Concepts inComputer rendering of stochastic models
Stochastic calculus
Stochastic calculus is a branch of mathematics that operates on stochastic processes. It allows a consistent theory of integration to be defined for integrals of stochastic processes with respect to stochastic processes. It is used to model systems that behave randomly.
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Rendering (computer graphics)
Rendering is the process of generating an image from a model (or models in what collectively could be called a scene file), by means of computer programs. A scene file contains objects in a strictly defined language or data structure; it would contain geometry, viewpoint, texture, lighting, and shading information as a description of the virtual scene.
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Fractional Brownian motion
In probability theory, a normalized fractional Brownian motion (fBm), also called a fractal Brownian motion, is a continuous-time Gaussian process BH(t) on [0, T 0, T], which starts at zero, has expectation zero for all t in [0, T 0, T], and has the following covariance function: where H is a real number in (0, 1), called the Hurst index or Hurst parameter associated with the fractional Brownian motion.
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Sample-continuous process
In mathematics, a sample-continuous process is a stochastic process whose sample paths are almost surely continuous functions.
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Stochastic process
In probability theory, a stochastic process, or sometimes random process (widely used) is a collection of random variables; this is often used to represent the evolution of some random value, or system, over time. This is the probabilistic counterpart to a deterministic process.
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Computer graphics
Computer graphics are graphics created using computers and, more generally, the representation and manipulation of image data by a computer with help from specialized software and hardware. The development of computer graphics has made computers easier to interact with, and better for understanding and interpreting many types of data. Developments in computer graphics have had a profound impact on many types of media and have revolutionized animation, movies and the video game industry.
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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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