Short and sweetSurface shape alters perceived
material softness

i-Perception
2024, Vol. 15(2), 1–4© The Author(s) 2024
DOI: 10.1177/20416695241245021
journals.sagepub.com/home/ipe

Hongbo Wang
Tokyo Metropolitan University, Tokyo, Japan

Qingyu Sun
University of Tokyo, Tokyo, Japan

Shogo Okamoto
Tokyo Metropolitan University, Tokyo, Japan

Abstract
When a human strokes the surface of an object with his/her ﬁnger, the surface shape inﬂuences theperceived softness of the object. This study introduced a curved surface softness illusion, whichalters the perception of material softness. When a surface with curvature is felt by sliding a ﬁnger
over it, it feels softer than a ﬂat surface made of the same material. In contrast, a rugged surface isperceived as harder. This illusion indicates that, in addition to mechanical hardness, humans judge
an object’s softness based on its surface shape.
Keywords
hardness, texture, elasticity
Date received: 12 November 2023; accepted: 19 March 2024

Many researchers believe that pressing is the most common and effective motion for exploring thesoftness of an object. However, to investigate softness, humans employ stroking or rubbing motions
as frequently as pressing motions (Arakawa et al., 2021; Cavdan et al., 2021). When a human strokes
the surface of an object with his/her ﬁnger, the surface topology also inﬂuences the softness felt by
the object. Thus far, the inﬂuence of surface shape on softness perception has not been demonstrated. The current study demonstrated the “curved surface softness illusion,” where objects withdifferent surface features feel differently soft even if they are made of the same material.
We created four three-dimensionally printed plastic specimens, as shown in Figure 1 and Table 1.
Two of these specimens were ﬂat and smooth, but different in terms of material hardness. One wasas hard as a plastic eraser (Young’s modulus: 2.46 MPa), and the other was as hard as a bouncing
Corresponding author:
Shogo Okamoto, Tokyo Metropolitan University, Tokyo, Japan.
Email: okamotos@tmu.ac.jp
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2i-Perception 15(2)Figure 1. Samples arranged from softest to hardest (left to right). From left: gently waved (9.35 MPa), ﬂat andsoft (2.46 MPa), ﬂat (9.35 MPa), and rugged (9.35 MPa).

Table 1. Stimuli parameters.
SoftnessrankSpecimen

Amplitude
A (mm)

Wavelength
λ (mm)

Young’smodulus (MPa)1134

Gently waved
Flat and soft
FlatRugged

0.5——
0.7550——109.35 (bouncing ball level)
2.46 (eraser level)
9.35 (bouncing ball level)
9.35 (bouncing ball level)

rubber ball (9.35 MPa). The other two specimens were composed of a resin with Youngs’ modulusof 9.35 MPa and exhibited sinusoidal surface displacements with distinct wavelengths (λ in mm) andamplitudes (A in mm). The values for one specimen were λ = 10 mm and A = 0.75 mm. The values
for the other specimens were λ = 50 mm and A = 0.5 mm.
We asked 15 university students to rank the four specimens in the order of their perceived softness. Blindfolded participants stroked the randomly arranged specimens with their index ﬁngers toprobe their softness without pressing. No reference speed and contact force were provided. The specimens were lubricated with talcum powder to eliminate the differences in surface adhesion.
As shown in Figure 2, all the participants judged the ﬂat specimen with Young’s modulus of 2.46
MPa to be softer than that of 9.35 MPa. The gently waved specimen felt softer than the ﬂat specimen
made of the same material (14 participants). Statistical signiﬁcance was determined for each of thesetwo pairs. Furthermore, the rugged surface felt harder than the ﬂat specimen made of the samematerial (12 participants). Nine participants judged the gently waved surface to be softer than aﬂat surface made of the softest material. Hence, they largely agreed on the order of softness asfollows: gently waved surface with Young’s modulus of 9.35 MPa, ﬂat surface of 2.46 MPa, ﬂatsurface of 9.35 MPa, and rugged surface of 9.35 MPa.
The question here is what caused these results. There are several possible explanations for this.
(i) Contact area and softness judgment. The above effect may be considered similar to the ﬁngersized bump illusion (Inoue et al., 2022), where pressing a ﬁnger-sized concave surface with aﬁngertip causes it to feel softer and a ﬁnger-sized convex surface to feel harder than a ﬂatsurface. Researchers have explained that a surface with a larger contact area feels softer,

Wang et al.

3Figure 2. Summary of the trends in softness judgment. Filled human ﬁgures indicate the number of people inagreement with softness inequality.

whereas evoking a smaller contact area feels harder. When a ﬁngertip glides over a sinusoidal
displacement of λ = 10 mm, which is smaller than the width of the ﬁngertip, the entire area of
the ﬁnger pad does not ﬁt into the sinusoidal groove, resulting in a small real contact area.
Hence, rugged surfaces can be felt harder. However, the gently waved specimen, whichfeels softer than the ﬂat surface, comprises both concave and convex surfaces that are slightly
larger than the ﬁngertip. Therefore, the ﬁnger-sized bump illusion does not fully explain thesoftness experienced when stroking such surface proﬁles.
(ii) Inﬂuence of slow changes in friction on softness. When a ﬁnger slides on a bumped surface, its
gradient is associated with alterations in the tangential resistive force (Robles-De-La-Torre &Hayward, 2001). According to an experiment conducted by Ito et al. (2017), such a variation inforce may evoke a sense of softness. However, their experiment does not explain why mostparticipants judged rugged surfaces to be hard.
(iii) Perceptual-linkage between roughness and softness. Hardness and roughness can be associatedwith each other through common sound symbols (Eitan & Rothschild, 2010). For example,
high-pitched sounds evoke sensations of roughness and decreased softness. If these two distinct
features share a similar multisensory process, it is conceivable that they can be conceptually
mixed. It is important to note that the present experiment does not involve sounds, and therugged surfaces used in our experiment suggest hardness without the involvement of sounds.
As mentioned above, the existing knowledge partly explains the effects of curved surfaces on softness judgment; however, the precise mechanisms underlying this experience remain unclear.
Multiple principles may interact with or offset each other under speciﬁc conditions, leading to
the complex mechanisms underlying this illusion. Further experimental validation is required tounderstand the effects of surface proﬁles on softness judgment.
This study found that the surface proﬁle affected the perception of softness when stroked by aﬁngertip. Thus, the ﬁndings of this study shed light on human haptic perception and may also
have implications in the ﬁeld of product design.
Author Contribution(s)Hongbo Wang: Data curation; Formal analysis; Investigation; Methodology; Resources; Visualization;
Writing – original draft; Writing – review & editing.

4i-Perception 15(2)Qingyu Sun: Conceptualization; Methodology; Writing – review & editing.
Shogo Okamoto: Conceptualization; Formal analysis; Formal analysis; Investigation; Methodology;
Project administration; Supervision; Writing – original draft; Writing – review & editing.

Declaration of Conﬂicting Interests
The authors declared no potential conﬂicts of interest with respect to the research, authorship, and/or publication of this article.

Funding
The authors received no ﬁnancial support for the research, authorship, and/or publication of this article.

ORCID iD
Shogo Okamoto

https://orcid.org/0000-0003-2116-7734

References
Arakawa, N., Watanabe, T., Fukushima, K., & Nakatani, M. (2021). Sensory words may facilitate certain haptic
exploratory procedures in facial cosmetics. International Journal of Cosmetic Science, 43, 78–87. https://doi.org/10.1111/ics.12671
Cavdan, M., Doerschner, K., & Drewing, K. (2021). Task and material properties interactively affect softness
explorations along different dimensions. IEEE Transactions on Haptics, 14, 603–614. https://doi.org/10.
1109/TOH.2021.3069626
Eitan, Z., & Rothschild, I. (2010). How music touches: Musical parameters and listeners’ audio-tactile metaphorical mappings. Psychology of Music, 39, 449–467. https://doi.org/10.1177/030573561037759
Inoue, K., Okamoto, S., Akiyama, Y., & Yamada, Y. (2022). Surfaces with ﬁnger-sized concave feel softer.
IEEE Transactions on Haptics, 15, 32–38. https://doi.org/10.1109/TOH.2021.3138640
Ito, K., Okamoto, S., Elfekey, H., Kajimoto, H., & Yamada, Y. (2017, October 24–27). Feeling softness on ahard touch panel using an electrostatic tactile texture display. In: 2017 IEEE 6th global conference on consumer electronics (GCCE), Nagoya, Japan, pp. 1–2. https://doi.org/10.1109/GCCE.2017.8229484
Robles-De-La-Torre, G., & Hayward, V. (2001). Force can overcome object geometry in the perception ofshape through active touch. Nature, 412, 445–448. https://doi.org/10.1038/35086588

How to cite this article
Wang, H., Sun, Q., & Okamoto, S. (2024). Surface shape alters perceived material softness. i-Perception,15(2), 1–4. https://doi.org/10.1177/20416695241245021