name implies, is the "force" that plus 
the surface toward the control vertices. 
3. RESULTS 
The interpolator was tested..in two 
consecutive patches. The cases bellow 
were studied: 
  
A) Linear case, with betal=1 (no bias), 
and beta2=90 (strong tension), both 
patches. 
B) Moderate bias, no tension. Patch 1 
bias 1/8, patch2 bias +8. This case 
models a river or valley. 
  
C) Moderate bias, no tension. Patch 1 
bias +8, patch2 bias 1/8. This case Fig. 1 - Original Data Set. 
models a ridge. 
Figure 1 is the original data set, taken 
from aereal photography, as courtesy of 
AERODATA S/A. Figure 2 presents the 
original figure undersampled; it will be 
used as our control polyhedron. 
Next set of figures are the terrain 
representations after the Beta-spline 
interpolator has been applied. Figure 3 
for case A, Figure 4 for case B, and 
Figure 5 for case C. 
4. CONCLUSIONS 
As seen from the figures of the previous 
session, the use of the Beta-splines can 
improve the terrain representation, 
especially if some knowledge about its 
the shape is known previously. This is a 
preliminar work, so there is much more 
study to be done, but the indications 
are that this interpolator has its place 
as another tool for the goal of obtaining 
better Digital Elevation Models. 
  
Fig. 2 - Original Undersampled. 
5. ACKNOWLEDGEMENTS 
The authors would like to thank INPE, 
AERODATA S/A, and the Paraiba Valley 
University, UNIVAP, for use of their 
equipment. IBM Brasil deserves special 
thanks for helpfull discussions with the 
colleagues from IBM Rio Scientific 
Center. 
6. BIBLIOGRAPHY 
BARSKY, B.A., 1987. Computer Graphics 
and Geometric Modelling Using 
Beta-splines. Springer Verlag, New York, 
NY, USA. 
  
FOLEY, J.D., and VanDam, A., 1984. 
Fundamentals of Interactive Computer : 
Graphics. Addison,Wesley, Reading, MA, Fig. 
USA. 
3 - Betal-1, Beta2-90. 
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