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Loop Subdivision Surface
In computer graphics, the Loop method for subdivision surfaces is an approximating subdivision scheme developed by Charles Loop in 1987 for triangular meshes. Prior methods, namely Catmull-Clark and Doo-Sabin (1978), focused on quad meshes. Loop subdivision surfaces are defined recursively, dividing each triangle into four smaller ones. The method is based on a quartic box spline. It generates C2 continuous limit surfaces everywhere except at extraordinary vertices, where they are C1 continuous. Applications Geologists have applied Loop subdivision surfaces to model erosion on mountain faces, specifically in the Appalachians The Appalachian Mountains, often called the Appalachians, (french: Appalaches), are a system of mountains in eastern to northeastern North America. The Appalachians first formed roughly 480 million years ago during the Ordovician Period. The .... See also * Geodesic polyhedron * Catmull-Clark subdivision surface * Doo-Sabin subdivision sur ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Loop Subdivision Icosahedron
Loop or LOOP may refer to: Brands and enterprises * Loop (mobile), a Bulgarian virtual network operator and co-founder of Loop Live * Loop, clothing, a company founded by Carlos Vasquez in the 1990s and worn by Digable Planets * Loop Mobile, an Indian mobile phone operator * Loop, a reusable container program announced in 2019 by TerraCycle Geography * Loop, Germany, a municipality in Schleswig-Holstein * Loop (Texarkana), a roadway loop around Texarkana, Arkansas, United States * Loop, Blair County, Pennsylvania, United States * Loop, Indiana County, Pennsylvania, United States * Loop, West Virginia, United States * Loop 101, a semi-beltway of the Phoenix Metropolitan Area * Loop 202, a semi-beltway of the Phoenix Metropolitan Area * Loop 303, a semi-beltway of the Phoenix Metropolitan Area * Chicago Loop, the downtown neighborhood of Chicago bounded by the elevated railway The Loop ** Loop Retail Historic District, a shopping district in the Chicago Loop * Delmar Loop, an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Parametric Continuity
In mathematical analysis, the smoothness of a function is a property measured by the number of continuous derivatives it has over some domain, called ''differentiability class''. At the very minimum, a function could be considered smooth if it is differentiable everywhere (hence continuous). At the other end, it might also possess derivatives of all orders in its domain, in which case it is said to be infinitely differentiable and referred to as a C-infinity function (or C^ function). Differentiability classes Differentiability class is a classification of functions according to the properties of their derivatives. It is a measure of the highest order of derivative that exists and is continuous for a function. Consider an open set U on the real line and a function f defined on U with real values. Let ''k'' be a non-negative integer. The function f is said to be of differentiability class ''C^k'' if the derivatives f',f'',\dots,f^ exist and are continuous on U. If f is k-dif ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geodesic Polyhedron
A geodesic polyhedron is a convex polyhedron made from triangles. They usually have icosahedral symmetry, such that they have 6 triangles at a vertex, except 12 vertices which have 5 triangles. They are the dual of corresponding Goldberg polyhedra with mostly hexagonal faces. Geodesic polyhedra are a good approximation to a sphere for many purposes, and appear in many different contexts. The most well-known may be the geodesic domes designed by Buckminster Fuller, which geodesic polyhedra are named after. Geodesic grids used in geodesy also have the geometry of geodesic polyhedra. The capsids of some viruses have the shape of geodesic polyhedra, and fullerene molecules have the shape of Goldberg polyhedra. Geodesic polyhedra are available as geometric primitives in the Blender 3D modeling software package, which calls them icospheres: they are an alternative to the UV sphere, having a more regular distribution of vertices than the UV sphere. The Goldberg–Coxeter construction ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Appalachians
The Appalachian Mountains, often called the Appalachians, (french: Appalaches), are a system of mountains in eastern to northeastern North America. The Appalachians first formed roughly 480 million years ago during the Ordovician Period. They once reached elevations similar to those of the Alps and the Rocky Mountains before experiencing natural erosion. The Appalachian chain is a barrier to east–west travel, as it forms a series of alternating ridgelines and valleys oriented in opposition to most highways and railroads running east–west. Definitions vary on the precise boundaries of the Appalachians. The United States Geological Survey (USGS) defines the ''Appalachian Highlands'' physiographic division as consisting of 13 provinces: the Atlantic Coast Uplands, Eastern Newfoundland Atlantic, Maritime Acadian Highlands, Maritime Plain, Notre Dame and Mégantic Mountains, Western Newfoundland Mountains, Piedmont, Blue Ridge, Valley and Ridge, St. Lawrence Valley, Appal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mountain Faces
A mountain is an elevated portion of the Earth's crust, generally with steep sides that show significant exposed bedrock. Although definitions vary, a mountain may differ from a plateau in having a limited summit area, and is usually higher than a hill, typically rising at least 300 metres (1,000 feet) above the surrounding land. A few mountains are isolated summits, but most occur in mountain ranges. Mountains are formed through tectonic forces, erosion, or volcanism, which act on time scales of up to tens of millions of years. Once mountain building ceases, mountains are slowly leveled through the action of weathering, through slumping and other forms of mass wasting, as well as through erosion by rivers and glaciers. High elevations on mountains produce colder climates than at sea level at similar latitude. These colder climates strongly affect the ecosystems of mountains: different elevations have different plants and animals. Because of the less hospitable terrain and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Erosion
Erosion is the action of surface processes (such as water flow or wind) that removes soil, rock, or dissolved material from one location on the Earth's crust, and then transports it to another location where it is deposited. Erosion is distinct from weathering which involves no movement. Removal of rock or soil as clastic sediment is referred to as ''physical'' or ''mechanical'' erosion; this contrasts with ''chemical'' erosion, where soil or rock material is removed from an area by dissolution. Eroded sediment or solutes may be transported just a few millimetres, or for thousands of kilometres. Agents of erosion include rainfall; bedrock wear in rivers; coastal erosion by the sea and waves; glacial plucking, abrasion, and scour; areal flooding; wind abrasion; groundwater processes; and mass movement processes in steep landscapes like landslides and debris flows. The rates at which such processes act control how fast a surface is eroded. Typically, physical ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geologists
A geologist is a scientist who studies the solid, liquid, and gaseous matter that constitutes Earth and other terrestrial planets, as well as the processes that shape them. Geologists usually study geology, earth science, or geophysics, although backgrounds in physics, chemistry, biology, and other sciences are also useful. Field research (field work) is an important component of geology, although many subdisciplines incorporate laboratory and digitalized work. Geologists can be classified in a larger group of scientists, called geoscientists. Geologists work in the energy and mining sectors searching for natural resources such as petroleum, natural gas, precious and base metals. They are also in the forefront of preventing and mitigating damage from natural hazards and disasters such as earthquakes, volcanoes, tsunamis and landslides. Their studies are used to warn the general public of the occurrence of these events. Geologists are also important contributors to climate cha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Box Spline
In the mathematical fields of numerical analysis and approximation theory, box splines are piecewise polynomial functions of several variables. Box splines are considered as a multivariate generalization of basis splines (B-splines) and are generally used for multivariate approximation/interpolation. Geometrically, a box spline is the shadow (X-ray) of a hypercube projected down to a lower-dimensional space. Box splines and simplex splines are well studied special cases of polyhedral splines which are defined as shadows of general polytopes. Definition A box spline is a multivariate function (\mathbb^d \to \mathbb) defined for a set of vectors, \xi \in \mathbb^d, usually gathered in a matrix \mathbf := \left xi_1 \dots \xi_N\right When the number of vectors is the same as the dimension of the domain (i.e., N = d ) then the box spline is simply the (normalized) indicator function of the parallelepiped formed by the vectors in \mathbf: : M_(\mathbf) := \frac\chi_(\mathbf) = \ ... [...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 graphics hardware, 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, computer generated imagery (CGI). The non-artistic aspects of computer graphics are the subject of Computer graphics (computer science), computer science research. Some topics in computer graphics include user interface design, sprite (graphics), sprite graphics, Rendering (computer graphics), rendering, ray tracing (graphics) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quartic Function
In algebra, a quartic function is a function of the form :f(x)=ax^4+bx^3+cx^2+dx+e, where ''a'' is nonzero, which is defined by a polynomial of degree four, called a quartic polynomial. A '' quartic equation'', or equation of the fourth degree, is an equation that equates a quartic polynomial to zero, of the form :ax^4+bx^3+cx^2+dx+e=0 , where . The derivative of a quartic function is a cubic function. Sometimes the term biquadratic is used instead of ''quartic'', but, usually, biquadratic function refers to a quadratic function of a square (or, equivalently, to the function defined by a quartic polynomial without terms of odd degree), having the form :f(x)=ax^4+cx^2+e. Since a quartic function is defined by a polynomial of even degree, it has the same infinite limit when the argument goes to positive or negative infinity. If ''a'' is positive, then the function increases to positive infinity at both ends; and thus the function has a global minimum. Likewise, if ''a'' is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Surfaces
A surface, as the term is most generally used, is the outermost or uppermost layer of a physical object or space. Surface or surfaces may also refer to: Mathematics *Surface (mathematics), a generalization of a plane which needs not be flat * Surface (differential geometry), a differentiable two-dimensional manifold *Surface (topology), a two-dimensional manifold * Algebraic surface, an algebraic variety of dimension two * Coordinate surfaces * Fractal surface, generated using a stochastic algorithm * Polyhedral surface *Surface area *Surface integral Arts and entertainment *Surface (band), an American R&B and pop trio ** ''Surface'' (Surface album), 1986 * Surfaces (band), American musical duo * ''Surface'' (Circle album), 1998 * "Surface" (Aero Chord song), 2014 * ''Surface'' (2005 TV series), an American science fiction show, 2005–2006 * ''Surface'' (2022 TV series), an American psychological thriller miniseries that began streaming in 2022 *''The Surface'', an American film ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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