Application of Gaussian Curvature in Surface Modeling

Because Gaussian curvature actually reflects the curvature degree of the surface, Gaussian curvature analysis is the main basis for analyzing the quality and connection of the inner surface when modeling the surface in 3D CAD software. When the Gaussian curvature of a surface changes greatly and rapidly, the internal variation of the surface is relatively large, which means that the smoothness of the surface is low. However, if the Gaussian curvature of two connected surfaces suddenly changes on the common boundary, it means that the Gaussian curvature of the two surfaces is discontinuous, that is, the connection of the two surfaces does not reach the G2 connection quality.

In 3D CAD software, Gaussian curvature distribution of surfaces is usually represented by color distribution and variation of surfaces, such as ProE software. Through the change of these colors, we can intuitively know the change of Gaussian curvature of the surface, and the sudden change of color is the sudden change of Gaussian curvature.