The triangulated irregular network data model, called TIN, is an alternative to the raster data model for representing continuous surfaces. It allows surface models to be generated efficiently to analyze and display terrain and other types of surfaces. It is a special type of vector data model.

TINs are useful for representing surfaces that are highly variable, and contain discontinuities and breaklines. A TIN connects a set of irregularly spaced xyz locations. Each location has significance in that it defines a point where there is a change in the surface. For example, all neighboring points of the peak of a mountain are downhill; all neighbors of a point along a stream, except for the downstream point, are uphill. The points used in defining the TIN are called mass points. Lines, such as streams and shorelines are called breaklines. Areas of constant elevation, such as lakes are called exclusion polygons. Mass points become nodes of triangles, while breaklines and exclusion polygon boundaries become triangle edges (ESRI, 1998).

**
8.2 Structure of TIN Data Model**

The TIN model represents a surface as a series of linked triangles, hence the adjective triangulated. Triangles are made from three points, which can occur at any location, giving the adjective, irregular. This contrasts with the raster model where points are spaced evenly in a lattice. Finally, the TIN model creates a network of triangles by storing the topological relationships of the triangles.

The fundamental building block of the TIN data model is the node. Nodes are connected to there nearest neighbors by edges, according to a set of rules. Left-right topology is associated with the edges to identify adjacent triangles.

Triangles are constructed based on the input of mass points and breaklines, which provide information and constraints about the surface.

The TIN model creates triangles from a set of points called mass points, which always become nodes. The user is not responsible for selecting all of the nodes to be used in creating triangles; additional nodes are added according to a set of rules. Mass points can be located anywhere, the more carefully selected, the more accurate the model of the surface. Well-placed mass points occur where there is a major change in the shape of the surface, for example, at the peak of a mountain, the floor of a valley, or at the edge (top and bottom) of cliffs. By connecting points on a valley floor or along the edge of a cliff, a linear break in the surface can be defined. These are called breaklines. Rivers and shorelines are often used as breaklines. As shown in the next figure, breaklines can control the shape of the surface model. They always form edges of triangles, and, generally, cannot be moved.

An original set of mass points shown in the first diagram results in the TIN shown in the middle. By adding a river as a breakline, a new set of triangles is formed with additional nodes (ESRI, 1998).

The topological structure of a TIN is defined by maintaining information defining each triangle’s nodes, edge numbers and type, and adjacency to other triangles. For each triangle, TIN records:

· The triangle number

· The numbers of each adjacent triangle

· The three nodes defining the triangle

· The x, y coordinates of each node

· The surface z value of each node

· The edge type of each triangle edge (hard or soft)

In addition, TIN maintains a list of all the edges that form the TIN’s hull and information defining the TIN’s projection and units of measure (ESRI, 1998).

TIN can be created from following triangulation methods: Delaunay, Important Points, and Adaptive Densification (Microimage, 1997).

A TIN is generated containing coordinate data that represent a surface as a set of adjacent, continuous triangles constructed from irregularly spaced three-dimensional points. The structure of a TIN is more restrictive than that of other coordinate data objects because every node is part of some polygon, every polygon is a triangle, and every triangle satisfies the Delaunay criterion.

The Delaunay criterion is as follows: Given any three points (in a group of points) used as corners of a triangle, another point can be constructed equidistant from the corner points. Using that point as the center, a circle that passes through all three corner points can be constructed. When the circle intersects only those three points, the triangle satisfies the Delaunay criterion.

Triangulation using the Delaunay triangulation method has the following distinctions. Triangles constructed are as small and equilateral as possible. Sensitivity to calculational precision that can occur when the triangles are elongated thereby is minimized. Delaunay triangulation creates facets such that every point on a facet is as close as possible to a node. For example, consider two edges of a narrow gorge connected by a straight line straight across the gorge: a point on the surface can be close to a node without correctly representing the gorge. Delaunay triangulation minimizes the distance between all surface points and nodes, which results in a highly accurate surface representation. Choosing points for a triangle is an arbitrary process; results are unique. The last property holds true when every point and vertex from the input vector object is used. Setting a non-zero tolerance (minimum distance between nodes in the output TIN object) causes some points to be discarded, based on their proximity to nodes already chosen to be part of the TIN (Microimage, 1997).

The Extract Important Points method creates vector points from raster elevation data. Points are created automatically for cell values at regular grid intersections or that mark significant changes in surface elevation, depending on the chosen point extraction method. The Extract Important Points process is an efficient and effective alternative for locating surface elevation features. The resulting three-dimensional vector data is converted into TINs for surface representation (Microimage, 1997).

**
8.4.3 Adaptive Densification Method **

The Adaptive Densification method is used to create TIN objects using raster surface data as the input object. The Adaptive Densification process interatively inserts nodes inside existing triangles at the location of maximum surface deviation from the plane of the triangle. The process starts with four nodes located at the corner of the raster and handles null value cells correctly, even if the corner of the raster contain null cells (Microimage, 1997).

**Nodes**

Nodes are the fundamental building blocks of the TIN. The nodes originate from the points and arc vertices contained in the input data sources. Every node is incorporated in the TIN triangulation. Every node in the TIN surface model must have a z value.

**
Edges**

Every node is joined with its nearest neighbors by edges to form triangles, which satisfy the Delaunay criterion. Each edge has two nodes, but a node may have two or more edges. Because edges have a node with a z value at each end, it is possible to calculate a slope along the edge from one node to the other.

Each feature in the input data sources used to build the TIN is processed in accordance with its surface feature type. Breakline features are always maintained as edges in the TIN triangulation. These breakline TIN edges are internally flagged as either HARD or SOFT edges.

**
Triangles**

Each triangular facet describes the behavior of a portion of the TIN’s surface. The x, y, z coordinate values of a triangle’s three nodes can be used to derive information about the facet, such as slope, aspect, surface area, and surface length. Considering the entire set of triangles as a whole, it is possible to derive additional information about the surface including volume, surface profiles, visibility analysis, and surface views.

Because each facet summarizes a certain surface behavior, it is important to ensure that the sample points are selected adaptively to give the best possible surface fit. A TIN surface model can yield poor results if important regions of the surface are under-sampled.

**
Hulls**

The hull of the TIN is formed by one or more polygons containing the entire set of data points used to construct the TIN. The hull polygons define the zone of interpolation of the TIN. Inside or on the edge of the hull polygons, it is possible to interpolate surface z values, perform analysis, and generate surface displays. Outside the hull polygons, it is not possible to derive information about the surface. The hull of a TIN can be formed by one or more polygons, which can be non-convex.

A non-convex hull must be user defined by including CLIP and ERASE exclusion features during the construction of the TIN. These features explicitly define the edge of the surface. When no exclusion features are used to define the hull, the TIN generator creates a convex hull to define the bounding edges of the TIN. A convex hull is a polygon with the property that any line connecting any two points of the TIN must itself lie inside or define the edge of the convex hull. The definition of a non-convex hull is essential to prevent the generation of erroneous information in regions of the TIN outside the actual data set, but inside the convex hull. Consider the next diagram.

This TIN was generated from the same data set, but without the use of CLIP features. Within the shaded areas, it is possible to derive false surface information about the surface.

**
**

**
Breaklines**

Breaklines define and control surface behavior in terms of smoothness and continuity. As their name implies, breaklines are linear features. They have a significant effect in terms of describing surface behavior when incorporated in a surface model. Breaklines can describe and enforce a change in the behavior of the surface. Z values along a breakline can be constant, or can vary throughout its length. Three types of breaklines can be employed to describe surface behavior: hard breaklines, soft breaklines, and faults.

**
breaklines**

Soft breaklines are used to ensure that known z values along a linear feature are maintained in the TIN. Soft breaklines can also be used to ensure that linear features and polygon edges are maintained in the TIN surface model by enforcing the breakline as TIN edges. However, soft breaklines do not define interruptions in surface smoothness.

Here is an example of how the inclusion of a soft breakline can enforce a different surface behavior. Note how the TIN builder has added extra vertices along the breakline to ensure that the line is maintained in the TIN. The z values for these new nodes have been derived by linear interpolation along the breakline

The input data to build a TIN includes four points and one line with two nodes.

Here is the TIN that results when the points and nodes are processed as mass points.

When the line is enforced as a breakline, the line is maintained in the TIN. Note the z values of the introduced nodes.

As with all breaklines, soft breaklines can have constant or varying z values. For example, a section of pipe with a constant elevation can be defined as a soft breakline. In contrast, a highway with fluctuating elevation can be incorporated into a TIN surface model as a soft breakline.

**
Hard breaklines**

Hard breaklines define interruptions in surface smoothness. They are probably the most common and easily understood type of a breakline. Hard breaklines are typically used to define streams, ridges, shorelines, building footprints, dams, and other locations of abrupt surface change.

In the case of a hard breakline defining a stream, the breakline has varying z values throughout its length. The surface exhibits smooth behavior on both sides of the stream, but the slope normals are radically different on opposite sides of the breakline.

**Faults**

Faults represent interruptions in surface continuity. Geological faults are probably the most common type of fault. In the case below, the Earth’s surface has been shifted vertically, causing a ‘stair step’ discontinuity in the surface. Faults have more than one z value for a given x, y location; an elevation exists at the same x, y location at both the top and the bottom of the fault.

Faults are not limited to vertical faults, but can be shifted in both the vertical and horizontal dimensions. Because functional surfaces are capable of storing only one z value for a given x, y location, they are not capable of directly storing faults. It is possible to represent a nearly vertical fault as two parallel breaklines; one containing surface z values at the top of the fault, and a second with z values at the bottom.

**
8.6
Application of Raster Data Model**

**3D
Visualization of Urban Setting Based on
Tin Data Model with Hypertext
Markup Language (Html) and
Virtual Reality Modeling Language (Vrml)**

Geographic Information Systems depicts spatially distributed data as they would be shown on a map, a two dimensional surface, viewed from nadir via a high platform, with spatial objects represented by a mosaic of colors and patterns. The land surface is undulating, objects viewed are three dimensional and have characteristic structures, appear smaller in the distance, and features are located above, below and around the observer. Recently the 3D GIS has added more freedom to visualize the global and spatial data more similar to actual world. The HTML and VRML techniques can add new dimension to 3D GIS. Through this techniques 3D GIS can be presented such a way as if it is real.

A Geographic Information System provides access to data that are keyed to a place and time and supports the visualization and analysis of those data. Place and time require four dimensions – two map coordinates, elevation, and time. But most GIS software inherently supports only the map dimensions. Elevation and time are handled by ad-hoc methods or specialized expensive software (Bill, 2000). So the output of 3D GIS can not be presented widely. With VRML and HTML this data can be presented through web and can be presented without any specialized expensive software.

City is an important application field of GIS. 3D city model is required in many application fields such as urban planning, visibility analysis, urban engineering and communication design. In traditional 2D GIS, 3D city shape is represented by point, line and polygon in 2D plane. Sometime 2.5D display is produced. But, in this situation the representation is very abstract. There is no realistic 3D visualization and also difficult to carry out 3D manipulation and analysis. Along with the development of computer technique, especially in 3D graphics and visualization, the people have ability and deeply wish to increase 3D function in 2D GIS system in order to realize 3D display, manipulation and analysis for more and more application requirements. Also, 3D modeling and visualization are important techniques of Digital Earth which is presented in recent years (Qingquan, Wenzhong, Bisheng, 1999). In 3D city model, major objects are topography and buildings. The formal is natural irregular object and the latter is man made regular object. For buildings people focus and attention is not only to its outside shape and description but also to geometrical structure and attribute at different layers as well as the relationship between layers. The important spatial analysis and manipulation are geometrical analysis and spatial query.

TIN data model is widely used to represent trained surface and 3D GIS analysis. It can produce 3D visualization. 3D map have a great usefulness in urban planning. It can give a virtual view of an area. This study produces three 3D maps of three selected site of Khulna City in ArcView 3D Analyst and with the help of Hyper Text Markup Language (HTML) and Virtual Reality Modeling Language (VRML) the out put has been presented in web page without using ArcView 3D Analyst.

Spot heights of the selected areas have been interpolated to prepare surface DEM. The surface DEM is converted to TIN in ArcView 3D analyst. Z-value tolerance has been set to 0.1 ft to make the surface smooth enough that is 0.1 ft will be the unit height of Z-value. It may be termed as Z-value resolution of TIN.

Polygon topology theme of road, building, water body and Surface TIN has been added to 3D Scenes Document of ArcView. 3D theme properties have been declared to generate 3D visualization. The parameters of the theme properties was –

**3D properties of surface TIN**

Base height Surface: Surface TIN

coverage

Z factor: 1

Offset height value: 0

Show Shading for feature: on

**Figure 8.1** shows the
parameters

**3D properties of Buildings**

Base height Surface: Surface TIN

coverage

Z factor: 1

Offset height value: 0

Extrude feature expression: [strd] * X

Extrude to adding to min z value

Show Shading for feature: on

**Figure 8.2** shows the
parameters

**3D properties of Road **

Base height Surface: Surface TIN

coverage

Z factor: 1

Offset height value: 0

Extrude feature expression: 1

Extrude to adding to min z value

Show Shading for feature: on

**Figure 8.2** shows a
similar parameter window

**3D properties of water body
**

Base height Surface: Surface TIN coverage

Offset height value: -5

Extrude feature expression: 6

Show Shading for feature: on

Extrude to adding to min z value

*Advanced options *(**Figure
8.3**)

Draw theme when intersecting: 1 second

Draw theme when not intersecting: 1 second

Percent transparent: 30 %

**Figure 8.2** shows a
similar parameter window

3D scene properties set the
parameter to enhance the 3D visualization the parameters windows for the three
selected area presented in **Figure 8.4**, **Figure 8.5** and **Figure
8.5** (Under developed area, mixed use area and planned residential area
respectively)

**Figure 8.4:**
3D scene properties used for 3D visualization of an underdeveloped area

**Figure 8.5:**
3D scene properties used for 3D visualization of a mixed use area

**Figure 8.6:**
3D scene properties used for 3D visualization of a planned residential area

3D scenes
have been exported to VRML 2 format from ArcView. Editing the VRML files
presentable VRML file (**ANNEXURE D**) has been created. Web page is
designed to present the virtual view of the sites which creates links between
the VRML layers.

**Figure 8.7:** Virtual view of urban settings

1.
Selected underdeveloped area (**Map 8.1**) contains a lot of open land. The
structures are mainly katcha but contain some TIN shaded structures and
buildings. There are no buildings over two storied. The 3D map is presented at
**Map 8.2** and 3D VRML view is presented in a CD at **ANNEXURE E**.

2. The
mixed use naturally growing area (**Map 8.1**) is very much congested. It
has very less open space. Main structure type is one to five storied building
but it also contains cluster of katcha structures. The 3D map is presented at
**Map 8.3** and 3D VRML view is presented in a CD at **ANNEXURE E**.

3.
Structures of planned residential area (**Map 8.1**) are very much regular.
Many plots of the area are still undeveloped. There is no katcha and TIN
shaded structure found

in source
map of this area. The buildings are one to five stored. The 3D map is
presented at **Map 8.4** and 3D VRML view is presented in a CD at **
ANNEXURE E**.

A lot of research works have been completed in theory and application about 3D modeling. Some commercial GIS software has starts to provide 3D function in their traditional 2D GIS. Especially, lots of results in 3D data model and some prototype systems are developed. However 3D GIS need to be researched deeply in theory and application due to the complex of 3D objects in geometrical structure and attribute (Qingquan, Wenzhong, Bisheng, 1999). During 3D GIS applications, 3D city model or visualization is useful in many application fields. There are lots of objects which are included in 3D city. But the major are topography and building. In order to represent terrain and building in 3D city TIN model are applied to represent 3D objects and topography of urban area.