Large-scale Three-dimensional Geographic Information Systems meet the Systems for Architecture, Engineering and Construction

By Roberto Lattuada and Jonathan Raper

Lattuada_Raper Historically GIS and AEC have developed as solutions to different problems in different domains: the former optimized for the modelling of new, but well defined objects; the latter for the re-construction of existing objects about which only sparse and incomplete information is available.

The modelling of complex systems that go beyond the drawing part of the problem well into the simulation, budgeting, environmental impact analysis and decision support makes a strong case for a tighter integration of GIS and CAD/AEC in a full three-dimensional environment.

GIS and AEC object types
In CAD/AEC oriented systems the main target is to define objects using geometric primitives to design, evaluate, edit, and construct.Classical CAD methods are used to interactively design curves and surfaces, Bezier and Spline techniques have been used extensively for this purpose, because they generate nice smooth geometries that are storage-efficient and easy to manipulate interactively.

In AEC systems:

  • we build mathematical descriptions of objects whose shape is well known
  • the editing and drawing step is crucial as very little data is initially available
  • the modelling process is targeted at manufacturing these objects
  • well known, simple shaped objects, with a corresponding efficient mathematical description, are often used in the modelling process to build more complex structures (CSG)
  • the final object is well defined, to any degree of precision required.
Much CAD/AEC graphics technology was developed to serve mechanical engineering disciplines; designing cars bodies, buildings, machined parts and other man-made objects.These are not easy tasks but are completely different from modelling natural objects, especially geo-scientific objects.Unlike "designed" objects, geo-scientific objects are revealed by limited samples, or by indicative data which is highly irregular and complex with many more parameters than simple geometry.

In GIS systems:

  • we build statistical descriptions of objects whose shape is not well known
  • the capability to handle large amounts of diverse input data is crucial (seismic data, boreholes data, known geo-morphological shapes, etc.)
  • spatial functions like adjacency, proximity, connectivity, inclusion/exclusion are required, complex spatial relationships need to be determined and simulated to place the data in context and truly create a model
  • only limited editing is usually required
  • many models may be created for a particular project and they should be filed and managed with their respective source data and modelling parameters.
Spatial representations
Once defined, the CAD/AEC and GIS objects need to be stored and logically connected.The way in which spatial data are numerically stored, linked and processed in a computer constitutes a spatial representation.

Common approaches to representing spatial objects include the following.

  • Mesh representations:
    • the model is described as a collection of polygonal facets called mesh
    • the information relative to the vertices position and how they combine to form facets needs to be stored
    • vertices and edges are only represented as part of a facet
    • a boundary representation of the object is obtained
  • B-Rep representation
    • basic elements like faces, edges and vertices are explicitly represented and their shape and position recorded
    • a topology description records the connectivity of faces, edges and vertices and the overall structure (adjacency, orientation, inside/outside)
    • geometry can be of arbitrary shape (not limited to planar)
    • a boundary representation of the object is obtained
  • Constructive Solid Geometry
    • the object is represented as a hierarchy of Boolean operations between simple geometric primitives (i.e. spheres, cylinders, blocks)
    • a volume representation of the object is obtained
  • Voxel representations (including Spatial Occupancy Enumeration and Cell Decomposition)
    • the object is represented as a uniform grid of voxel elements
    • a volume representation of the object is obtained
The border between the various data models is not always clear, industry systems tend to adopt the best features of each modelling technique, it is therefore not uncommon to work with hybrid data models that inherit from the surface, volume or voxel-based representations.

Requirements for a common 3D GIS/AEC data modelling solution
From the previous sections we see how a unified data modelling solution must be functional not only in the aspect of modelling, but also in analysis and visualization; some of the most important requirements are:

  • integration of spatial and non-spatial objects
  • maintenance of spatial relationships (implicit or calculated topology)
  • fast search and application of spatial, statistical, mathematical and geometrical functions
  • efficient storage and data handling
  • ability to operate on object composites, join several objects of similar types, apply spatial set operations
  • handling of geometrical and numerical constraints.
In particular, a comprehensive handling of geometrical constraints is crucial when we want to merge objects that originated in different systems.

The Extended Simplex Model (ESM)
The simplex model utilized as part of the proposed solution evolves from the 3D FDS and TEN models as described in [Molenaar 1990], [Slatanova ] and [Pilouk 1996].The basic geometric entities or constructive objects are n-dimensional simplices: point, edge, triangle and tetrahedron. Differently from previous work, besides the basic constructive objects the system is completed with:

  • an efficient storage structure based on octrees
  • a method to build a triangulated model (Delaunay triangulation) from a set of points (0-dimensional simplices)
  • procedures to generate constrained triangulations incorporating 1- and 2-dimensional simplices (edges and triangles)
  • fast searching routines with bounded "neighbourhood" searches
  • minimal storage requirements achieved by separating the geometric information from the triangulation-derived explicit topology information
The triangulation process generates explicit topological information that describes in full the relationship between the tetrahedral elements in the model; other relationships (i.e point on face, edge on face, etc.) are not stored nor maintained but can be easily calculated when needed.

Conclusions
The Extended Simplex Model satisfies most of the requirements for an integrated modelling framework where CAD, AEC and GIS models can be brought together as:

  • it provides an integrated spatial addressing schema and an homogenous construction approach for the geometry of surfaces and volumes in three dimensions
  • it offers a minimal space partitioning solution and fast generation of 3D subdivision of space
  • has the ability to create efficient representations for display purposes (VRML, triangular meshes)
  • offers fast object access and data structure traversal
  • point level editing can be performed on the merged model without a recursive import/export to the original modelling package
  • boundaries and constraints can be easily integrated into a model
  • the model generation and constraints recovery processes are automatic.
Finally the simplex model could be easily adopted by the OGC as a natural extension to the simple-features schema.

Published Thursday, September 9th, 2004

Written by Roberto Lattuada and Jonathan Raper



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