3-2 Triangulated Irregular Network (TIN)

Triangulated irregular network or TIN is a DEM with a network of triangles at randomly located terrain points. Irregular spaced sample points are measured with more points in areas of rough terrain and fewer in smooth terrain. These sample points are connected by lines to form triangles under Delaunay criterion. A circle drawn through three points of the triangle contains no other points as shown in Figure 3.3. Such triangle is called a Delaunay triangle.

Delaunay triangles can be created from Thiessen polygons (see Figure 2.5) in such a way that two vertices are connected to form the Delaunay triangle if their Thiessen polygons share an edge as shown in Figure 3.4.

There are three data structures for storing TIN model (see Figure 3.5 and Table 3.1)

Triangle -based structure (see Table 3.1 (a)): efficient for slope analysis
Triangle ID
Three node IDs and coordinates
Neighbors of triangle

Point-based structure (see Table 3.1 (b)): efficient for contouring and other traversing
Point ID
Coordinates
Neighbors of point

Side-based structure (see Table 3.1 (C)): also efficient for contouring
Point file with ID and coordinates
Triangle file with ID and and three point IDs
Side file with ID, two point IDs and neighbor triangle (left and right)

Contouring of TINs is based on the following procedure. (see Figure 3.6)

step 1: find the intersect of contour and a side
step 2: assign the "reference point" with the symbol r to the vertex above the contour height and the "sub-point" with the symbol
s to the vertex below the contour height.
Step 3: shift over to the transversing to find the third vertex in the triangle by checking whether it is a reference point (r) or sub-point (s).