|
Geometric Model
__NOTOC__ Geometric modeling is a branch of applied mathematics and computational geometry that studies methods and algorithms for the mathematical description of shapes. The shapes studied in geometric modeling are mostly two- or three-dimensional (''solid figures''), although many of its tools and principles can be applied to sets of any finite dimension. Today most geometric modeling is done with computers and for computer-based applications. Two-dimensional models are important in computer typography and technical drawing. Three-dimensional models are central to computer-aided design and manufacturing (CAD/CAM), and widely used in many applied technical fields such as civil and mechanical engineering, architecture, geology and medical image processing. Geometric models are usually distinguished from procedural and object-oriented models, which define the shape implicitly by an opaque algorithm that generates its appearance. They are also contrasted with digital image ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Applied Mathematics
Applied mathematics is the application of mathematics, mathematical methods by different fields such as physics, engineering, medicine, biology, finance, business, computer science, and Industrial sector, industry. Thus, applied mathematics is a combination of mathematical science and specialized knowledge. The term "applied mathematics" also describes the profession, professional specialty in which mathematicians work on practical problems by formulating and studying mathematical models. In the past, practical applications have motivated the development of mathematical theories, which then became the subject of study in pure mathematics where abstract concepts are studied for their own sake. The activity of applied mathematics is thus intimately connected with research in pure mathematics. History Historically, applied mathematics consisted principally of Mathematical analysis, applied analysis, most notably differential equations; approximation theory (broadly construed, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Procedural Modeling
Procedural modeling is an umbrella term for a number of techniques in computer graphics to create 3D models and textures from sets of rules that may be easily changed over time. L-Systems, fractals, and generative modeling are procedural modeling techniques since they apply algorithms for producing scenes. The set of rules may either be embedded into the algorithm, configurable by parameters, or the set of rules is separate from the evaluation engine. The output is called procedural content, which can be used in computer games, films, be uploaded to the internet, or the user may edit the content manually. Procedural models often exhibit database amplification, meaning that large scenes can be generated from a much smaller number of rules. If the employed algorithm produces the same output every time, the output need not be stored. Often, it suffices to start the algorithm with the same random seed to achieve this. Although all modeling techniques on a computer require algorithm ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer-aided Engineering
Computer-aided engineering (CAE) is the general usage of technology to aid in tasks related to engineering analysis. Any use of technology to solve or assist engineering issues falls under this umbrella. Overview Following alongside the consistent improvement in computer graphics and speed, computer aid assists engineers with once complicated and time consuming tasks with the input of information and a press of a button. It includes finite element method or analysis (FEA), computational fluid dynamics (CFD), multibody dynamics (MBD), durability and optimization. It is included with computer-aided design (CAD) and computer-aided manufacturing (CAM) in a collective term and abbreviation computer-aided technologies (CAx). The term CAE has been used to describe the use of computer technology within engineering in a broader sense than just engineering analysis. It was in this context that the term was coined by Jason Lemon, founder of Structural Dynamics Research Corporation ( ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computational Topology
Algorithmic topology, or computational topology, is a subfield of topology with an overlap with areas of computer science, in particular, computational geometry and computational complexity theory. A primary concern of algorithmic topology, as its name suggests, is to develop efficient algorithms for solving problems that arise naturally in fields such as computational geometry, graphics, robotics, social science, structural biology, and chemistry, using methods from computable topology. Major algorithms by subject area Algorithmic 3-manifold theory A large family of algorithms concerning 3-manifolds revolve around normal surface theory, which is a phrase that encompasses several techniques to turn problems in 3-manifold theory into integer linear programming problems. * ''Rubinstein and Thompson's 3-sphere recognition algorithm''. This is an algorithm that takes as input a triangulated 3-manifold and determines whether or not the manifold is homeomorphic to the 3-sphere. I ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conformal Geometry
In mathematics, conformal geometry is the study of the set of angle-preserving ( conformal) transformations on a space. In a real two dimensional space, conformal geometry is precisely the geometry of Riemann surfaces. In space higher than two dimensions, conformal geometry may refer either to the study of conformal transformations of what are called "flat spaces" (such as Euclidean spaces or spheres), or to the study of conformal manifolds which are Riemannian or pseudo-Riemannian manifolds with a class of metrics that are defined up to scale. Study of the flat structures is sometimes termed Möbius geometry, and is a type of Klein geometry. Conformal manifolds A conformal manifold is a Riemannian manifold (or pseudo-Riemannian manifold) equipped with an equivalence class of metric tensors, in which two metrics ''g'' and ''h'' are equivalent if and only if :h = \lambda^2 g , where ''λ'' is a real-valued smooth function defined on the manifold and is called the conformal fa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Architectural Geometry
Architectural geometry is an area of research which combines applied geometry and architecture, which looks at the design, analysis and manufacture processes. It lies at the core of architectural design and strongly challenges contemporary practice, the so-called architectural practice of the digital age. Architectural geometry is influenced by following fields: differential geometry, topology, fractal geometry, and cellular automata. Topics include: * freeform curves and surfaces creation * developable surfaces * discretisation * generative design * digital prototyping and manufacturing See also *Geometric design * Computer-aided architectural design *Mathematics and architecture *Fractal geometry *Blobitecture Blobitecture (from blob architecture), blobism and blobismus are terms for a movement in architecture in which buildings have an organic, amoeba-shaped building form. Though the term ''blob architecture'' was already in vogue in the mid-1990s, th ... References E ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
2D Geometric Modeling
A 2D geometric model is a geometric model of an object as a two-dimensional figure, usually on the Euclidean or Cartesian plane. Even though all material objects are three-dimensional, a 2D geometric model is often adequate for certain flat objects, such as paper cut-outs and machine parts made of sheet metal. Other examples include circles used as a model of thunderstorms, which can be considered flat when viewed from above. 2D geometric models are also convenient for describing certain types of artificial images, such as technical diagrams, logos, the glyphs of a font, etc. They are an essential tool of 2D computer graphics and often used as components of 3D geometric models, e.g. to describe the decals to be applied to a car model. Modern architecture practice "digital rendering" which is a technique used to form a perception of a 2-D geometric model as of a 3-D geometric model designed through descriptive geometry and computerized equipment. 2D geometric modeling techniques ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Circle
A circle is a shape consisting of all point (geometry), points in a plane (mathematics), plane that are at a given distance from a given point, the Centre (geometry), centre. The distance between any point of the circle and the centre is called the radius. The length of a line segment connecting two points on the circle and passing through the centre is called the diameter. A circle bounds a region of the plane called a Disk (mathematics), disc. The circle has been known since before the beginning of recorded history. Natural circles are common, such as the full moon or a slice of round fruit. The circle is the basis for the wheel, which, with related inventions such as gears, makes much of modern machinery possible. In mathematics, the study of the circle has helped inspire the development of geometry, astronomy and calculus. Terminology * Annulus (mathematics), Annulus: a ring-shaped object, the region bounded by two concentric circles. * Circular arc, Arc: any Connected ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Square (geometry)
In geometry, a square is a regular quadrilateral. It has four straight sides of equal length and four equal angles. Squares are special cases of rectangles, which have four equal angles, and of rhombuses, which have four equal sides. As with all rectangles, a square's angles are right angles (90 degrees, or /2 radians), making adjacent sides perpendicular. The area of a square is the side length multiplied by itself, and so in algebra, multiplying a number by itself is called squaring. Equal squares can tile the plane edge-to-edge in the square tiling. Square tilings are ubiquitous in tiled floors and walls, graph paper, image pixels, and game boards. Square shapes are also often seen in building floor plans, origami paper, food servings, in graphic design and heraldry, and in instant photos and fine art. The formula for the area of a square forms the basis of the calculation of area and motivates the search for methods for squaring the circle by compass and straightedge ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Color
Color (or colour in English in the Commonwealth of Nations, Commonwealth English; American and British English spelling differences#-our, -or, see spelling differences) is the visual perception based on the electromagnetic spectrum. Though color is not an inherent property of matter, color perception is related to an object's light absorption, emission spectra, emission, Reflection (physics), reflection and Transmittance, transmission. For most humans, colors are perceived in the visible light spectrum with three types of cone cells (trichromacy). Other animals may have a different number of cone cell types or have eyes sensitive to different wavelengths, such as bees that can distinguish ultraviolet, and thus have a different color sensitivity range. Animal perception of color originates from different light wavelength or spectral sensitivity in cone cell types, which is then processed by the brain. Colors have perceived properties such as hue, colorfulness (saturation), and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fractal
In mathematics, a fractal is a Shape, geometric shape containing detailed structure at arbitrarily small scales, usually having a fractal dimension strictly exceeding the topological dimension. Many fractals appear similar at various scales, as illustrated in successive magnifications of the Mandelbrot set. This exhibition of similar patterns at increasingly smaller scales is called self-similarity, also known as expanding symmetry or unfolding symmetry; if this replication is exactly the same at every scale, as in the Menger sponge, the shape is called affine geometry, affine self-similar. Fractal geometry lies within the mathematical branch of measure theory. One way that fractals are different from finite geometric figures is how they Scaling (geometry), scale. Doubling the edge lengths of a filled polygon multiplies its area by four, which is two (the ratio of the new to the old side length) raised to the power of two (the conventional dimension of the filled polygon). ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Volumetric Model
In 3D computer graphics and modeling, a volumetric mesh is a polyhedral representation of the interior region of an object. It is unlike polygon meshes, which represent only the surface as polygons. Applications One application of volumetric meshes is in finite element analysis, which may use regular or irregular volumetric meshes to compute internal stresses and forces in an object throughout the entire volume of the object. Volume meshes may also be used for portal rendering. See also * B-rep * Voxels * Hypergraph * Volume rendering In scientific visualization and computer graphics, volume rendering is a set of techniques used to display a 2D projection of a 3D discretely sampled data set, typically a 3D scalar field. A typical 3D data set is a group of 2D slice image ... References 3D computer graphics Computer graphics data structures Mesh generation {{mathapplied-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
