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Triangulated Irregular Network 
The TIN model represents a surface as a set of contiguous, nonoverlapping triangles. Within each triangle the surface is represented by a plane. The triangles are made from a set of points called mass points. Mass points can occur at any location, the more carefully selected, the more accurate the model of the surface. Wellplaced 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. The TIN model is attractive because of its simplicity and economy and is a significant alternative to the regular raster of the GRID model. Quick comparison: 
TIN  GRID  
Advantages 


Disadvantages 


The Delaunay Triangulation Delaunay triangulation is a proximal method that satisfies the requirement that a circle drawn through the three nodes of a triangle will contain no other node
Delaunay triangulation has several advantages over other triangulation methods:
TINs from contours Contours are a common source of digital elevation data. In general all the vertices of the contour lines are used as mass points for triangulation. In many cases this will cause the presence of flat triangles in the surface. Flat triangles are created whenever a triangle is formed from three nodes with the same elevation value Flat triangles are frequently generated along contours when the sample points occur along the contour at a distance that is less than the distance between contours. When these "excess" vertices are not removed , the Delaunay triangulation discovers that the closest sample points are those along the same contour, causing the generation of flat triangles. The flat triangles have a slope of 0 and do not have defined aspect. They might cause problems when the surface is used for modeling. Example 
The contours  The triangulation  We can see several flat triangles here 
The elevation  The slope The green areas indicate Slope = 0 (flat triangles) 
How can we avoid the flat triangles ?
Break lines Linear features which define and control surface behavior in terms of smoothness and continuity are called break lines. Types break lines:
Example: 
No break lines  Soft break lines  Hard break lines  
The Data  
The Triangulation  
The Surface  
3D View 
Storing TINs There are basically two ways of storing triangulated networks:
The first method is better for storing attributes (slope, aspect ..) for each triangle, but uses more storage space. The second one is better for generating contours and uses less storage space, but slope, aspect , etc. must be calculated and stored separately. TIN and ET Surface ET Surface 4.0 and above can store TINs using both data structures above. 
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