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GEOS (software Library)
JTS Topology Suite (Java Topology Suite) is an open-source Java software library that provides an object model for Euclidean planar linear geometry together with a set of fundamental geometric functions. JTS is primarily intended to be used as a core component of vector-based geomatics software such as geographical information systems."The 2012 Free and Open Source GIS Software Map – A Guide to facilitate Research, Development and Adoption" S. Steiniger and A.J.S. Hunter It can also be used as a general-purpose library providing s in |
Java SE
Java Platform, Standard Edition (Java SE) is a computing platform for development and deployment of portable code for desktop and server environments. Java SE was formerly known as Java 2 Platform, Standard Edition (J2SE). The platform uses Java programming language and is part of the Java software-platform family. Java SE defines a range of general-purpose APIs—such as Java APIs for the Java Class Library—and also includes the Java Language Specification and the Java Virtual Machine Specification. OpenJDK is the official reference implementation since version 7. Nomenclature, standards and specifications The platform was known as ''Java 2 Platform, Standard Edition'' or ''J2SE'' from version 1.2, until the name was changed to ''Java Platform, Standard Edition'' or ''Java SE'' in version 1.5. The "SE" is used to distinguish the base platform from the Enterprise Edition (Java EE) and Micro Edition (Java ME) platforms. The "2" was originally intended to emphasize the maj ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Intersection (set Theory)
In set theory, the intersection of two sets A and B, denoted by A \cap B, is the set containing all elements of A that also belong to B or equivalently, all elements of B that also belong to A. Notation and terminology Intersection is written using the symbol "\cap" between the terms; that is, in infix notation. For example: \\cap\=\ \\cap\=\varnothing \Z\cap\N=\N \\cap\N=\ The intersection of more than two sets (generalized intersection) can be written as: \bigcap_^n A_i which is similar to capital-sigma notation. For an explanation of the symbols used in this article, refer to the table of mathematical symbols. Definition The intersection of two sets A and B, denoted by A \cap B, is the set of all objects that are members of both the sets A and B. In symbols: A \cap B = \. That is, x is an element of the intersection A \cap B if and only if x is both an element of A and an element of B. For example: * The intersection of the sets and is . * The number 9 is in t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Line Segment Intersection
In geometry, an intersection is a point, line, or curve common to two or more objects (such as lines, curves, planes, and surfaces). The simplest case in Euclidean geometry is the line–line intersection between two distinct lines, which either is one point or does not exist (if the lines are parallel). Other types of geometric intersection include: * Line–plane intersection * Line–sphere intersection * Intersection of a polyhedron with a line * Line segment intersection * Intersection curve Determination of the intersection of flats – linear geometric objects embedded in a higher-dimensional space – is a simple task of linear algebra, namely the solution of a system of linear equations. In general the determination of an intersection leads to non-linear equations, which can be solved numerically, for example using Newton iteration. Intersection problems between a line and a conic section (circle, ellipse, parabola, etc.) or a quadric (sphere, cylinder, hyperboloid, et ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hausdorff Distance
In mathematics, the Hausdorff distance, or Hausdorff metric, also called Pompeiu–Hausdorff distance, measures how far two subsets of a metric space are from each other. It turns the set of non-empty compact subsets of a metric space into a metric space in its own right. It is named after Felix Hausdorff and Dimitrie Pompeiu. Informally, two sets are close in the Hausdorff distance if every point of either set is close to some point of the other set. The Hausdorff distance is the longest distance you can be forced to travel by an adversary who chooses a point in one of the two sets, from where you then must travel to the other set. In other words, it is the greatest of all the distances from a point in one set to the closest point in the other set. This distance was first introduced by Hausdorff in his book ''Grundzüge der Mengenlehre'', first published in 1914, although a very close relative appeared in the doctoral thesis of Maurice Fréchet in 1906, in his study of the space of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Smallest Enclosing Rectangle
In computational geometry, the smallest enclosing box problem is that of finding the oriented minimum bounding box enclosing a set of points. It is a type of bounding volume. "Smallest" may refer to volume, area, perimeter, ''etc.'' of the box. It is sufficient to find the smallest enclosing box for the convex hull of the objects in question. It is straightforward to find the smallest enclosing box that has sides parallel to the coordinate axes; the difficult part of the problem is to determine the orientation of the box. Two dimensions For the convex polygon, a linear time algorithm for the minimum-area enclosing rectangle is known. It is based on the observation that a side of a minimum-area enclosing box must be collinear with a side of the convex polygon. It is possible to enumerate boxes of this kind in linear time with the approach called rotating calipers by Godfried Toussaint in 1983.. The same approach is applicable for finding the minimum-perimeter enclosing rectan ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Voronoi Diagram
In mathematics, a Voronoi diagram is a partition of a plane into regions close to each of a given set of objects. In the simplest case, these objects are just finitely many points in the plane (called seeds, sites, or generators). For each seed there is a corresponding region, called a Voronoi cell, consisting of all points of the plane closer to that seed than to any other. The Voronoi diagram of a set of points is dual to that set's Delaunay triangulation. The Voronoi diagram is named after mathematician Georgy Voronoy, and is also called a Voronoi tessellation, a Voronoi decomposition, a Voronoi partition, or a Dirichlet tessellation (after Peter Gustav Lejeune Dirichlet). Voronoi cells are also known as Thiessen polygons. Voronoi diagrams have practical and theoretical applications in many fields, mainly in science and technology, but also in visual art. The simplest case In the simplest case, shown in the first picture, we are given a finite set of points in the Euclidean p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Delaunay Triangulation
In mathematics and computational geometry, a Delaunay triangulation (also known as a Delone triangulation) for a given set P of discrete points in a general position is a triangulation DT(P) such that no point in P is inside the circumcircle of any triangle in DT(P). Delaunay triangulations maximize the minimum of all the angles of the triangles in the triangulation; they tend to avoid sliver triangles. The triangulation is named after Boris Delaunay for his work on this topic from 1934. For a set of points on the same line there is no Delaunay triangulation (the notion of triangulation is degenerate for this case). For four or more points on the same circle (e.g., the vertices of a rectangle) the Delaunay triangulation is not unique: each of the two possible triangulations that split the quadrangle into two triangles satisfies the "Delaunay condition", i.e., the requirement that the circumcircles of all triangles have empty interiors. By considering circumscribed spheres, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linear Reference System
Linear referencing, also called linear reference system or linear referencing system (LRS), is a method of spatial referencing in engineering and construction, in which the locations of physical features along a linear element are described in terms of measurements from a fixed point, such as a milestone along a road. Each feature is located by either a point (e.g. a signpost) or a line (e.g. a no-passing zone). If a segment of the linear element or route is changed, only those locations on the changed segment need to be updated. Linear referencing is suitable for management of data related to linear features like roads, railways, oil and gas transmission pipelines, power and data transmission lines, and rivers. Motivation A system for identifying the location of pipeline features and characteristics is by measuring distance from the start of the pipeline. An example linear reference address is: Engineering Station 1145 + 86 on pipeline Alpha = 114,586 fee ... [...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. It produces the most accurate generalization, but it is also more time-consuming. 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. Initi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cartographic Generalization
Cartographic generalization, or map generalization, includes all changes in a map that are made when one derives a smaller-scale map from a larger-scale map or map data. It is a core part of cartographic design. Whether done manually by a cartographer or by a computer or set of algorithms, generalization seeks to abstract spatial information at a high level of detail to information that can be rendered on a map at a lower level of detail. The cartographer has license to adjust the content within their maps to create a suitable and useful map that conveys spatial information, while striking the right balance between the map's purpose and the precise detail of the subject being mapped. Well generalized maps are those that emphasize the most important map elements while still representing the world in the most faithful and recognizable way. History During the first half of the 20th century, cartographers began to think seriously about how the features they drew depended on scale. E ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Convex Hull
In geometry, the convex hull or convex envelope or convex closure of a shape is the smallest convex set that contains it. The convex hull may be defined either as the intersection of all convex sets containing a given subset of a Euclidean space, or equivalently as the set of all convex combinations of points in the subset. For a bounded subset of the plane, the convex hull may be visualized as the shape enclosed by a rubber band stretched around the subset. Convex hulls of open sets are open, and convex hulls of compact sets are compact. Every compact convex set is the convex hull of its extreme points. The convex hull operator is an example of a closure operator, and every antimatroid can be represented by applying this closure operator to finite sets of points. The algorithmic problems of finding the convex hull of a finite set of points in the plane or other low-dimensional Euclidean spaces, and its dual problem of intersecting half-spaces, are fundamental problems of com ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Buffer (GIS)
In geographic information systems (GIS) and spatial analysis, buffer analysis is the determination of a zone around a geographic feature containing locations that are within a specified distance of that feature, the buffer zone (or just buffer). A buffer is likely the most commonly used tool within the proximity analysis methods.Wade, T. and Smmer, S. eds. A to Z GIS' History The buffer operation has been a core part of GIS functionality since the original integrated GIS software packages of the late 1970s and early 1980s, such as ARC/INFO, Odyssey, and MOSS. Although it has been one of the most widely used GIS operations in subsequent years, in a wide variety of applications, there has been little published research on the tool itself, except for the occasional development of a more efficient algorithm. Basic algorithm The fundamental method to create a buffer around a geographic feature stored in a vector data model, with a given radius ''r'' is as follows: * Single point: C ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
