Concepts inOut-of-core and compressed level set methods
Level set method
The level set method (sometimes abbreviated as LSM) is a numerical technique for tracking interfaces and shapes. The advantage of the level set method is that one can perform numerical computations involving curves and surfaces on a fixed Cartesian grid without having to parameterize these objects (this is called the Eulerian approach).
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Out-of-core algorithm
Out-of-core or External memory algorithms are algorithms that are designed to process data that is too large to fit into a computer's main memory at one time. Such algorithms must be optimized to efficiently fetch and access data stored in slow bulk memory such as hard drive or tape drives. A typical example is geographic information systems, especially digital elevation models, where the full data set easily exceeds several gigabytes or even terabytes of data.
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Data compression
In computer science and information theory, data compression, source coding, or bit-rate reduction involves encoding information using fewer bits than the original representation. Compression can be either lossy or lossless. Lossless compression reduces bits by identifying and eliminating statistical redundancy. No information is lost in lossless compression. Lossy compression reduces bits by identifying marginally important information and removing it.
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Signed distance function
In mathematics and applications, the signed distance function of a set S in a metric space determines how close a given point x is to the boundary of S, with that function having positive values at points x inside S, it decreases in value as x approaches the boundary of S where the signed distance function is zero, and it takes negative values outside of S. Formally, if (X, d) is a metric space, the signed distance function f is defined by where and 'inf' denotes the infimum.
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Fluid simulation
Fluid simulation is an increasingly popular tool in computer graphics for generating realistic animations of water, smoke, explosions, and related phenomena. Given some input configuration of fluid and scene geometry, a fluid simulator evolves the motion of the fluid forward in time, making use of the (possibly heavily simplified) Navier-Stokes equations which describe the physics of fluids.
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Level set
In mathematics, a level set of a real-valued function f of n variables is a set of the form that is, a set where the function takes on a given constant value c. When the number of variables is two, a level set is generically a curve, called a level curve, contour line, or isoline. When n = 3, a level set is called a level surface, and for higher values of n the level set is a level hypersurface.
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Computational fluid dynamics
Computational fluid dynamics, usually abbreviated as CFD, is a branch of fluid mechanics that uses numerical methods and algorithms to solve and analyze problems that involve fluid flows. Computers are used to perform the calculations required to simulate the interaction of liquids and gases with surfaces defined by boundary conditions. With high-speed supercomputers, better solutions can be achieved.
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Scalar field
In mathematics and physics, a scalar field associates a scalar value to every point in a space. The scalar may either be a mathematical number, or a physical quantity. Scalar fields are required to be coordinate-independent, meaning that any two observers using the same units will agree on the value of the scalar field at the same point in space (or spacetime).
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