|
Quad-edge Data Structure
A quad-edge data structure is a computer representation of the topology of a two-dimensional or three-dimensional map, that is, a graph drawn on a (closed) surface. It was first described by Jorge Stolfi and Leonidas J. Guibas. It is a variant of the earlier winged edge data structure. Overview The fundamental idea behind the quad-edge structure is the recognition that a single edge, in a closed polygonal mesh topology, sits between exactly two faces and exactly two vertices. The quad-edge data structure represents an edge, along with the edges it is connected to around the adjacent vertices and faces to encode the topology of the graph. An example implementation of the quad-edge data-type is as follows typedef struct quadedge; typedef struct quadedge_ref; Each quad-edge contains four references to adjacent quad-edges. Each of the four references points to the next edge counter-clockwise around either a vertex or a face. Each of these references represent either the or ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Data Structure
In computer science, a data structure is a data organization and storage format that is usually chosen for Efficiency, efficient Data access, access to data. More precisely, a data structure is a collection of data values, the relationships among them, and the Function (computer programming), functions or Operator (computer programming), operations that can be applied to the data, i.e., it is an algebraic structure about data. Usage Data structures serve as the basis for abstract data types (ADT). The ADT defines the logical form of the data type. The data structure implements the physical form of the data type. Different types of data structures are suited to different kinds of applications, and some are highly specialized to specific tasks. For example, Relational database, relational databases commonly use B-tree indexes for data retrieval, while compiler Implementation, implementations usually use hash tables to look up Identifier (computer languages), identifiers. Data s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
C (programming Language)
C (''pronounced'' '' – like the letter c'') is a general-purpose programming language. It was created in the 1970s by Dennis Ritchie and remains very widely used and influential. By design, C's features cleanly reflect the capabilities of the targeted Central processing unit, CPUs. It has found lasting use in operating systems code (especially in Kernel (operating system), kernels), device drivers, and protocol stacks, but its use in application software has been decreasing. C is commonly used on computer architectures that range from the largest supercomputers to the smallest microcontrollers and embedded systems. A successor to the programming language B (programming language), B, C was originally developed at Bell Labs by Ritchie between 1972 and 1973 to construct utilities running on Unix. It was applied to re-implementing the kernel of the Unix operating system. During the 1980s, C gradually gained popularity. It has become one of the most widely used programming langu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Doubly Connected Edge List
The doubly connected edge list (DCEL), also known as half-edge data structure, is a data structure to represent an embedding of a planar graph in the plane, and polytopes in 3D. This data structure provides efficient manipulation of the topological information associated with the objects in question (vertices, edges, faces). It is used in many algorithms of computational geometry to handle polygonal subdivisions of the plane, commonly called planar straight-line graphs (PSLG). For example, a Voronoi diagram is commonly represented by a DCEL inside a bounding box. This data structure was originally suggested by Muller and Preparata for representations of 3D convex polyhedra. Simplified versions of the data structure, as described here, only consider connected graphs, but the DCEL structure may be extended to handle disconnected graphs as well by introducing dummy edges between disconnected components. Data structure DCEL is more than just a doubly linked list of edges. In th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Combinatorial Maps
A combinatorial map is a combinatorial representation of a graph on an orientable surface. A combinatorial map may also be called a combinatorial embedding, a rotation system, an orientable ribbon graph, a fat graph, or a cyclic graph. More generally, an n-dimensional combinatorial map is a combinatorial representation of a graph on an n-dimensional orientable manifold. Combinatorial maps are used as efficient data structures in image representation and processing, in geometrical modeling. This model is related to simplicial complexes and to combinatorial topology. A combinatorial map is a boundary representation model; it represents object by its boundaries. History The concept of a combinatorial map was introduced informally by J. Edmonds for polyhedral surfaces which are planar graphs. It was given its first definite formal expression under the name "Constellations" by A. Jacques but the concept was already extensively used under the name "rotation" by Gerhard Ringel and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Winged Edge
In computer graphics, the winged edge data structure is a way to represent polygon meshes in computer memory. It is a type of boundary representation and describes both the geometry and topology of a model. Three types of records are used: vertex records, edge records, and face records. Given a reference to an edge record, one can answer several types of adjacency queries (queries about neighboring edges, vertices and faces) in constant time. This kind of adjacency information is useful for algorithms such as subdivision surface. Features The winged edge data structure explicitly describes the geometry and topology of faces, edges, and vertices when three or more surfaces come together and meet at a common edge. The ordering is such that the surfaces are ordered counter-clockwise with respect to the innate orientation of the intersection edge. Moreover the representation allows numerically unstable situations like that depicted below. The winged edge data structure allows ... [...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] |
3D Computer Graphics
3D computer graphics, sometimes called Computer-generated imagery, CGI, 3D-CGI or three-dimensional Computer-generated imagery, computer graphics, are graphics that use a three-dimensional representation of geometric data (often Cartesian coordinate system#Cartesian coordinates in three dimensions, Cartesian) that is stored in the computer for the purposes of performing calculations and rendering digital images, usually 2D images but sometimes 3D images. The resulting images may be stored for viewing later (possibly as an Computer animation, animation) or displayed in Real-time computer graphics, real time. 3D computer graphics, contrary to what the name suggests, are most often displayed on two-dimensional displays. Unlike 3D film and similar techniques, the result is two-dimensional, without visual depth perception, depth. More often, 3D graphics are being displayed on 3D displays, like in virtual reality systems. 3D graphics stand in contrast to 2D computer graphics which t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dual Graph
In the mathematics, mathematical discipline of graph theory, the dual graph of a planar graph is a graph that has a vertex (graph theory), vertex for each face (graph theory), face of . The dual graph has an edge (graph theory), edge for each pair of faces in that are separated from each other by an edge, and a self-loop when the same face appears on both sides of an edge. Thus, each edge of has a corresponding dual edge, whose endpoints are the dual vertices corresponding to the faces on either side of . The definition of the dual depends on the choice of embedding of the graph , so it is a property of plane graphs (graphs that are already embedded in the plane) rather than planar graphs (graphs that may be embedded but for which the embedding is not yet known). For planar graphs generally, there may be multiple dual graphs, depending on the choice of planar embedding of the graph. Historically, the first form of graph Duality (mathematics), duality to be recognized was ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Winged Edge
In computer graphics, the winged edge data structure is a way to represent polygon meshes in computer memory. It is a type of boundary representation and describes both the geometry and topology of a model. Three types of records are used: vertex records, edge records, and face records. Given a reference to an edge record, one can answer several types of adjacency queries (queries about neighboring edges, vertices and faces) in constant time. This kind of adjacency information is useful for algorithms such as subdivision surface. Features The winged edge data structure explicitly describes the geometry and topology of faces, edges, and vertices when three or more surfaces come together and meet at a common edge. The ordering is such that the surfaces are ordered counter-clockwise with respect to the innate orientation of the intersection edge. Moreover the representation allows numerically unstable situations like that depicted below. The winged edge data structure allows ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer
A computer is a machine that can be Computer programming, programmed to automatically Execution (computing), carry out sequences of arithmetic or logical operations (''computation''). Modern digital electronic computers can perform generic sets of operations known as Computer program, ''programs'', which enable computers to perform a wide range of tasks. The term computer system may refer to a nominally complete computer that includes the Computer hardware, hardware, operating system, software, and peripheral equipment needed and used for full operation; or to a group of computers that are linked and function together, such as a computer network or computer cluster. A broad range of Programmable logic controller, industrial and Consumer electronics, consumer products use computers as control systems, including simple special-purpose devices like microwave ovens and remote controls, and factory devices like industrial robots. Computers are at the core of general-purpose devices ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Leonidas J
Leonidas I (; , ''Leōnídas''; born ; died 11 August 480 BC) was king of the Ancient Greek city-state of Sparta. He was the son of king Anaxandridas II and the 17th king of the Agiad dynasty, a Spartan royal house which claimed descent from the mythical demigod Heracles. Leonidas I ascended to the throne in , succeeding his half-brother king Cleomenes I. He ruled jointly along with king Leotychidas until his death in 480 BC, when he was succeeded by his son, Pleistarchus. At the Second Greco-Persian War, Leonidas led the allied Greek forces in a last stand at the Battle of Thermopylae (480 BC), attempting to defend the pass from the invading Persian army, and was killed early during the third and last day of the battle. Leonidas entered myth as a hero and the leader of the 300 Spartans who died in battle at Thermopylae. While the Greeks lost this battle, they were able to expel the Persian invaders in the following year. Life According to Herodotus, Leonidas' mother was n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
