1-5 Distance

Distance is one of the important elements in measuring spatial objects in GIS. Several different concepts of distance are defined as follows.

Euclidean Distance
Euclidean distance D is the defined as the distance measured along a straight line from point (x1, y1 ) to point (x2, y2 ) in Cartesian coordinate system (see Figure 1.15 (a).

D2 = ( x1 - x2 ) + ( y1- y2 )2

Manhattan Distance
Manhattan distance D is defined as the rectilinear rout measured along parallels to X and Y axes as shown in Figure 1.15 (b).

D = | x1 - x2| + | y1- y2|
Great Circle Distance
Great circle distance D is defined as distance along the great circle of the spherical Earth surface from a point (j 1 l 1; latitude and longitude) to another point (j 2 l 2) as shown in Figure 1.15 (c).

where R is the radius of the Earth (R = 6370.3 km) on the assumption that

the Earth is a sphere.

Mahalanobis Distance
Mahalanobis distance D is a normalized distance in the normal distribution from the center () to a point (X) in case of n dimensional normal distribution. Mahalanobis distance is used in the maximum likelihood method for the classification of multi-spectral satellite images.

where S: variance-covariance matrix

Time Distance
Time distance is defined as the time required to move from point B to point A by using specific transportation means.

Figure 1.15 shows major distances.