Abstract. Physically based simulations are important for predicting the future states of the objects in consideration, and have been one of the major research topics in computer graphics. Applications include optical simulations for realistic image synthesis given a 3D scene, and rigid/fluid dynamics for computer animations. The need for the ultimate realism may sometimes ask for more efficient and accurate methods than those available in other fields. In addition, physically based optimizations are useful for designing and fabricating man-made objects given some desirable functionalities governed by physical laws. The ability to incorporate predictive simulations also allows us to build smarter robots that can optimize for their next movement based on the predictions. We introduce some of our work performed from this perspective.
IntroductionOur world is governed by physical laws: the way how light travels from the light source to our eye can be described by the radiative transport equation; the way how the water in a cup behaves as we interact with the cup is described by the Navier-Stokes equations. The ability of predicting such physical behaviors would allow us to estimate how objects would deform and how they would look like, and is hence useful for computer animations.Physical laws also come into play when we want to design and fabricate man-made objects. For example, understanding how the light refracts is essential for designing lenses, and understanding how the contact and frictional forces act against the gravity is important for designing a stable sculpture that is assembled from a number of small bricks. Optimizations with physically based constraints in consideration are thus fundamental for designing and fabricating functional man-made objects.With the ability to incorporate predictive simulations in planning, we can also build smarter robots that use vision techniques to acquire the external information, perform predictive simulations to estimate the future states of the objects, and determine the appropriate control based on the predicted states. In this paper, we will review and introduce a series of our past work done from the above perspective.