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Polyline
In geometry, a polygonal chain is a connected series of line segments. More formally, a polygonal chain is a curve specified by a sequence of points (A_1, A_2, \dots, A_n) called its vertices. The curve itself consists of the line segments connecting the consecutive vertices. Name A polygonal chain may also be called a polygonal curve, polygonal path, polyline,. piecewise linear curve, broken line or, in geographic information systems, a linestring or linear ring. Variations A simple polygonal chain is one in which only consecutive (or the first and the last) segments intersect and only at their endpoints. A closed polygonal chain is one in which the first vertex coincides with the last one, or, alternatively, the first and the last vertices are also connected by a line segment. A simple closed polygonal chain in the plane is the boundary of a simple polygon. Often the term "polygon" is used in the meaning of "closed polygonal chain", but in some cases it is important to dr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Composite Bézier Curve
In geometric modelling and in computer graphics, a composite Bézier curve or Bézier spline is a spline made out of Bézier curves that is at least C^0 continuous. In other words, a composite Bézier curve is a series of Bézier curves joined end to end where the last point of one curve coincides with the starting point of the next curve. Depending on the application, additional smoothness requirements (such as C^1 or C^2 continuity) may be added. A continuous composite Bézier is also called a polybezier, by similarity to polyline, but whereas in polylines the points are connected by straight lines, in a polybezier the points are connected by Bézier curves. A beziergon (also called bezigon) is a closed path composed of Bézier curves. It is similar to a polygon in that it connects a set of vertices by lines, but whereas in polygons the vertices are connected by straight lines, in a beziergon the vertices are connected by Bézier curves. Some authors even call a C^0 composi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bend Minimization
In graph drawing styles that represent the edges of a graph by polylines (sequences of line segments connected at bends), it is desirable to minimize the number of bends per edge (sometimes called the curve complexity). or the total number of bends in a drawing.. Bend minimization is the algorithmic problem of finding a drawing that minimizes these quantities. Eliminating all bends The prototypical example of bend minimization is Fáry's theorem, which states that every planar graph can be drawn with no bends, that is, with all its edges drawn as straight line segments. Drawings of a graph in which the edges are both bendless and axis-aligned are sometimes called ''rectilinear drawings'', and are one way of constructing RAC drawings in which all crossings are at right angles. However, it is NP-complete to determine whether a planar graph has a planar rectilinear drawing, and NP-complete to determine whether an arbitrary graph has a rectilinear drawing that allows crossings.. Bend ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Graph Drawing
Graph drawing is an area of mathematics and computer science combining methods from geometric graph theory and information visualization to derive two-dimensional depictions of graph (discrete mathematics), graphs arising from applications such as social network analysis, cartography, linguistics, and bioinformatics. A drawing of a graph or network diagram is a pictorial representation of the vertex (graph theory), vertices and edge (graph theory), edges of a graph. This drawing should not be confused with the graph itself: very different layouts can correspond to the same graph., p. 6. In the abstract, all that matters is which pairs of vertices are connected by edges. In the concrete, however, the arrangement of these vertices and edges within a drawing affects its understandability, usability, fabrication cost, and aesthetics. The problem gets worse if the graph changes over time by adding and deleting edges (dynamic graph drawing) and the goal is to preserve the user's menta ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ramer–Douglas–Peucker Algorithm
The Ramer–Douglas–Peucker algorithm, also known as the Douglas–Peucker algorithm and iterative end-point fit algorithm, is an algorithm that decimates a curve composed of line segments to a similar curve with fewer points. It was one of the earliest successful algorithms developed for cartographic generalization. Idea The purpose of the algorithm is, given a curve composed of line segments (which is also called a ''Polyline'' in some contexts), to find a similar curve with fewer points. The algorithm defines 'dissimilar' based on the maximum distance between the original curve and the simplified curve (i.e., the Hausdorff distance between the curves). The simplified curve consists of a subset of the points that defined the original curve. Algorithm The starting curve is an ordered set of points or lines and the distance dimension . The algorithm recursively divides the line. Initially it is given all the points between the first and last point. It automatically ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chain (algebraic Topology)
In algebraic topology, a -chain is a formal linear combination of the -cells in a cell complex. In simplicial complexes (respectively, cubical complexes), -chains are combinations of -simplices (respectively, -cubes), but not necessarily connected. Chains are used in homology; the elements of a homology group are equivalence classes of chains. Definition For a simplicial complex X, the group C_n(X) of n-chains of X is given by: C_n(X) = \left\ where \sigma_i are singular n-simplices of X. Note that any element in C_n(X) not necessary to be a connected simplicial complex. Integration on chains Integration is defined on chains by taking the linear combination of integrals over the simplices in the chain with coefficients (which are typically integers). The set of all ''k''-chains forms a group and the sequence of these groups is called a chain complex. Boundary operator on chains The boundary of a chain is the linear combination of boundaries of the simplices in the chain. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Well-known Text Representation Of Geometry
Well-known text (WKT) is a text markup language for representing vector geometry objects. A binary equivalent, known as well-known binary (WKB), is used to transfer and store the same information in a more compact form convenient for computer processing but that is not human-readable. The formats were originally defined by the Open Geospatial Consortium (OGC) and described in their Simple Feature Access. The current standard definition is in the ISO/IEC 13249-3:2016 standard. Geometric objects WKT can represent the following distinct geometric objects: *Point, MultiPoint * LineString, MultiLineString *Polygon, MultiPolygon, Triangle * PolyhedralSurface *TIN (Triangulated irregular network) *GeometryCollection Coordinates for geometries may be 2D (''x'', ''y''), 3D (''x'', ''y'', ''z''), 4D (''x'', ''y'', ''z'', ''m'') with an ''m'' value that is part of a linear referencing system or 2D with an ''m'' value (''x'', ''y'', ''m''). Three-dimensional geometries are designated by a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
SIAM Journal On Computing
The ''SIAM Journal on Computing'' is a scientific journal focusing on the mathematical and formal aspects of computer science. It is published by the Society for Industrial and Applied Mathematics (SIAM). Although its official ISO abbreviation is ''SIAM J. Comput.'', its publisher and contributors frequently use the shorter abbreviation ''SICOMP''. SICOMP typically hosts the special issues of the IEEE Annual Symposium on Foundations of Computer Science (FOCS) and the Annual ACM Symposium on Theory of Computing (STOC), where about 15% of papers published in FOCS and STOC each year are invited to these special issues. For example, Volume 48 contains 11 out of 85 papers published in FOCS 2016. References * External linksSIAM Journal on Computing on |
Binary Search
In computer science, binary search, also known as half-interval search, logarithmic search, or binary chop, is a search algorithm that finds the position of a target value within a sorted array. Binary search compares the target value to the middle element of the array. If they are not equal, the half in which the target cannot lie is eliminated and the search continues on the remaining half, again taking the middle element to compare to the target value, and repeating this until the target value is found. If the search ends with the remaining half being empty, the target is not in the array. Binary search runs in logarithmic time in the worst case, making O(\log n) comparisons, where n is the number of elements in the array. Binary search is faster than linear search except for small arrays. However, the array must be sorted first to be able to apply binary search. There are specialized data structures designed for fast searching, such as hash tables, that can be searched mor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Planar Subdivision
In computational geometry and geometric graph theory, a planar straight-line graph, in short ''PSLG'', (or ''straight-line plane graph'', or ''plane straight-line graph'') is a term used for an embedding of a planar graph in the plane such that its edges are mapped into straight-line segments. Fáry's theorem (1948) states that every planar graph has this kind of embedding. In computational geometry, PSLGs have often been called planar subdivisions, with an assumption or assertion that subdivisions are polygonal rather than having curved boundaries. PSLGs may serve as representations of various maps, e.g., geographical maps in geographical information systems. Special cases of PSLGs are triangulations (polygon triangulation, point-set triangulation). Point-set triangulations are maximal PSLGs in the sense that it is impossible to add straight edges to them while keeping the graph planar. Triangulations have numerous applications in various areas. PSLGs may be seen as a special k ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Franco P
Franco may refer to: Name * Franco (name) * Francisco Franco (1892–1975), Spanish general and dictator of Spain from 1939 to 1975 * Franco Luambo (1938–1989), Congolese musician, the "Grand Maître" Prefix * Franco, a prefix used when referring to France, a country * Franco, a prefix used when referring to French people and their diaspora, e.g. Franco-Americans, Franco-Mauritians * Franco, a prefix used when referring to Franks, a West Germanic tribe Places * El Franco, a municipality of Asturias in Spain * Presidente Franco District, in Paraguay * Franco, Virginia, an unincorporated community, in the United States Other uses * Franco (band), Filipino band * Franco (''General Hospital''), a fictional character on the American soap opera ''General Hospital'' * Franco, the Luccan franc, a 19th-century currency of Lucca, Italy * ''Franco, Ciccio e il pirata Barbanera'', a 1969 Italian comedy film directed by Mario Amendola * ''Franco, ese hombre'', a 1964 documentary fi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Der-Tsai Lee
Der-Tsai Lee (aka. D. T. Lee) is a Taiwanese computer scientist, known for his work in computational geometry. For many years he was a professor at Northwestern University. He has been a distinguished research fellow of the Institute for Information Science at the Academia Sinica in Taipei, Taiwan since 1998. From 1998 to 2008, he was director of this institute. He was the 14th President of National Chung Hsing University from August 1, 2011. Lee received a B.S. degree in electrical engineering from National Taiwan University in 1971, an M.S. from the University of Illinois at Urbana-Champaign in 1976, and a Ph.D. from UIUC under the supervision of Franco Preparata in 1978. After holding a faculty position at Northwestern University for 20 years, he moved to the Academia Sinica in 1998. He also holds faculty positions at National Taiwan University, National Taiwan University of Science and Technology, and National Chiao Tung University. He is a Fellow of the IEEE and the ACM. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
