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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] |
Saddle Pt
The saddle is a supportive structure for a rider of an animal, fastened to an animal's back by a girth. The most common type is equestrian. However, specialized saddles have been created for oxen, camels and other animals. It is not known precisely when riders first began to use some sort of padding or protection, but a blanket attached by some form of surcingle or girth was probably the first "saddle", followed later by more elaborate padded designs. The solid saddle tree was a later invention, and though early stirrup designs predated the invention of the solid tree, the paired stirrup, which attached to the tree, was the last element of the saddle to reach the basic form that is still used today. Today, modern saddles come in a wide variety of styles, each designed for a specific equestrianism discipline, and require careful fit to both the rider and the horse. Proper saddle care can extend the useful life of a saddle, often for decades. The saddle was a crucial step i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Virtual Reality
Virtual reality (VR) is a simulated experience that employs pose tracking and 3D near-eye displays to give the user an immersive feel of a virtual world. Applications of virtual reality include entertainment (particularly video games), education (such as medical or military training) and business (such as virtual meetings). Other distinct types of VR-style technology include augmented reality and mixed reality, sometimes referred to as extended reality or XR, although definitions are currently changing due to the nascence of the industry. Currently, standard virtual reality systems use either virtual reality headsets or multi-projected environments to generate realistic images, sounds and other sensations that simulate a user's physical presence in a virtual environment. A person using virtual reality equipment is able to look around the artificial world, move around in it, and interact with virtual features or items. The effect is commonly created by VR headsets consisting ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tessellation
A tessellation or tiling is the covering of a surface, often a plane (mathematics), plane, using one or more geometric shapes, called ''tiles'', with no overlaps and no gaps. In mathematics, tessellation can be generalized to high-dimensional spaces, higher dimensions and a variety of geometries. A periodic tiling has a repeating pattern. Some special kinds include ''regular tilings'' with regular polygonal tiles all of the same shape, and ''semiregular tilings'' with regular tiles of more than one shape and with every corner identically arranged. The patterns formed by periodic tilings can be categorized into 17 wallpaper groups. A tiling that lacks a repeating pattern is called "non-periodic". An ''aperiodic tiling'' uses a small set of tile shapes that cannot form a repeating pattern. A ''tessellation of space'', also known as a space filling or honeycomb, can be defined in the geometry of higher dimensions. A real physical tessellation is a tiling made of materials such a ... [...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 polyhedral object. The faces usually consist of triangles (triangle mesh), quadrilaterals (quads), or other simple convex polygons ( n-gons), since this simplifies rendering, but may also be more generally composed of concave polygons, or even polygons with holes. The study of 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 may include: Boolean logic ( Constructive solid geometry), smoothing, simplification, and many others. Algorithms also exist for ray tracing, collision detection, and rigid-body dynamics with polygon meshes. If the mesh's edges are rendered instead of the faces, then the model becomes a wireframe model. Volumetric meshes are distinct f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Finite Element Analysis
The finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical problem areas of interest include the traditional fields of structural analysis, heat transfer, fluid flow, mass transport, and electromagnetic potential. The FEM is a general numerical method for solving partial differential equations in two or three space variables (i.e., some boundary value problems). To solve a problem, the FEM subdivides a large system into smaller, simpler parts that are called finite elements. This is achieved by a particular space discretization in the space dimensions, which is implemented by the construction of a mesh of the object: the numerical domain for the solution, which has a finite number of points. The finite element method formulation of a boundary value problem finally results in a system of algebraic equations. The method approximates the unknown function over the domain. The sim ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer-aided Engineering
Computer-aided engineering (CAE) is the broad usage of computer software to aid in engineering analysis tasks. It includes , , , durability and optimization. It is included with computer-aided design (CAD) and computer-aided manufacturing (CAM) in the collective abbreviation " CAx". Overview Computer-aided engineering primarily uses computer-aided design (CAD) software, which are sometimes called CAE tools. CAE tools are used, to analyze the robustness and performance of components and assemblies. CAE tools encompass simulation, validation, and optimization of products and manufacturing tools. CAE systems aim to be major providers of information to help support design teams in decision-making. Computer-aided engineering is used in various fields, like automotive, aviation, space, and shipbuilding industries. CAE systems can provide support to businesses. This is achieved by the use of reference architectures and their ability to place information views on the business proc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Voxel
In 3D computer graphics, a voxel represents a value on a regular grid in three-dimensional space. As with pixels in a 2D bitmap, voxels themselves do not typically have their position (i.e. coordinates) explicitly encoded with their values. Instead, rendering systems infer the position of a voxel based upon its position relative to other voxels (i.e., its position in the data structure that makes up a single volumetric image). In contrast to pixels and voxels, polygons are often explicitly represented by the coordinates of their vertices (as points). A direct consequence of this difference is that polygons can efficiently represent simple 3D structures with much empty or homogeneously filled space, while voxels excel at representing regularly sampled spaces that are non-homogeneously filled. Voxels are frequently used in the visualization and analysis of medical and scientific data (e.g. geographic information systems (GIS)). Some volumetric displays use voxels to describe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Facet
Facets () are flat faces on geometric shapes. The organization of naturally occurring facets was key to early developments in crystallography, since they reflect the underlying symmetry of the crystal structure. Gemstones commonly have facets cut into them in order to improve their appearance by allowing them to reflect light. Facet arrangements Of the hundreds of facet arrangements that have been used, the most famous is probably the round brilliant cut, used for diamond and many colored gemstones. This first early version of what would become the modern Brilliant Cut is said to have been devised by an Italian named Peruzzi, sometime in the late 17th century.Gems, 5th edition, Webster, 1995.Gemstones of the world, Schumann, 1977. Later on, the first angles for an "ideal" cut diamond were calculated by Marcel Tolkowsky in 1919. Slight modifications have been made since then, but angles for "ideal" cut diamonds are still similar to Tolkowsky's formula. Round brilliants cut befo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Freeform Surface Modeling
Freeform surface modelling is a technique for engineering freeform surfaces with a CAD or 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 ( 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 surfaces; or via bridging and blending between groups of surfaces. Surfaces Freeform surface, or freeform sur ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
NURBS
Non-uniform rational basis spline (NURBS) is a mathematical model using basis splines (B-splines) that is commonly used in computer graphics for representing curves and surfaces. It offers great flexibility and precision for handling both analytic (defined by common mathematical formulae) and modeled shapes. It is a type of curve modeling, as opposed to polygonal modeling or digital sculpting. NURBS curves are commonly used in computer-aided design (CAD), manufacturing (CAM), and engineering (CAE). They are part of numerous industry-wide standards, such as IGES, STEP, ACIS, and PHIGS. Tools for creating and editing NURBS surfaces are found in various 3D graphics and animation software packages. They can be efficiently handled by computer programs yet allow for easy human interaction. NURBS surfaces are functions of two parameters mapping to a surface in three-dimensional space. The shape of the surface is determined by control points. In a compact form, NURBS surfaces can re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
