Computer Graphics: Geometric Modeling & Processing

The mathematical tools needed for the geometrical aspects of computer graphics and especially for modeling smooth shapes. The course covers classical computer-aided design, geometry processing, and data-driven approaches for shape generation. Fundamentals: homogeneous coordinates and transformation. Theory of parametric and implicit curve and surface models: polar forms, Bézier arcs and de Casteljau subdivision, continuity constraints, B-splines, tensor product, and triangular patch surfaces. Subdivision surfaces and multi-resolution representations of geometry. Surface reconstruction from scattered data points. Geometry processing on meshes, including simplification and parametrization. Deep neural generative models for 3D geometry: parametric and implicit approaches, VAEs and GANs. Prerequisite: linear algebra at the level of CME103. Recommended: CS248.