as observations within the neighborhood.
Since the local DTMs of the neighboring points are
strongly correlated to each other, the whole terrain model con-
sists of those local DTMs will form a smooth surface. Contour
lines redrawn as dropped on this surface are expected to be fine
and beautiful(Fig 1). This redrawing process is carried out mov-
ing only the planimetry of every point which forms contour
lines. In a strict way, change of elevation should be concerned,
however, the accuracy of elevation observation in normal situ-
ation is good enough to ignore the effect of its correction.
obtained
data
Collect observations within the
neighborhood of A
Y
Generate a local DTM
(1st/2nd/3rd order polynomial)
E
pr
Calculate the distance
between A and the local DTM
v
Correct A's planimetry coordinates
Fig 1 The flow chart of the Local DTM editing
2.2 Mathematical model of Local DTM
In the following, n is used as the number of observed points
which are found within the area of radius r around a concerned
point A(x,.y,,z,). By using the least square method, the surface
function of DTM is determined which approximates those ob-
servations best. Before calculation, all these observed data are
transformed into local coordinates so as to let A be the
origin(Fig 2).
Fig 2 Local area around point A
862
2.2.1 Type of the Local DTM The local DTM of the point
A is expressed as an equation of elevation z functioned by its
planimetry as follows:
z = f(x,y) (2.1)
In each local DTM type of 1st, 2nd and 3rd order polynomial
will be expressed as:
z = a+bx+cy (2.2)
z = a+bx+cy+dx"+exy+fy? (2.3)
z = a+bx+cy+dx*+exy+fy?+g x +hx?y+ixy?+jy? (2.4)
In the following explanation, the type of 2nd order DTM(2.?) ;
used.
2.2.2 Observation equations In order to determine the
best fit DTM polynomial, the least square method using the
coordinates of points in the local area is adopted. Let [oZ lis
be observations of elevation at each point, V, be corrections for
them, and function (2.3) be the type of local DTM. The
observation equations are given as:
LeX=C+V (2.5)
where:
2 2
1 X NH XN
s : 12 2
L- 1 X, Yo X% X» Y,
Dx y 4 ry 2
