So: ro =up-R-Xop [1] 
up = length factor 
R = rotation matrix [3x3] (camera orientation) 
C = cameraconstant 
The length factor up takes care of the difference between the 
light ray's path from P to O as expressed in Upo and the 
light path from O to P as expressed in R-Xop. 
The problem of monoplotting is finding the terrain 
coordinates UP, VP, WP when the camera coordinates Xp, 
Yp of the image points are known. It is clear from the 
derivation of relationship /77 that this is possible only if the 
position of the perspective centre is known in both the 
camera system and the georeference system. Furthermore, 
the camera orientation (R) and the length factor up should be 
known. 
The position of the perspective centre and the camera's 
orientation is easily computed by means of a numerical 
restitution. These parameters of the numerical restitution can 
only be found if at least three image points for which the 
vector Xop is known and their corresponding georeferenced 
coordinates (ground control points) in position and height are 
known. 
When R and Uo, Vo, Wo are known, the problem of 
monoplotting is to find the coordinates Up, Vp, Wp for each 
point for which Xp and Yp are known. From equation [I] 
follows : 
  
Up Uo Xp-Xo 
Vp = Vo -up 'R Yp-Yo [2] 
Wp Wo C 
  
  
  
  
For each measured image point there are three equations with 
four unknown quantities: 
- the georeferenced coordinates of the image point 
(Up, Vp, Wp) 
- the length factor up. 
Additional information is needed for monoplotting: 
- the height Wp. 
BASIC PRINCIPLES OF THE INTERPOLATION 
METHOD 
When the first prototype of the monoplotting program 
package was developed in 1986 at the WAU, height 
information had to be introduced by means of the computer's 
keyboard for every measured point. This cumbersome 
operation did not give too many problems in flat or hilly 
terrain with medium and small scale photography. However 
it could not be denied that an automated procedure to find the 
height from a pre-determined DEM would reduce mistakes 
during measuring, speed up the whole monoplotting process 
and make this process more accessible to  non- 
photogrammetric users. To achieve this, an interpolation 
procedure needed to be developed according to the 
mathematical equations of monoplotting. 
As stated earlier, every vector goes through the perspective 
centre. One vector is orthogonally defined to the 
georeference of the ground control points. This vector is 
parallel to the height axis (W) and perpendicular to the plain 
defined by the U,V axis (see Fig 2). 
W 
  
Fig.2 
This means that a perpendicular plain to the U,V axis of the 
georeference can always be defined for every image point 
except for the image point which lies in the extension of 
vector ON. This image point is also referred to as the nadir 
point (see Fig. 3). 
Nadir point 
  
Fig. 3 
Using the reference height (W=0) of the georeference's 
origin and the image point's X,Y coordinates, the U,V 
position of the image point can be determined by using 
equation /2/. This means that every image point except the 
nadir point defines a plain which pivots around the vector 
ON (see Fig. 4). 
  
P1 
  
  
Fig. 4 
The correct height needed to compute the corresponding U,V 
coordinates of an image point can be found on the vector OP. 
When introducing a DEM into the computation, the 
minimum and maximum heights of the DEM are used to 
speed up the computation because the correct height and 
position lie between the two points Pmax and Pmin on the 
vector OP (see Fig. 5). 
  
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