Topological Modeling for Visualization

Part 1 Foundation: curves; the notion of a Riemannian metric; local theory of surfaces; the classification of surfaces; abstract manifolds; critical points and Morse theory; analyzing human body motions using manifolds and critical points; computer examination of surfaces and Morse functions; height functions and discrete functions; homotopies and surface generation; homology; geodesics; transformation groups. Part 2 Advanced subjects: hyperbolic geometry and topology; Hamiltonian system with two degrees of freedom; topological and orbital analysis of integrable Hamiltonian systems; ridges, ravines and singularities.