Quantification of “complexity” in curved surface shape using total absolute curvature

Taishi Matsumoto, Koichiro Sato, Yoshiyuki Matsuoka, Takeo Kato

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)


In recent years, with the popularization of 3D-CAD, various curved surface shapes have been used in the styling of industrial products. However, evaluation and control of shape features are done in trial and error based on the experience and intuition of the designer, causing the inefficiency of styling design. Therefore, this study aims to support the styling design by quantifying cognitive characteristics in curved surface shape. First, this research proposed total absolute curvature to quantify “complexity”, which is one of the shape features related to “beauty”, and described its geometric meaning as the total area of the Gauss map on the curved surface shape. Next, the tangible calculation method is shown by applying it to the curved surface shape represented by a triangular polygon mesh. Then, sensory evaluation experiments were carried out using three types of shapes generated by extrusion, rotation, and emergent shape generation system to confirm the applicability of the proposed quantification method. Finally, the result revealed that the logarithmic approximation between the proposed index and human perceived “complexity”.

Original languageEnglish
Pages (from-to)108-115
Number of pages8
JournalComputers and Graphics (Pergamon)
Publication statusPublished - 2019 Feb


  • Gaussian curvature
  • Shape complexity
  • Surface design

ASJC Scopus subject areas

  • Software
  • Signal Processing
  • Engineering(all)
  • Human-Computer Interaction
  • Computer Vision and Pattern Recognition
  • Computer Graphics and Computer-Aided Design


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