Ebook Computing in geographic information systems: Part 2
➤ Gửi thông báo lỗi ⚠️ Báo cáo tài liệu vi phạmNội dung chi tiết: Ebook Computing in geographic information systems: Part 2
Ebook Computing in geographic information systems: Part 2
7Computational Geometry and ItsApplication to GISComputational geometry is defined broadly as the design and analysis of algorithms for solving proble Ebook Computing in geographic information systems: Part 2 ems involving geometric objects. Use of the term 'computational geometry' and its meaning differs in different, application contexts. Most researchers in computer science interpret the subject as design and optimization of algorithms involving geometric problems. The term vigor'll.hm design' carries Ebook Computing in geographic information systems: Part 2 the connotation of discrete algorithms as opposed to the algorithms used in numerical analysis. The numerical analysis problems are used for solvingEbook Computing in geographic information systems: Part 2
computational problems in continuous domains. Computational geomet ry is useful in solving problems of discrete combinatorial geometry rather than con7Computational Geometry and ItsApplication to GISComputational geometry is defined broadly as the design and analysis of algorithms for solving proble Ebook Computing in geographic information systems: Part 2 are used to process spatial data winch arc the primary inputs of GIS.Computational geometry emerged as a field of research three decades ago. Since this area has been identified, a number of core geometric problems have emerged. A number of com pi 11 at ional geomet l ie algorit hms have been design Ebook Computing in geographic information systems: Part 2 ed to solve these problems. These algorithms arc optimized for their computation time and memory. Research in computational geometry is progressing toEbook Computing in geographic information systems: Part 2
compute large volumes of geoinet lie data and degenerate data. Therefore the robust versions of these algorithms have been devised for processing the7Computational Geometry and ItsApplication to GISComputational geometry is defined broadly as the design and analysis of algorithms for solving proble Ebook Computing in geographic information systems: Part 2 roductionMany of the problems that arise in application areas such as computer graphics, computer-aided design and manufacturing, robotics, (ns. computer vision, human-computer interface, astronomy, computational fluid dynamics, molecular biology etc. can be described using discrete geometrical stru Ebook Computing in geographic information systems: Part 2 ctures. These problems can be solved using a set of algorithms known as computational geometric algorithms. However it should be remembered that not aEbook Computing in geographic information systems: Part 2
ll the geo-119120Computing in Geographic Information Systemsmetric applications can be modelled using the discrete geometric structures or solved usin7Computational Geometry and ItsApplication to GISComputational geometry is defined broadly as the design and analysis of algorithms for solving proble Ebook Computing in geographic information systems: Part 2 plane, but using a matrix of digit ized locat ions of pixels. Problems in computer-aided manufacturing often involve curved surfaces rather than polyhedral surfaces. Problems in fluid dynamics are generally of a continuous nature defined by differential equations, rims, computational geometry as it Ebook Computing in geographic information systems: Part 2 is commonly defined is not quite broad enough to address all problems in all these areas. However, the field is broad enough such that virtually all oEbook Computing in geographic information systems: Part 2
f these application areas can use some of the algorithms in computational geometry. A good introduction to computational geometry along with the algor7Computational Geometry and ItsApplication to GISComputational geometry is defined broadly as the design and analysis of algorithms for solving proble Ebook Computing in geographic information systems: Part 2 with their applications to GTS ill the context of processing spatial data pertaining to land, sea and air are listed below.1.Algorithms to determine line-line intersection.2.Algorithms to find whether a point lies inside a triangle, polygon, circle, or sphere.3.Algorithms for computing convex hull. Ebook Computing in geographic information systems: Part 2 1.Computing triangulation of a simple polygon in 2D.5. Computing Delaunay triangulation of a set of points ill a plane.(5. Computing the Voronoi tesseEbook Computing in geographic information systems: Part 2
llation of a set of points ill a plane.These sets of algorit Inns are often called Computational Geometric Algo rithmic Library (CGAL). The input io C7Computational Geometry and ItsApplication to GISComputational geometry is defined broadly as the design and analysis of algorithms for solving proble Ebook Computing in geographic information systems: Part 2 e segments (communication lines such as roads, rails, power Iransniission lines etc.), polygons (coverage of stales within the geographic boundary of a country, water bodies), polyhedrons, circles, spheres in the Euclidean space.7.2Definitions7.2.1 Triangulation and PartitioningTriangulation is a ge Ebook Computing in geographic information systems: Part 2 neric method for subdividing a complex domain into a disjoint collection of 'simple' objects. A triangle is the simplest region into which one can decEbook Computing in geographic information systems: Part 2
ompose a plane and this process is known as triangulation. TheComputational Geometry and Its Application to GIS121higher dimensional generalization of7Computational Geometry and ItsApplication to GISComputational geometry is defined broadly as the design and analysis of algorithms for solving proble Ebook Computing in geographic information systems: Part 2 ation is typically a first step performed in number of algorithms. These triangles are then subjected to computational operations through an iterative process to compute the objective and analyze the overall domain.Triangulation 'T' is tessellation of a polygonal region of the plane into nonoverlapp Ebook Computing in geographic information systems: Part 2 ing, continuous triangles T-i such that, their intersection is empty, or it is coincident with a vertex, or an edge of both triangles.rnir =(7.1)j-1whEbook Computing in geographic information systems: Part 2
ere, |/j is the number of triangles in the domain. Hence the domain of T is the plane curved by its triangles. In addition to the above definition, if7Computational Geometry and ItsApplication to GISComputational geometry is defined broadly as the design and analysis of algorithms for solving proble Ebook Computing in geographic information systems: Part 2 elaunay Triangulation (DT). This is known as the empty circumcircle property of DT.7.2.2Convex HullPerhaps the first problem ill the field of com pi I tat ional geomel ry is I he problem of comput ing convex hulls, I hat is, 1 he smallest convex shape t hat surrounds a given set of objects. In other Ebook Computing in geographic information systems: Part 2 words, it suffices to say that the convex hull can be imagined as a stretched elastic membrane surrounding the objects which snap tightly around theEbook Computing in geographic information systems: Part 2
objects. Il is an interesting problem both because of its applications as an initial step towards solving other algorithms, and the number of interest7Computational Geometry and ItsApplication to GISComputational geometry is defined broadly as the design and analysis of algorithms for solving proble Ebook Computing in geographic information systems: Part 2 tions as follows.Let s be a set of discrete objects in 21) plane, rhe set is convex ifXcS A YcS & XYcS(7.2)Generally segment. xy is I he set of points X, y of 1 he form (ư+ 3y I and a > 0 and /3 > 0.7.2.3Voronoi Diagram and Delaunay TriangulationGiven a collection of points in space, perhaps the mos Ebook Computing in geographic information systems: Part 2 t important geometric data structures for describing the relationships among these points and the7Computational Geometry and ItsApplication to GISComputational geometry is defined broadly as the design and analysis of algorithms for solving proble7Computational Geometry and ItsApplication to GISComputational geometry is defined broadly as the design and analysis of algorithms for solving probleGọi ngay
Chat zalo
Facebook