This course covers the path from a conceptual vision of a shape to a concrete computer-based description that is suitable for manufacturing. It covers various solids modeling techniques, including volume representations, boundary representations, instantiation and Boolean combinations of shapes, and procedural generation such as sweeps.
Overview of current concepts and issues in CAGD with emphasis on free-form surface design; mathematics of free-form curve and surface representations, including Coons patches, Gregory patches, Bezier method, B-splines, NURBS, triangular interpolants, and their geometric consequences; creating objects with smooth surfaces, covering assembling spline patches, geometric and parametric continuity, texture mapping onto complex shapes, subdivision surfaces, surface evolution, and global optimization.
This course covers fundamental techniques in multimedia systems for capturing, managing, accessing and delivering digital media over local, wide-area and wireless network technology. The core topics will emphasize the digital media (images, video, audio) and the algorithms to generate, store, access and process it. Network concepts will be presented at a high level only.
This course covers a mixture of core techniques related to systems for constructing and modeling virtual environments, such as model- building, image-based rendering, head-mounted hardware, stereo image generation, head- tracking, and immersive display technology. The core topics will be presented using textbooks and papers from the current literature. A substantial group project will provide hands-on experience with the concepts, algorithms and technology.
The objective of the course is to prepare students for research in the field of supervisory control of discrete event systems (DES's). Logical models, supervising control. Stability and optimal control of DES, complexity analysis and other related research areas will be covered.
Overview of modern artificial intelligence. Covers topics such as searching and game trees, knowledge representation techniques, methods to represent uncertain information and to reason about it, reasoning about action and planning, expert systems, machine learning and neural networks.
The problem of correct transmission of data in a noisy environment. The design and analysis of codes that efficiently (in terms of data rate and encryption and decryption speed) correct errors. Linear and nonlinear block codes, general encoding and decoding techniques, fundamental bounds, dual codes, cyclic codes. Specific codes will be studied, including Hamming, BCH, Reed- Muller, Reed-Solomon, trellis, and convolutional codes.
Solving problems that are intractable. Exact techniques such as search integer programming and dynamic programming. Approximation techniques including local search, divide and conquer, and greedy algorithms. Methods based upon natural models such as force-directed iteration, simulated annealing, genetic algorithms, and neural networks. Examples will be selected from active research areas.
The formal study of computation, including computability and computation with limited resources. Church's thesis and models of computation. Topics will include Turing machines or other basic models of computation; reductions; computable and computably enumerable sets; Rice's Theorem; decidability and undecidability; basic complexity theory; NP-completeness and notions of intractability.
The study of intrinsic parallelism in computational problems and the design of fast and efficient parallel algorithms. Parallel algorithms for prefix computation, selection, merging, sorting, routing, arithmetic, graph, and systolic algorithms.
