Gaussian Curvature Entropy for Curved Surface Shape Generation

Area of Science:

• Industrial Design
• Computational Geometry
• Aesthetics

Background:

• Shape features like complexity and order are crucial in industrial product design.
• Controlling these features is challenging, relying heavily on designer intuition.
• Shape complexity influences perceived beauty and user preference.

Purpose of the Study:

• To propose a quantitative index for the complexity of curved surface shapes.
• To develop a shape generation method based on this complexity index for industrial design support.

Main Methods:

• Developed Gaussian curvature entropy as a complexity index for curved surfaces.
• Calculated the index using sampled and quantized Gaussian curvature data.
• Validated the index through sensory evaluation experiments with sample shapes.
• Constructed a shape generation method controlled by the complexity index.

Main Results:

• The proposed Gaussian curvature entropy index showed a strong correlation with perceived shape complexity (determination coefficient > 0.8).
• The shape generation method effectively produced diverse shapes by controlling complexity.
• The method was confirmed applicable in a car design context.

Conclusions:

• Gaussian curvature entropy is a reliable measure of perceived shape complexity.
• The developed shape generation method can assist designers by providing a range of complexity-controlled shapes.
• This approach offers a data-driven tool to enhance the design process for industrial products.