalities; (2) soft shapes are associated with cooler colours and harder shapes with warmer colours; (3) high brightness is associated with combinations of soft-rounded, or spiky shapes while darker colours are associated with harder-rounded shapes; (4) soft-rounded shapes are associated with pleasant feelings, while harder, spiky shapes tend to evoke unpleasantness; (5) for creating excitement, spiky shapes are efective, while rounder shapes are suitable for calmer design; and (6) rounder protruding shapes convey a sense of high control and making them softer can enhance this feeling.These conclusions and their accompanying design guidelines aim to support designers and researchers in efectively engaging specifc human senses in the next generation of physical user interfaces.

Figure 2 :
Figure 2: The four Shapes used in the study (Left to right: Curve, Sinuous, Emerge, and Porous) for each of their Angularity's (Top: Kiki, Bottom: Bouba).Each shape was cast three times at the three Stifness levels.The image shows the Medium stifness versions of the shapes.

Figure 3 :
Figure 3: The three Stifnesses used in the study (Left to right: Soft, Medium, and Hard), when pressed with 500g by the index fnger of force on the Curved shape set.

Figure 4 :
Figure 4: Colour selection interface used in the study.The colour columns(2,5) were the primary selection columns, while adjacent columns (1, 3) and (4, 6), respectively, displayed the primary selection colour at its brightest (right) and darkest (left).The selected colour appears to the left of the slider, the brightness slider allows the participant to adjust the brightness before the fnal selection.

Figure 5 :
Figure 5: Left: Circuit diagram for FSR used in the study.Right: Force Platform used for each shape, with a Curve Bouba shape on it.

Figure 6 :
Figure 6: Study setup from the participant's perspective during the colour tactile-only condition.The touchscreen monitor is used to answer questions (on the left), the box cover is used to hide the stimuli (right).

Figure 7 :
Figure 7: Overview of Shapes for each Angularity (Columns: Bouba, Kiki), and Stifness (Rows: Soft, Medium, Hard) and associated colour values (for median Hue and average Brightness value) selected by the participants.

Figure 8 :
Figure 8: Overview distribution of emotion associations with deformable shapes across both Visibility conditions.Each of the emotions is plotted on axes from 0 to 100.Left: the shapes plotted for pleasure and arousal.Right: the shapes plotted for the dominance scale.The emotions value positions along the axes from 0-100.

Table 1 :
Signifcant efects from the ANOVA of Stifness, Angularity, and Visibility on Brightness for colour associations.

Table 3 :
Signifcant efects from ANOVA test of Stifness, Angularity, and Visibility on Pleasure for emotion associations.
* .011−.476) for Bouba over Kiki.For Stifness a post hoc analysis showed Hard was associated with a signifcantly higher control than Soft (

Table 6 :
Signifcant efects from ANOVA test of Stifness, Angularity, and Visibility on force participants applied during the colour associations tasks.value are marked with * for signifcant results where < .05,* * signifcance of < .01,and * * * for signifcance of < .001.

Table 7 :
Overview of force values (grams) applied by the participants for associations made during the colour tasks averaged across task Visibility conditions.

Table 8 :
Signifcant efects from ANOVA test of Stifness, Angularity, and Visibility on force participants applied during the Emotion association tasks.value are marked with * for signifcant results where < .05,* * signifcance of < .01,and * * * for signifcance of < .001.

Table 9 :
Overview of force values (Grams) applied by the participants for associations made during the emotions averaged across task Visibility conditions.