On Skin Model Describability using Laplace-Beltrami Operator for Geometrical Product Specification and Verification

The skin model serves as a foundational concept defined in ISO standards on Geometrical Product Specifications and verification (ISO GPS), facilitating the consideration of geometric variations on the surfaces of mechanical products. However, the lack of a solid scientific foundation and practical operational applications has become a barrier for skin model concept to keep up with the development of standardized feature operations. A previous investigation was devoted to a scientific approach to defining and interpreting the skin model for ISO GPS, grounded in the structure of solids and set theory. In this paper, the use of the Laplace-Beltrami Operator (LBO) is explored as a mathematical operation to enhance the computational representations of the skin model. The describability of skin model is achieved by applying LBO in both continuous and discrete cases. Geometric filter banks, established through LBO, are employed for skin model to identify defects at various scales of observation. An application of LBO is demonstrated through a case study to highlight the use of established geometric filter banks for skin model. Further discussions show that the spectral analysis of a surface using LBO enables the characterization of skin model, contributing to the current and future standardization of geometrical product specification and verification. Finally, conclusion and future works are highlighted.