Discrete Differential Geometry

This lecture covers topics in discrete differential geometry, starting with differential operators like divergence and Laplace operator. It then delves into Laplace-Beltrami operator, functions on triangle meshes, basis functions, discrete curvatures, and Laplace operator in 1D and 2D. The instructor explains the discretization of differential operators on triangle meshes, including the computation of Gauss curvature and mean curvature. Various discretization methods such as uniform discretization and cotangent discretization are discussed, along with their properties and implications. The lecture concludes with the computation of principal curvatures from mean and Gaussian curvatures.