This study assumed two key parameters that describe smoothness. Previously, the number of studies that defined smoothness with the concept of curvature has been limited. The parameters were the two physical characteristics of curvature: the number of waves and the amplitude of them. The purpose of the study was to observe which of the two parameters influences the perception of smoothness and to examine the relationship between the sense of aesthetic beauty and smoothness. The visual stimuli used in the study were transformed three-dimensional spheres, based on the combination of the three levels of the two parameters of nine distinct conditions. We analyzed the three responses that measured the preference of each visual stimuli, the familiarity score, and the smoothness evaluation score, each with the linear mixed model whose fixed effects were the two parameters and random effects were the participants' individual differences. Nearly the eighty percent of the variance of the smoothness evaluation score was explained by the linear model with the two key parameters and their interaction. The physical characteristics of a viewed object were far more significant than individual differences such as personality factors and the manner of art appreciation. In conclusion, the study examined the perception of smoothness based on the change of the physical characteristics of a shape. The study further recognized the relationship between smoothness and the aesthetic preference. No significant influence of the participants' individual difference such as gender, the degree in fine arts, personality factors, and the manner of art appreciation was observed. The amplitude of waves, rather than the number of them, was far more significant to the perception of smoothness.
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