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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. Later, a somewhat different data structure was suggested, but the name "DCEL" was retained. For simplicity, only connected graphs are considered, however the DCEL structure may be extended to handle disconnected graphs as well by introducing dummy edges between disconnected components. Data structure ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Data Structure
In computer science, a data structure is a data organization, management, 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 functions or 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 identifiers. Data structures provide a means to manage large amounts of data efficiently for uses such a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Graph Data Structures
Graph may refer to: Mathematics *Graph (discrete mathematics), a structure made of vertices and edges **Graph theory, the study of such graphs and their properties *Graph (topology), a topological space resembling a graph in the sense of discrete mathematics *Graph of a function *Graph of a relation *Graph paper * Chart, a means of representing data (also called a graph) Computing *Graph (abstract data type), an abstract data type representing relations or connections *graph (Unix), Unix command-line utility *Conceptual graph, a model for knowledge representation and reasoning Other uses * HMS ''Graph'', a submarine of the UK Royal Navy See also *Complex network *Graf *Graff (other) *Graph database *Grapheme, in linguistics *Graphemics *Graphic (other) *-graphy (suffix from the Greek for "describe," "write" or "draw") *List of information graphics software *Statistical graphics Statistical graphics, also known as statistical graphical techniques, are graphi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Combinatorial Map
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] |
Doubly Linked Face List
In applied mathematics, a doubly linked face list (DLFL) is an efficient data structure for storing 2-manifold mesh data. The structure stores linked lists for a 3D mesh's faces, edges, vertices, and corners. The structure guarantees the preservation of the manifold In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point. More precisely, an n-dimensional manifold, or ''n-manifold'' for short, is a topological space with the property that each point has a ... property.. References 3D imaging Applied mathematics Linked lists {{Applied-math-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 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 refe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Face (geometry)
In solid geometry, a face is a flat surface (a planar region) that forms part of the boundary of a solid object; a three-dimensional solid bounded exclusively by faces is a '' polyhedron''. In more technical treatments of the geometry of polyhedra and higher-dimensional polytopes, the term is also used to mean an element of any dimension of a more general polytope (in any number of dimensions).. Polygonal face In elementary geometry, a face is a polygon on the boundary of a polyhedron. Other names for a polygonal face include polyhedron side and Euclidean plane ''tile''. For example, any of the six squares that bound a cube is a face of the cube. Sometimes "face" is also used to refer to the 2-dimensional features of a 4-polytope. With this meaning, the 4-dimensional tesseract has 24 square faces, each sharing two of 8 cubic cells. Number of polygonal faces of a polyhedron Any convex polyhedron's surface has Euler characteristic :V - E + F = 2, where ''V'' is the number ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vertex (graph Theory)
In discrete mathematics, and more specifically in graph theory, a vertex (plural vertices) or node is the fundamental unit of which graphs are formed: an undirected graph consists of a set of vertices and a set of edges (unordered pairs of vertices), while a directed graph consists of a set of vertices and a set of arcs (ordered pairs of vertices). In a diagram of a graph, a vertex is usually represented by a circle with a label, and an edge is represented by a line or arrow extending from one vertex to another. From the point of view of graph theory, vertices are treated as featureless and indivisible objects, although they may have additional structure depending on the application from which the graph arises; for instance, a semantic network is a graph in which the vertices represent concepts or classes of objects. The two vertices forming an edge are said to be the endpoints of this edge, and the edge is said to be incident to the vertices. A vertex ''w'' is said to be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Doubly Linked List
In computer science, a doubly linked list is a linked data structure that consists of a set of sequentially linked records called nodes. Each node contains three fields: two link fields (references to the previous and to the next node in the sequence of nodes) and one data field. The beginning and ending nodes' previous and next links, respectively, point to some kind of terminator, typically a sentinel node or null, to facilitate traversal of the list. If there is only one sentinel node, then the list is circularly linked via the sentinel node. It can be conceptualized as two singly linked lists formed from the same data items, but in opposite sequential orders. The two node links allow traversal of the list in either direction. While adding or removing a node in a doubly linked list requires changing more links than the same operations on a singly linked list, the operations are simpler and potentially more efficient (for nodes other than first nodes) because there is no ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Connected Graph
In mathematics and computer science, connectivity is one of the basic concepts of graph theory: it asks for the minimum number of elements (nodes or edges) that need to be removed to separate the remaining nodes into two or more isolated subgraphs. It is closely related to the theory of network flow problems. The connectivity of a graph is an important measure of its resilience as a network. Connected vertices and graphs In an undirected graph , two '' vertices'' and are called connected if contains a path from to . Otherwise, they are called disconnected. If the two vertices are additionally connected by a path of length , i.e. by a single edge, the vertices are called adjacent. A graph is said to be connected if every pair of vertices in the graph is connected. This means that there is a path between every pair of vertices. An undirected graph that is not connected is called disconnected. An undirected graph ''G'' is therefore disconnected if there exist two vertic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Graph Embedding
In topological graph theory, an embedding (also spelled imbedding) of a graph G on a surface \Sigma is a representation of G on \Sigma in which points of \Sigma are associated with vertices and simple arcs ( homeomorphic images of ,1/math>) are associated with edges in such a way that: * the endpoints of the arc associated with an edge e are the points associated with the end vertices of e, * no arcs include points associated with other vertices, * two arcs never intersect at a point which is interior to either of the arcs. Here a surface is a compact, connected 2- manifold. Informally, an embedding of a graph into a surface is a drawing of the graph on the surface in such a way that its edges may intersect only at their endpoints. It is well known that any finite graph can be embedded in 3-dimensional Euclidean space \mathbb^3.. A planar graph is one that can be embedded in 2-dimensional Euclidean space \mathbb^2. Often, an embedding is regarded as an equivalence class ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
