Make it Stand: Geometric Computing

This lecture explores the concept of making a geometric object stand by analyzing static equilibria, geometric data representations, and shape optimization. It delves into torque and force balance, the equivalence of gravity with point load, and the conditions for an object to be in stable equilibrium. The instructor discusses barycentric coordinates, balancing a triangle, and the computation of centroids in triangle meshes. Additionally, transformations such as scaling, rotation, and shear are examined, focusing on how they affect the centroid of a triangle. The importance of shape preservation in maintaining the initial shape of an object is emphasized throughout the lecture.