International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B6. Istanbul 2004 
e A group of 9 high rise, flat roof buildings with a road 
along them; 
e A landscape with a road, a house and a lake; 
e A regular grid DTM pattern. 
A version with the same functionality for push broom scanner 
images is not yet finalized but a variety of spreadsheets with 
similar principles was produced to show: 
e A satellite orbiting a rotating globe, 
e The principle ofa laser scanner, 
e Geometric transformations of square grid patterns, 
e A geocentric and a local coordinate system. 
The spreadsheets can be used directly to show the changing 
graphics in Excel, but the graphics can also be imported into 
other software, to prepare digital slides or illustrations in a text 
file. 
MS Excel, MS Visual Basic and MS PowerPoint are products 
of Microsoft Corporation. 
REALIZATION 
Perspective View : 
With the usual (photogrammetric) camera parameters the 
functionality was disappointing, as rotations of the camera 
made the object move out of the field of view. I therefore 
changed the calculations such, that the rotation axes did not 
pass through the projection center (O), but through the “viewed 
point” (M), which one can best choose in the middle of the 
object area. The projection center (O) is calculated such, that 
point M is in the camera axis, at a distance (D) from O, which is 
variable by the user. In addition to the three angles of rotation, 
the coordinates of *M" and the distance "D", the user can 
specify: 
e The image coordinates of the image of point M (xm, 
ym), being the coordinates of the principal point, 
e The "image scale" (s), being the ratio between the 
principal distance and the “object distance” (D). 
This gave the functionality, that the object remained in view 
with angular changes, and the “object distance" controlled the 
amount of perspectivity in the image, without changing its size. 
  
  
  
  
  
Figure 1. Two views to the same “view point” (M) 
The formulas used are: 
130 
  
c= Ds; r,:(U-U, )*tru:(V -Vy)try: (W -Wy) sem (1) 
R r(U-Us )tru:(V-V,)tr-(W -W,)*D 
yED.s ry (U-U,)+r, «V -V)tr,:(W -W,) + ym 
  
rr (UmUpy J 41s (VV J+ 1s (W=W, )+ D 
where x, y = image coordinates 
xm, ym = coordinates of principal point 
D = object distance 
s = image scale 
r = elements of rotation matrix 
Um, Vm, Wa = coordinates of “view point” (M) 
U, V, W = object coordinates of any point 
In the case of zero rotations (as the view from O” in figure |.) 
the viewing is in the V-direction, while x is parallel to U and y 
is parallel to W. Different from the usual situation in terrestrial 
photogrammetry, Kappa rotates the view around an axis parallel 
to the W-axis, thus allows to “dance” around the object, while 
Omega inclines the direction of viewing (up or down). 
Movie like motion 
To find good viewing parameters by typing new values was far 
from optimal, so 1 developed a few macros to allow easy 
change of the parameters. Not familiar with Visual Basic, | 
simply recorded a macro to add (and another to subtract) the 
value of a particular cell from the selected one by "Paste 
Special”. The letter I assigned to the macro was simply the one 
in the left upper corner of the keyboard, the letter “Q”. 
Later | changed the macros for more robustness, but the 
principle remained the same: the value of a particular cell, the 
"increment" was added to selected one by pressing "Ctrl-Q" 
and it was subtracted by pressing *Ctrl-Shift-Q". When the key- 
combination is held, then the increment is added (or subtracted) 
repeatedly. The graphics, which are visible in other windows 
are continuously updated, which creates an almost continuous 
motion. The speed of the motion depends on the "increment". 
Also for changing this “increment” a macro was made, using 
the next letter in the row, the “W”. “Ctrl-W” will multiply it by 
10 and *Ctrl-Shift-W" will divide it by 10, but the macros will 
not set values outside the range from 0.001 to 10. 
In this situation the sheet containing the parameters must be 
open in window number 1 of the spreadsheet and the parameter 
to change must be selected there. Another approach using much 
more macros, in order to allow selection of parameters, 
incrementing them and changing the speed without having the 
parameters visible on the screen is presently under construction. 
Camera(s) above the object 
In order to show the relief- and tilt-displacement, which has to 
be corrected in orthophoto production 1 wanted to show a 
DTM-grid together with its image in a camera above it, so | had 
to calculate the imaging of the DTM grid into the image plane 
of the camera. The orientation parameters of the camera were 
added to the parameters sheet, thus they were variable using the 
same macros. The typical photogrammetric parameters of 
interior and exterior orientation were used, but object 
coordinates of the image points had to be calculated rather than 
image coordinates.