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
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.
Figure 1.15 shows major distances.