Physically-based modeling and simulation attempts to map a natural phenomena to a computer simulation program. There are two basic processes in this mapping: mathematical modeling and numerical solution. The goal of this introductory course is to understand both of them. The mathematical modeling concerns the description of natural phenomena by mathematical equations. Differential equations that govern dynamics and geometric representation of objects are typical ingredients of the mathematical model. The numerical solution involves computing an efficient and accurate solution of the mathematical equations. Finite precision of numbers, limited computational power and memory forces us to approximate the mathematical model with simple procedures.

There are two major research directions in computer vision: reconstruction aims at geometrically recreating the 3D world from the 2D photos/videos and recognition aims at extracting the semantics of objects and actions out of the images.