Concepts inFast and robust tracking of fluid surfaces
Fluid
In physics, a fluid is a substance that continually deforms (flows) under an applied shear stress. Fluids are a subset of the phases of matter and include liquids, gases, plasmas and, to some extent, plastic solids. In common usage, "fluid" is often used as a synonym for "liquid", with no implication that gas could also be present. For example, "brake fluid" is hydraulic oil and will not perform its required function if there is gas in it.
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Surface
In mathematics, specifically in topology, a surface is a two-dimensional topological manifold. The most familiar examples are those that arise as the boundaries of solid objects in ordinary three-dimensional Euclidean space R ¿ for example, the surface of a ball. On the other hand, there are surfaces, such as the Klein bottle, that cannot be embedded in three-dimensional Euclidean space without introducing singularities or self-intersections.
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Video tracking
Video tracking is the process of locating a moving object (or multiple objects) over time using a camera. It has a variety of uses, some of which are: human-computer interaction, security and surveillance, video communication and compression, augmented reality, traffic control, medical imaging and video editing. Video tracking can be a time consuming process due to the amount of data that is contained in video.
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Calculus of moving surfaces
The calculus of moving surfaces (CMS) is an extension of the classical tensor calculus to deforming manifolds. Central to the CMS is the -derivative whose original definition was put forth by Jacques Hadamard. It plays the role analogous to that of the covariant derivative on differential manifolds. In particular, it has the property that it produces a tensor when applied to a tensor. Suppose that is the evolution of the surface indexed by a time-like parameter .
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Marching cubes
Marching cubes is a computer graphics algorithm, published in the 1987 SIGGRAPH proceedings by Lorensen and Cline, for extracting a polygonal mesh of an isosurface from a three-dimensional scalar field. An analogous two-dimensional method is called the marching squares algorithm.
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Flow velocity
In fluid dynamics the flow velocity, or velocity field, of a fluid is a vector field which is used to mathematically describe the motion of a fluid. The length of the flow velocity vector is the flow speed.
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Advection
In chemistry, engineering and earth sciences, advection is a transport mechanism of a substance or conserved property by a fluid due to the fluid's bulk motion. An example of advection is the transport of pollutants or silt in a river by bulk water flow downstream. Another commonly advected quantity is energy or enthalpy. Here the fluid may be any material that contains thermal energy, such as water or air.
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Free surface
In physics, a free surface is the surface of a fluid that is subject to constant perpendicular normal stress and zero parallel shear stress, such as the boundary between two homogenous fluids, for example liquid water and the air in the Earth's atmosphere. Unlike liquids, gases cannot form a free surface on their own. A liquid in a gravitational field will form a free surface if unconfined from above.
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