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Marching Squares
In computer graphics, marching squares is an algorithm that generates contours for a two-dimensional scalar field (rectangular array of individual numerical values). A similar method can be used to contour 2D triangle meshes. The contours can be of two kinds: * ''Isolines'' – lines following a single data level, or ''isovalue''. * ''Isobands '' – filled areas between isolines. Typical applications include the contour lines on topographic maps or the generation of isobars for weather maps. Marching squares takes a similar approach to the 3D marching cubes algorithm: * Process each cell in the grid independently. * Calculate a cell index using comparisons of the contour level(s) with the data values at the cell corners. * Use a pre-built lookup table, keyed on the cell index, to describe the output geometry for the cell. * Apply linear interpolation along the boundaries of the cell to calculate the exact contour position. Basic algorithm Here are the steps of the algorithm: ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Graphics
Computer graphics deals with generating images with the aid of computers. Today, computer graphics is a core technology in digital photography, film, video games, cell phone and computer displays, and many specialized applications. A great deal of specialized hardware and software has been developed, with the displays of most devices being driven by computer graphics hardware. It is a vast and recently developed area of computer science. The phrase was coined in 1960 by computer graphics researchers Verne Hudson and William Fetter of Boeing. It is often abbreviated as CG, or typically in the context of film as computer generated imagery (CGI). The non-artistic aspects of computer graphics are the subject of computer science research. Some topics in computer graphics include user interface design, sprite graphics, rendering, ray tracing, geometry processing, computer animation, vector graphics, 3D modeling, shaders, GPU design, implicit surfaces, visualization, scientific c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Marching Squares Algorithm
In computer graphics, marching squares is an algorithm that generates contours for a two-dimensional scalar field (rectangular array of individual numerical values). A similar method can be used to contour 2D triangle meshes. The contours can be of two kinds: * ''Isolines'' – lines following a single data level, or ''isovalue''. * ''Isobands '' – filled areas between isolines. Typical applications include the contour lines on topographic maps or the generation of isobars for weather maps. Marching squares takes a similar approach to the 3D marching cubes algorithm: * Process each cell in the grid independently. * Calculate a cell index using comparisons of the contour level(s) with the data values at the cell corners. * Use a pre-built lookup table, keyed on the cell index, to describe the output geometry for the cell. * Apply linear interpolation along the boundaries of the cell to calculate the exact contour position. Basic algorithm Here are the steps of the algorithm: ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quadrilateral
In geometry a quadrilateral is a four-sided polygon, having four edges (sides) and four 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 (not self-intersecting), or complex (self-intersecting, or crossed). Simple quadrilaterals are either convex or concave. The interior angles of a simple (and planar) quadrilateral ''ABCD'' add up to 360 degrees of arc, that is :\angle A+\angle B+\angle C+\angle D=360^. This is a special case of the ''n''-gon interior angle sum formula: ''S'' = (''n'' − 2) × 180°. All non-self-crossing quadrilaterals tile the plane, b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Topology
In mathematics, topology (from the Greek language, Greek words , and ) is concerned with the properties of a mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformations, such as Stretch factor, stretching, Twist (mathematics), twisting, crumpling, and bending; that is, without closing holes, opening holes, tearing, gluing, or passing through itself. A topological space is a set (mathematics), set endowed with a structure, called a ''Topology (structure), topology'', which allows defining continuous deformation of subspaces, and, more generally, all kinds of continuity (mathematics), continuity. Euclidean spaces, and, more generally, metric spaces are examples of a topological space, as any distance or metric defines a topology. The deformations that are considered in topology are homeomorphisms and homotopy, homotopies. A property that is invariant under such deformations is a topological property. Basic exampl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Marching Triangles Isobands
Marching refers to the organized, uniformed, steady walking forward in either rhythmic or route-step time; and, typically, it refers to overland movements on foot of military troops and units under field orders. Marching is often performed to march music and is typically associated with military and civilian ceremonial parades. It is a major part of military basic training in most countries and usually involves a system of drill commands. Purpose It is said that many ancient empires first developed marching as a way to move troops from one place to another without them getting mixed up with other troops. A soldier learning to march to drum cadences, martial music and shouted commands is considered an essential element of teaching military discipline. In the United States Marine Corps, close order drill is used to promote exercise, obeying orders, discipline, esprit de corps, confidence, and leadership. Military paces In the military venue there are various rhythmic mili ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Level Set
In mathematics, a level set of a real-valued function of real variables is a set where the function takes on a given constant value , that is: : L_c(f) = \left\~, When the number of independent variables is two, a level set is called a level curve, also known as ''contour line'' or ''isoline''; so a level curve is the set of all real-valued solutions of an equation in two variables and . When , a level set is called a level surface (or ''isosurface''); so a level surface is the set of all real-valued roots of an equation in three variables , and . For higher values of , the level set is a level hypersurface, the set of all real-valued roots of an equation in variables. A level set is a special case of a fiber. Alternative names Level sets show up in many applications, often under different names. For example, an implicit curve is a level curve, which is considered independently of its neighbor curves, emphasizing that such a curve is defined by an implicit e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Marching Triangles Isolines
Marching refers to the organized, uniformed, steady walking forward in either rhythmic or route-step time; and, typically, it refers to overland movements on foot of military troops and units under field orders. Marching is often performed to march music and is typically associated with military and civilian ceremonial parades. It is a major part of military basic training in most countries and usually involves a system of drill commands. Purpose It is said that many ancient empires first developed marching as a way to move troops from one place to another without them getting mixed up with other troops. A soldier learning to march to drum cadences, martial music and shouted commands is considered an essential element of teaching military discipline. In the United States Marine Corps, close order drill is used to promote exercise, obeying orders, discipline, esprit de corps, confidence, and leadership. Military paces In the military venue there are various rhythmic mili ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Isolines
A contour line (also isoline, isopleth, or isarithm) of a function of two variables is a curve along which the function has a constant value, so that the curve joins points of equal value. It is a plane section of the three-dimensional graph of the function f(x,y) parallel to the (x,y)-plane. More generally, a contour line for a function of two variables is a curve connecting points where the function has the same particular value. In cartography, a contour line (often just called a "contour") joins points of equal elevation (height) above a given level, such as mean sea level. A contour map is a map illustrated with contour lines, for example a topographic map, which thus shows valleys and hills, and the steepness or gentleness of slopes. The contour interval of a contour map is the difference in elevation between successive contour lines. The gradient of the function is always perpendicular to the contour lines. When the lines are close together the magnitude of the gradie ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Simplex
In geometry, a simplex (plural: simplexes or simplices) is a generalization of the notion of a triangle or tetrahedron to arbitrary dimensions. The simplex is so-named because it represents the simplest possible polytope in any given dimension. For example, * a 0-dimensional simplex is a point, * a 1-dimensional simplex is a line segment, * a 2-dimensional simplex is a triangle, * a 3-dimensional simplex is a tetrahedron, and * a 4-dimensional simplex is a 5-cell. Specifically, a ''k''-simplex is a ''k''-dimensional polytope which is the convex hull of its ''k'' + 1 vertices. More formally, suppose the ''k'' + 1 points u_0, \dots, u_k \in \mathbb^ are affinely independent, which means u_1 - u_0,\dots, u_k-u_0 are linearly independent. Then, the simplex determined by them is the set of points : C = \left\ This representation in terms of weighted vertices is known as the barycentric coordinate system. A regular simplex is a simplex that is also a regular polytope. A ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Plane (geometry)
In mathematics, a plane is a Euclidean (flat), two-dimensional surface that extends indefinitely. A plane is the two-dimensional analogue of a point (zero dimensions), a line (one dimension) and three-dimensional space. Planes can arise as subspaces of some higher-dimensional space, as with one of a room's walls, infinitely extended, or they may enjoy an independent existence in their own right, as in the setting of two-dimensional Euclidean geometry. Sometimes the word ''plane'' is used more generally to describe a two-dimensional surface, for example the hyperbolic plane and elliptic plane. When working exclusively in two-dimensional Euclidean space, the definite article is used, so ''the'' plane refers to the whole space. Many fundamental tasks in mathematics, geometry, trigonometry, graph theory, and graphing are performed in a two-dimensional space, often in the plane. Euclidean geometry Euclid set forth the first great landmark of mathematical thought, an axiomatic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Delaunay Triangulation
In mathematics and computational geometry, a Delaunay triangulation (also known as a Delone triangulation) for a given set P of discrete points in a general position is a triangulation DT(P) such that no point in P is inside the circumcircle of any triangle in DT(P). Delaunay triangulations maximize the minimum of all the angles of the triangles in the triangulation; they tend to avoid sliver triangles. The triangulation is named after Boris Delaunay for his work on this topic from 1934. For a set of points on the same line there is no Delaunay triangulation (the notion of triangulation is degenerate for this case). For four or more points on the same circle (e.g., the vertices of a rectangle) the Delaunay triangulation is not unique: each of the two possible triangulations that split the quadrangle into two triangles satisfies the "Delaunay condition", i.e., the requirement that the circumcircles of all triangles have empty interiors. By considering circumscribed spheres, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Marching Squares Isobands
Marching refers to the organized, uniformed, steady walking forward in either rhythmic or route-step time; and, typically, it refers to overland movements on foot of military troops and units under field orders. Marching is often performed to march music and is typically associated with military and civilian ceremonial parades. It is a major part of military basic training in most countries and usually involves a system of drill commands. Purpose It is said that many ancient empires first developed marching as a way to move troops from one place to another without them getting mixed up with other troops. A soldier learning to march to drum cadences, martial music and shouted commands is considered an essential element of teaching military discipline. In the United States Marine Corps, close order drill is used to promote exercise, obeying orders, discipline, esprit de corps, confidence, and leadership. Military paces In the military venue there are various rhythmic mili ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
