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T-spline
In computer graphics, a T-spline is a mathematical model for defining freeform surfaces. A T-spline surface is a type of surface defined by a network of control points where a row of control points is allowed to terminate without traversing the entire surface. The control net at a terminated row resembles the letter "T". B-Splines are a type of curve widely used in CAD modeling. They consist of a list of control points (a list of (X, Y) or (X, Y, Z) coordinates) and a knot vector (a list increasing numbers, usually between 0 and 1). In order to perfectly represent circles and other conic sections, a weight component is often added, which extends B-Splines to rational B-Splines, commonly called NURBS. A NURBS curve represents a 1D perfectly smooth curve in 2D or 3D space. To represent a three-dimensional solid object, or a patch of one, B-Spline or NURBS curves are extended to surfaces. These surfaces consist of a rectangular grid of control points, called a control grid or con ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polygon Mesh
In 3D computer graphics and solid modeling, a polygon mesh is a collection of , s and s that defines the shape of a polyhedron, polyhedral object's surface. It simplifies Rendering (computer graphics), rendering, as in a wire-frame model. The face (geometry), faces usually consist of triangles (triangle mesh), quadrilaterals (quads), or other simple convex polygon, convex polygons (n-gons). A polygonal mesh may also be more generally composed of concave polygon, concave polygons, or even Polygon with holes, polygons with holes. The study of Polygon (computer graphics), polygon meshes is a large sub-field of computer graphics (specifically 3D computer graphics) and geometric modeling. Different representations of polygon meshes are used for different applications and goals. The variety of operations performed on meshes includes Boolean logic (Constructive solid geometry), Subdivision surfaces, smoothing, and Level of detail (computer graphics), simplification. Algorithms also exist ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Non-uniform Rational B-spline
Non-uniform rational basis spline (NURBS) is a mathematical model using B-spline, basis splines (B-splines) that is commonly used in computer graphics for representing curves and Surface (mathematics), surfaces. It offers great flexibility and precision for handling both analytic (defined by common mathematical formulae) and 3D modeling, modeled shapes. It is a type of 3D modeling#Process, curve modeling, as opposed to polygonal modeling or digital sculpting. NURBS curves are commonly used in computer-aided design (CAD), Computer-aided manufacturing, manufacturing (CAM), and Computer-aided engineering, engineering (CAE). They are part of numerous industry-wide standards, such as IGES, ISO 10303, STEP, ACIS, and PHIGS. Tools for creating and editing NURBS surfaces are found in various 3D computer graphics software, 3D graphics, Rendering (computer graphics), rendering, and 3D Animation, animation software packages. They can be efficiently handled by computer programs yet allow for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Graphics
Computer graphics deals with generating images and art with the aid of computers. Computer graphics is a core technology in digital photography, film, video games, digital art, 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 (computer graphics), sprite graphics, raster graphics, Rendering (computer graph ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Model
A mathematical model is an abstract and concrete, abstract description of a concrete system using mathematics, mathematical concepts and language of mathematics, language. The process of developing a mathematical model is termed ''mathematical modeling''. Mathematical models are used in applied mathematics and in the natural sciences (such as physics, biology, earth science, chemistry) and engineering disciplines (such as computer science, electrical engineering), as well as in non-physical systems such as the social sciences (such as economics, psychology, sociology, political science). It can also be taught as a subject in its own right. The use of mathematical models to solve problems in business or military operations is a large part of the field of operations research. Mathematical models are also used in music, linguistics, and philosophy (for example, intensively in analytic philosophy). A model may help to explain a system and to study the effects of different components, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Freeform Surface Modelling
Freeform surface modelling is a technique for engineering freeform Computer representation of surfaces, surfaces with a Computer-aided design, CAD or Computer-aided industrial design, CAID system. The technology has encompassed two main fields. Either creating aesthetic surfaces (class A surfaces) that also perform a function; for example, car bodies and consumer product outer forms, or technical surfaces for components such as gas turbine blades and other fluid dynamic engineering components. CAD software packages use two basic methods for the creation of surfaces. The first begins with construction curves (Spline (mathematics), splines) from which the 3D surface is then swept (section along guide rail) or meshed (lofted) through. The second method is direct creation of the surface with manipulation of the surface poles/control points. From these initially created surfaces, other surfaces are constructed using either derived methods such as offset or angled extensions from ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Representation Of Surfaces
In technical applications of 3D computer graphics ( CAx) such as computer-aided design and computer-aided manufacturing, surfaces are one way of representing objects. The other ways are wireframe (lines and curves) and solids. Point clouds are also sometimes used as temporary ways to represent an object, with the goal of using the points to create one or more of the three permanent representations. Open and closed surfaces If one considers a local parametrization of a surface: :\mathbf = \mathbf (u, v), then the curves obtained by varying ''u'' while keeping ''v'' fixed are coordinate lines, sometimes called the ''u'' ''flow lines''. The curves obtained by varying ''v'' while ''u'' is fixed are called the ''v'' flow lines. These are generalizations of the ''x'' and ''y'' Cartesian coordinate lines in the plane coordinate system and of the meridians and circles of latitude on a spherical coordinate system. Open surfaces are not closed in either direction. This means ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Control Point (mathematics)
In computer-aided geometric design a control point is a member of a set of Point (geometry), points used to determine the shape of a spline curve or, more generally, a computer representation of surfaces, surface or higher-dimensional object. For Bézier curves, it has become customary to refer to the -vectors in a parametric representation \sum_i \mathbf p_i \phi_i of a curve or surface in -space as control points, while the Scalar field, scalar-valued functions , defined over the relevant parameter domain, are the corresponding weight function, ''weight'' or ''blending functions''. Some would reasonably insist, in order to give intuitive geometric meaning to the word "control", that the blending functions form a partition of unity, i.e., that the are nonnegative and sum to one. This property implies that the curve lies within the convex hull of its control points.. This is the case for Bézier's representation of a polynomial curve as well as for the B-spline representation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Smooth Function
In mathematical analysis, the smoothness of a function is a property measured by the number of continuous derivatives (''differentiability class)'' it has over its domain. A function of class C^k is a function of smoothness at least ; that is, a function of class C^k is a function that has a th derivative that is continuous in its domain. A function of class C^\infty or C^\infty-function (pronounced C-infinity function) is an infinitely differentiable function, that is, a function that has derivatives of all orders (this implies that all these derivatives are continuous). Generally, the term smooth function refers to a C^-function. However, it may also mean "sufficiently differentiable" for the problem under consideration. 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Subdivision Surface
In the field of 3D computer graphics, a subdivision surface (commonly shortened to SubD surface or Subsurf) is a curved Computer representation of surfaces, surface represented by the specification of a coarser polygon mesh and produced by a recursive algorithmic method. The curved surface, the underlying ''inner mesh'', can be calculated from the coarse mesh, known as the ''control cage'' or ''outer mesh'', as the functional Limit (mathematics), limit of an iterative process of subdividing each polygonal Face (geometry), face into smaller faces that better approximate the final underlying curved surface. Less commonly, a simple algorithm is used to add geometry to a mesh by subdividing the faces into smaller ones without changing the overall shape or volume. The opposite is reducing polygons or un-subdividing. Overview A subdivision surface algorithm is recursive in nature. The process starts with a base level polygonal mesh. A refinement scheme is then applied to this mesh. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Smoothness
In mathematical analysis, the smoothness of a function is a property measured by the number of continuous derivatives (''differentiability class)'' it has over its domain. A function of class C^k is a function of smoothness at least ; that is, a function of class C^k is a function that has a th derivative that is continuous in its domain. A function of class C^\infty or C^\infty-function (pronounced C-infinity function) is an infinitely differentiable function, that is, a function that has derivatives of all orders (this implies that all these derivatives are continuous). Generally, the term smooth function refers to a C^-function. However, it may also mean "sufficiently differentiable" for the problem under consideration. 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 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Intersection
In mathematics, the intersection of two or more objects is another object consisting of everything that is contained in all of the objects simultaneously. For example, in Euclidean geometry, when two lines in a plane are not parallel, their intersection is the point at which they meet. More generally, in set theory, the intersection of sets is defined to be the set of elements which belong to all of them. Unlike the Euclidean definition, this does not presume that the objects under consideration lie in a common space. It simply means the overlapping area of two or more objects or geometries. Intersection is one of the basic concepts of geometry. An intersection can have various geometric shapes, but a point is the most common in a plane geometry. Incidence geometry defines an intersection (usually, of flats) as an object of lower dimension that is incident to each of the original objects. In this approach an intersection can be sometimes undefined, such as for paral ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Industrial Design
Industrial design is a process of design applied to physical Product (business), products that are to be manufactured by mass production. It is the creative act of determining and defining a product's form and features, which takes place in advance of the manufacture or production of the product. Industrial manufacture consists of predetermined, standardized and repeated, often automated, acts of replication, while craft-based design is a process or approach in which the form of the product is determined personally by the product's creator largely concurrent with the act of its production. All manufactured products are the result of a design process, but the nature of this process can vary. It can be conducted by an individual or a team, and such a team could include people with varied expertise (e.g. designers, engineers, business experts, etc.). It can emphasize intuitive creativity or calculated Evidence-based design, scientific decision-making, and often emphasizes a mix of b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
