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.

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

**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.

**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

**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.