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Polygonal Curve
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] |
Chainline
Chainline is the angle of a bicycle chain relative to the centerline of the bicycle frame. A bicycle is said to have perfect chainline if the chain is parallel to the centerline of the frame, which means that the rear sprocket is directly behind the front chainring. Chainline also refers to the distance between a sprocket and the centerline of the frame. Bicycles without a straight chainline are slightly less efficient due to frictional losses incurred by running the chain at an angle between the front chainring and rear sprocket. This is the main reason that a single-speed bicycle can be more efficient than a derailleur geared bicycle. Single-speed bicycles should have the straightest possible chainline. See also * Bicycle gearing Bicycle gearing is the aspect of a bicycle drivetrain that determines the relation between the cadence, the rate at which the rider pedals, and the rate at which the drive wheel turns. On some bicycles there is only one gear and, therefore, ... ... [...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 ass |
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