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Particle System
A particle system is a technique in game physics, motion graphics, and computer graphics that uses many minute sprites, 3D models, or other graphic objects to simulate certain kinds of "fuzzy" phenomena, which are otherwise very hard to reproduce with conventional rendering techniques – usually highly chaotic systems, natural phenomena, or processes caused by chemical reactions. Introduced in the 1982 film '' Star Trek II: The Wrath of Khan'' for the fictional "Genesis effect", other examples include replicating the phenomena of fire, explosions, smoke, moving water (such as a waterfall), sparks, falling leaves, rock falls, clouds, fog, snow, dust, meteor tails, stars and galaxies, or abstract visual effects like glowing trails, magic spells, etc. – these use particles that fade out quickly and are then re-emitted from the effect's source. Another technique can be used for things that contain many strands – such as fur, hair, and grass – involving rendering an e ...
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Particle Sys Fire
In the physical sciences, a particle (or corpuscle in older texts) is a small localized object which can be described by several physical or chemical properties, such as volume, density, or mass. They vary greatly in size or quantity, from subatomic particles like the electron, to microscopic particles like atoms and molecules, to macroscopic particles like powders and other granular materials. Particles can also be used to create scientific models of even larger objects depending on their density, such as humans moving in a crowd or celestial bodies in motion. The term ''particle'' is rather general in meaning, and is refined as needed by various scientific fields. Anything that is composed of particles may be referred to as being particulate. However, the noun ''particulate'' is most frequently used to refer to pollutants in the Earth's atmosphere, which are a suspension of unconnected particles, rather than a connected particle aggregation. Conceptual properties The co ...
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Dust
Dust is made of particle size, fine particles of solid matter. On Earth, it generally consists of particles in the atmosphere that come from various sources such as soil lifted by wind (an aeolian processes, aeolian process), Types of volcanic eruptions, volcanic eruptions, and pollution. Dust in homes is composed of about 20–50% dead skin Cell (biology), cells. The rest, and in offices and other built environments, is composed of small amounts of plant pollen, human hairs, animal fur, textile fibers, paper fibers, minerals from outdoor soil, burnt meteorite particles, and many other materials which may be found in the local environment. Atmospheric Atmospheric or wind-borne fugitive dust, also known as ''aeolian dust'', comes from dry regions where high-speed winds can remove mostly silt-sized material, abrading susceptible surfaces. This includes areas where grazing, ploughing, vehicle use, and other human behaviors have further destabilized the land, though not all so ...
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Quadrilateral
In Euclidean geometry, geometry a quadrilateral is a four-sided polygon, having four Edge (geometry), edges (sides) and four Vertex (geometry), corners (vertices). The word is derived from the Latin words ''quadri'', a variant of four, and ''latus'', meaning "side". It is also called a tetragon, derived from Greek "tetra" meaning "four" and "gon" meaning "corner" or "angle", in analogy to other polygons (e.g. pentagon). Since "gon" means "angle", it is analogously called a quadrangle, or 4-angle. A quadrilateral with vertices A, B, C and D is sometimes denoted as \square ABCD. Quadrilaterals are either simple polygon, simple (not self-intersecting), or complex polygon, complex (self-intersecting, or crossed). Simple quadrilaterals are either convex polygon, convex or concave polygon, concave. The Internal and external angle, interior angles of a simple (and Plane (geometry), planar) quadrilateral ''ABCD'' add up to 360 Degree (angle), degrees, that is :\angle A+\angle B+\angle ...
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Texture Mapped
Texture mapping is a term used in computer graphics to describe how 2D images are projected onto 3D models. The most common variant is the UV unwrap, which can be described as an inverse paper cutout, where the surfaces of a 3D model are cut apart so that it can be unfolded into a 2D coordinate space (UV Space). Semantic Texture mapping can both refer to the task of unwrapping a 3D model, the abstract that a 3D model has textures applied to it and the related algorithm of the 3D software. Texture map refers to a Raster graphics also called image, texture. If the texture stores a specific property it's also referred to as color map, roughness map, etc. The coordinate space which converts from the 3D space of a 3D model into a 2D space so that it can sample from the Texture map is called: UV Space, UV Coordinates, Texture Space. Algorithm A simplified explanation of how an algorithm could work to render an image: # For each pixel we trace the coordinates of the screen ...
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Collision Detection
Collision detection is the computational problem of detecting an intersection of two or more objects in virtual space. More precisely, it deals with the questions of ''if'', ''when'' and ''where'' two or more objects intersect. Collision detection is a classic problem of computational geometry with applications in computer graphics, physical simulation, video games, robotics (including autonomous driving) and computational physics. Collision detection algorithms can be divided into operating on 2D or 3D spatial objects. Overview Collision detection is closely linked to calculating the distance between objects, as two objects (or more) intersect when the distance between them reaches zero or even becomes negative. Negative distance indicates that one object has penetrated another. Performing collision detection requires more context than just the distance between the objects. Accurately identifying the points of contact on both objects' surfaces is also essential for the co ...
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Translation (geometry)
In Euclidean geometry, a translation is a geometric transformation that moves every point of a figure, shape or space by the same Distance geometry, distance in a given direction (geometry), direction. A translation can also be interpreted as the addition of a constant vector space, vector to every point, or as shifting the Origin (mathematics), origin of the coordinate system. In a Euclidean space, any translation is an isometry. As a function If \mathbf is a fixed vector, known as the ''translation vector'', and \mathbf is the initial position of some object, then the translation function T_ will work as T_(\mathbf)=\mathbf+\mathbf. If T is a translation, then the image (mathematics), image of a subset A under the function (mathematics), function T is the translate of A by T . The translate of A by T_ is often written as A+\mathbf . Application in classical physics In classical physics, translational motion is movement that changes the Position (geometry), positio ...
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Surface Normal
In geometry, a normal is an object (e.g. a line, ray, or vector) that is perpendicular to a given object. For example, the normal line to a plane curve at a given point is the infinite straight line perpendicular to the tangent line to the curve at the point. A normal vector is a vector perpendicular to a given object at a particular point. A normal vector of length one is called a unit normal vector or normal direction. A curvature vector is a normal vector whose length is the curvature of the object. Multiplying a normal vector by results in the opposite vector, which may be used for indicating sides (e.g., interior or exterior). In three-dimensional space, a surface normal, or simply normal, to a surface at point is a vector perpendicular to the tangent plane of the surface at . The vector field of normal directions to a surface is known as '' Gauss map''. The word "normal" is also used as an adjective: a line ''normal'' to a plane, the ''normal'' component of ...
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Dynamic Simulation Of Air Particles (Bifröst)
Dynamics (from Greek δυναμικός ''dynamikos'' "powerful", from δύναμις ''dynamis'' "power") or dynamic may refer to: Physics and engineering * Dynamics (mechanics), the study of forces and their effect on motion Brands and enterprises * Dynamic (record label), an Italian record label in Genoa Mathematics * Dynamical system, a concept describing a point's time dependency ** Topological dynamics, the study of dynamical systems from the viewpoint of general topology * Symbolic dynamics, a method to model dynamical systems Social science * Group dynamics, the study of social group processes especially * Population dynamics, in life sciences, the changes in the composition of a population * Psychodynamics, the study of psychological forces driving human behavior * Social dynamics, the ability of a society to react to changes * Spiral Dynamics, a social development theory Other uses * Dynamics (music), the softness or loudness of a sound or note * DTA Dynamic, a ...
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Affine Transformations
In Euclidean geometry, an affine transformation or affinity (from the Latin, '' affinis'', "connected with") is a geometric transformation that preserves lines and parallelism, but not necessarily Euclidean distances and angles. More generally, an affine transformation is an automorphism of an affine space (Euclidean spaces are specific affine spaces), that is, a function which maps an affine space onto itself while preserving both the dimension of any affine subspaces (meaning that it sends points to points, lines to lines, planes to planes, and so on) and the ratios of the lengths of parallel line segments. Consequently, sets of parallel affine subspaces remain parallel after an affine transformation. An affine transformation does not necessarily preserve angles between lines or distances between points, though it does preserve ratios of distances between points lying on a straight line. If is the point set of an affine space, then every affine transformation on can be re ...
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Fluid Mechanics
Fluid mechanics is the branch of physics concerned with the mechanics of fluids (liquids, gases, and plasma (physics), plasmas) and the forces on them. Originally applied to water (hydromechanics), it found applications in a wide range of disciplines, including mechanical engineering, mechanical, aerospace engineering, aerospace, civil engineering, civil, chemical engineering, chemical, and biomedical engineering, as well as geophysics, oceanography, meteorology, astrophysics, and biology. It can be divided into ''fluid statics'', the study of various fluids at rest; and ''fluid dynamics'', the study of the effect of forces on fluid motion. It is a branch of ''continuum mechanics'', a subject which models matter without using the information that it is made out of atoms; that is, it models matter from a macroscopic viewpoint rather than from microscopic. Fluid mechanics, especially fluid dynamics, is an active field of research, typically mathematically complex. Many problems a ...
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Dynamical System
In mathematics, a dynamical system is a system in which a Function (mathematics), function describes the time dependence of a Point (geometry), point in an ambient space, such as in a parametric curve. Examples include the mathematical models that describe the swinging of a clock pendulum, fluid dynamics, the flow of water in a pipe, the Brownian motion, random motion of particles in the air, and population dynamics, the number of fish each springtime in a lake. The most general definition unifies several concepts in mathematics such as ordinary differential equations and ergodic theory by allowing different choices of the space and how time is measured. Time can be measured by integers, by real number, real or complex numbers or can be a more general algebraic object, losing the memory of its physical origin, and the space may be a manifold or simply a Set (mathematics), set, without the need of a Differentiability, smooth space-time structure defined on it. At any given time, ...
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Stochastic Processes
In probability theory and related fields, a stochastic () or random process is a mathematical object usually defined as a family of random variables in a probability space, where the index of the family often has the interpretation of time. Stochastic processes are widely used as mathematical models of systems and phenomena that appear to vary in a random manner. Examples include the growth of a bacterial population, an electrical current fluctuating due to thermal noise, or the movement of a gas molecule. Stochastic processes have applications in many disciplines such as biology, chemistry, ecology, neuroscience, physics, image processing, signal processing, control theory, information theory, computer science, and telecommunications. Furthermore, seemingly random changes in financial markets have motivated the extensive use of stochastic processes in finance. Applications and the study of phenomena have in turn inspired the proposal of new stochastic processes. Examples of su ...
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