International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B6. Istanbul 2004 
Laser Scanning 
This graphic shows the deflection of a laser beam by a rotating 
prism. 
  
  
  
  
Figure 10. laser scanning principle 
The user can rotate the prism, change the number of facets 
(between 3 and 20), and the speed of motion (30 to 3 steps per 
facet). After a change of the number of facets the reflection may 
be wrong such, that a reflection is shown outside the limits of a 
facet. After the rotation starts, this is corrected. 
Transformations of square grid patterns 
This graphic was made to illustrate the principles of resampling. 
Bilinear transformation is used here: 
x=a0+al-c+a2-r+ai-e-r (5) 
y=ad+aS-c+ab-r+a7-c-r 
where ¢. r= column and row coordinates 
X, y = output coordinates 
a0 to a7 = transformation parameters 
  
  
  
  
  
Figure 11. image transformation 
The parameters (a0 to a7) can be varied using macros. For 
affine transformation one can simply set the parameters a3 and 
a7 to zero, but for conformal transformation a modification of 
the sheet would be useful to couple a5 to a2 and a6 to al. 
For output driven resampling the grid pattern shows the pixels, 
which should be created and the circles show the positions of 
the pixel centers of the existing image transformed to the new 
geometry. When changing the parameters using the macros one 
can nicely demonstrate the effect of each one, like shift, change 
of scale, shear etcetera. 
Local and global coordinates 
For the illustration of the relations between a local and a global 
*Cartesian" coordinate system another spreadsheet was made. It 
shows a (spherical) globe, the axes of the geocentric coordinate 
system, the “local” meridian and the axes of the local 
coordinate system together with a horizontal square around the 
local origin. 
Besides the viewing parameters one can change the size of the 
globe, the longitude and the latitude of the local origin and the 
size of the horizontal square by macros. The size of the 
coordinate axes shown depend on those settings. The global 
axes are 2096 longer than the radius of the globe, while the local 
axes are equal to the sides of the square. 
  
  
  
  
  
Figure 12. local and global coodinates 
Conclusions and Outlook 
Spreadsheet graphics offer an easy tool to visualize objects and 
relations in 3D-space to anyone familiar with the spreadsheet 
software. This can be used to make “nice” teaching aids, but 
they can also be used as a teaching aid by themselves. 
The use of macros to easily increment or decrement some 
parameters can make it easy to select suitable parameters to use 
the graphic elsewhere, but they are even more valuable when 
using the spreadsheet itself as teaching aid, as it allows to show 
the effect of changes in a "continuous" mode. 
PowerPoint slides I have made with these tools are appreciated 
by students as well as colleagues, I have found these graphics in 
numerous presentations of colleagues. 
Besides the completion of the push broom functionality a 
version is envisaged to give two views from different positions, 
one in red and one in cyan, for stereoscopic viewing using the 
anaglyph principle.