Notes

Physically Based Modelling

  • Simulation of physical systems including particles, soft- and rigid-bodies, fluids (Lagrangian and Eulerian). Integration techniques such as Euler (explicit, implicit, symplectic), Runge-Kutta, Verlet, etc. Discussion of various acceleration structures such as octrees, kd-trees, and bounding volume hierarchies.

Randomized Algorithms

  • Randomized algorithms over a traditional setting such as polynomial identity testing and Karger's min cut, and in the streaming model such as Count-Sketch and Morris' counter. Other covered topics are concentration inequalities (Chebyshev, Chernov), dimensionality reduction (Johnson-Lindenstrauss), heavy-hitters, clustering, coresets, Lovasz local lemma, linear programming, differential privacy.

Geometric Modelling

  • Concepts relating and pertaining to geometric and solid modelling. Topics such as Euclidean and differential geometry, free-form curves and surfaces, mesh and subdivision surfaces, point-clouds, and neural methods and representations.

Computer Animation

  • Mixture of artist defined and physically based animation. Keyframe interpolation, linear blend skinning, blendshapes, inverse kinematics, cloth simulation, position based dynamics.

Artificial Intelligence

  • Foundations of artificial intelligence (not ML). Informed search, heuristics, iterative improvement, game search, propositional logic, first-order logic, satisfiability, planning, intelligent agents, and knowledge systems.

Computational Photography

  • Algorithms and systems to overcome limitations in photography with standard cameras, enabling novel applications. Image formation and perspective, image blending, point processing, image warping, automatic image alignment, RANSAC, light-field photography, high-dynamic range and tonemapping, scene completion.

Cryptography

  • An exploration into the mathematical foundations of cryptography and how they are used in public- and private-key cryptosystems, with topics covering modular groups and fields, primality testing, factorization, and elliptic curves.