Topology in 3rd Dimension and site location for urban facilitiesPoorya KhodaverdiTechnical Manager Al Amjad L.L.C. (Representative of Geovirtual S.L.), UAE Email: info@alamjadco.com Introduction Spatial Data in 3rd dimension is structured on the basis of DTM, satellite images and Aerial photography draped on them as the rasterized spatial data and vector data and 3D models of the features. This whole is known as the virtual recreation of real data on various scales. On the dawn of GIS software, this has been somehow the basis for visualizing map data on monitors. In addition to the important role of DTM and satellite images, 3D Geography’s perfection is reached by adding Geospatial vector data to the scene. In 2D spatial data management, geometries interact either explicitly or implicitly with each other in an advance way. These geometries are implemented based on point, line and area and their interactions would result in creation of “nodes, links and polygons”. Studies on relation of features, as geographical objects, determines in topological context and specifically in explicit ones two or more geometries have physical or logical interactions. In this article, inspired by the 2D Geospatial vector models, new practical definitions are suggested for the structure of 3D geographic objects. This new approach could be a base for creation of geospatial application models functioning in site location and infrastructure spatial data management systems for urban management purposes. This article offers a new approach to 3D geometry by introducing “3D Topo”, This topology explains smart geometric interaction accord geometries built up on a basis of simple topologies (node, link and polygon) and can create smart 3D objects together with mesh. These smart 3D objects, which are hereafter called “Holex”, would interact with each other through all their faces in a simulated geographical environment. Because these 3D objects are smartly enriched by knowledge-based non spatial information. Holex could differentiate their surrounding areas through all their faces and could even give you the information about the geometries in which they are embedded, connected and/or having interaction with. With help of Holex, algorithms could be developed functioning in implementation-analysis and reporting the results for site location and urban simulation purposes, pretty similar to the reality. As for the 4th dimension “TIME”; Storing 3D objects in databases on periodic basis enables tracing changes of your simulated environment (i.e. a city) in a time based manner. The latter is a time stamped databank which helps observing the changes of the geographical environment (provided the data related to that location are collected on a timely base and in 3D Geospatial databases). Holex will be the ultimate choice of implementation of systems for intelligent real estate management, natural terrains and man-made, also simulations of urban projects in this way could show the ecological, social, visual and human impacts of them before execution. To reach this goal, descriptive data would be stored in Holexes. Holexes would be attributed by descriptive data stored in them that enables them accept different characteristics and interpret the situation Topology Functioning in 2nd Dimension Two-dimensional GIS Softwares have created basic structure for topologies Point, line and Area connection by introducing Node, Link and Polygon. Depending on the Spatial Databases, these topologies are able to present features and objects having geometric relation with each other. In another word, these topologies show the superimposition between the spatial data that could be analyzed topologically too. Different rules could be set for two or more geometry interacting by programming. One of these rules is the split geometry or split topology showing interaction between a line and a point, or it could be none of the above. Look at figure (1), it shows the interaction between the line and the point linked to it:  Figure:1  We could assume the following structure could be generalized for 3rd dimension and in the same way that spatial geometry is originated from basic geometry, topology could be generalized in 3D geometry to create 3D geographic objects.  Figure:2 The important tool in the hands of urban management is the ability to analyze the information of the artificial features and objects. When a city grows the number of these feature increases and part of the evaluation and management of city is dedicated to do structural analysis, lay out analysis and their connection to other social, economical and political information. Since the mesh are evolved from the basic geometry, then we could explain new definitions for the superimposition and interaction between points, lines, areas and objects in 3D. This paper suggests that these objects forming a topological structure in 3 Dimension, could be called “Holex”. Holexes have topology on their all surfaces and represent topology in 3D. For example, connection between each line and surface causes the logical division of the line and surface and split of a mesh by a surface forms shared surfaces. 3D Topological relation In order to implement Holexes and to show the interaction between a 3D object and its surrounding, complicated set of interactive rules for the relation of each component of the Holex and the relation between Holex and link, Line and Mesh are needed to be established. In this way, by relating two objects they could behave as two intelligent 3D objects who query their position in relation to other objects. This could help urban decoration analysis by defining the necessary conditions of an urban plan for site location analysis. The analysis could show the visual aspects of the site locating process in addition to the calculations.  Figure:3 Storing 3D objects in databases on periodic basis enables tracing changes of your simulated environment (i.e. a city) in a time-based manner. Different periods for updating information related to these features could be set. Provided the data is stored properly, on updating, one could study a Holex in different periods and even simulate the Holex for a definite period. This would help the developments in cities to be virtually simulated from past to present time and be a guide for future decision-making. Holex Data Storage The main issue in such system is to establish databases in large volume, having easy access to data and the system management. Different methods for data entry and storage for Holex could be suggested. One of these methods is HSIM (Hierarchical Spatial Model Indexing). In HSIM model spatial index, which defines the existing place of spatial data themselves, is separated from the body of spatial data. HSIM employs a cache mechanism to load immediately requested spatial data by referring to spatial indexes. As a result, not-so-high-spec PCs have become able to manipulate enormous spatial data on a real-time basis. The suggested method would simplify the data storage and access in databases. An example for 3D Spatial Site locating If such system is implemented, 3d algorithm could be defined for 3D environment and in parallel with urban planning and data analysis procedures, visual aspects of the element’s lay outs for various features could be presented and studied. Bellow is an example for these algorithms implementation There are various constraints, conditions and parameters for urban infrastructure and residential areas site locating.  Figure:4 To choose the optimized location in a Geographic region, the space could be defined by 3D cubes that are recognized by a value related to a specific land us. By changing the location in these cubes and calculating the torque of these values through following conceptual equation: T = v (x, y, z) d(x. y. z) f(x) Where w: value d: distance between the current space and the nearest unoccupied space F(x): the constraints and conditions function The optimized location is recognized by the minimum value of the Torque. |