Surfaces with Variable Curvature

This lecture covers the concept of surfaces with variable curvature, focusing on the analysis of Gaussian curvature and the mean curvature at a given point. It explains how to distinguish between convex and concave regions on a surface based on the sign of the curvature. The lecture also delves into the importance of the Gaussian curvature, which remains independent of the orientation of surface normals. Additionally, it discusses the average curvature and the minimal oriented curvature, essential for understanding the machining capabilities of a surface. Various notions of curvature are explored, including the mean curvature and the radius of curvature, providing insights into surface properties and tooling requirements.