Gaussian curvature entropy for curved surface shape generation

Akihiro Okano, Taishi Matsumoto, Takeo Kato

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


The overall shape features that emerge from combinations of shape elements, such as "complexity" and "order", are important in designing shapes of industrial products. However, controlling the features of shapes is difficult and depends on the experience and intuition of designers. Among these features, "complexity" is said to have an influence on the "beauty" and "preference" of shapes. This research proposed a Gaussian curvature entropy as a "complexity" index of a curved surface shape. The proposed index is calculated based on Gaussian curvature, which is obtained by the sampling and quantization of a curved surface shape and validated by the sensory evaluation experiment while using two types of sample shapes. The result indicates the correspondence of the index to perceived "complexity" (the determination coefficient is greater than 0.8). Additionally, this research constructed a shape generation method that was based on the index as a car design supporting apparatus, in which the designers can refer many shapes generated by controlling "complexity". The applicability of the proposed method was confirmed by the experiment while using the generated shapes.

Original languageEnglish
Article number353
Issue number3
Publication statusPublished - 2020 Mar 1


  • Complexity
  • Entropy
  • Gaussian curvature
  • Generative design

ASJC Scopus subject areas

  • General Physics and Astronomy


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