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NUMERICAL INTERPOLATION IN FLIGHT SIMULATORS FOR 
MICROCOMPUTERS USING DIGITAL ELEVATION MODELS 
Ricardo Rodrigues Rangel 
Instituto de Estudos Avangados - IEAv - CTA 
12.2317990 = 
Sáo José dos Campos - SP 
rangel@ieav.cta.br 
Luiz Alberto Vieira Dias 
Instituto Nacional de Pesquisas Espaciais - INPE 
12.227-010Gr 
Sáo José dos Campos - SP 
vdias@ltid.inpe.br 
KEYWORDS: DEM/DTM K122, Simulation K101, Software K165 
ABSTRACT: 
This work presents Numerical Interpolation applications for Flight Simulators terrain 
visualization. The terrain may be synthetic or real, obtained through Digital Elevation 
Models. Using Computer Graphics techniques, 
reasonable realistic results. The Geometric Transformations and Interpolations must be 
sufficient fast and precise, in order 
performance. 
1. INTRODUCTION 
A Flight Simulator; has the’ purpose to 
simulate the several steps of a real 
flight in a icomputational 'environment. 
Basically it consists of an animation 
over a Digital Elevation Model (DEM) , 
where the model movement simulates the 
airplane movement. 
If «the purpose is .to .simulate in. real 
time, the frames have to be displayed 
faster than the human vision can 
perceive, or about 24 frames per second ( 
as in motion pictures). 
In Computer Graphics the terrain is 
represented by regular, or irregular 
grids, with, the grid points representing 
the terrain altitude. For microcomputers 
the number of samples have to be kept to 
a minimum. The sampling of the altitude 
points may be obtained from maps of by 
photogrammetry. 
2. NUMERICAL INTERPOLATION 
It is important that the numerical model 
could reproduce the original terrain with 
certain fidelity. If microcomputers are 
used, due to memory and speed 
limitations, the number of samples have 
to be kept to a minimum, so the 
interpolators used have to be very fast 
that the 
907 
it is possible to generate animations with 
Simulator would achieve a good 
and reliable. The main, purpose is to 
reconstruct the terrain, with the minimum 
possible points, and with the maximum 
fidelity. In this paper it will be used a 
regular grid. 
Let's briefly recall some interpolation 
methods. The linear  interpolators are 
very fast, and, if the number of samples 
enough, the results are very good. 
However for insufficient sampling the 
results do not resemble the reality. In 
this paper the linear interpolators were 
used for illumination, shading and 
rendering of the frames. 
The Akima interpolator, on the other 
hand, is also very fast, and does an 
excellent work in terrain reconstruction. 
It has partial second derivatives 
continuity on the patches junctions ( 
Akima, 1974). This interpolator was used 
in this paper for the reconstruction of 
the sampled grids. 
As an example Figure 2.1 below presents 
the result of the interpolation, by 
several methods, of a real terrain 
(region centered on 41925'N and 
74959'W, on the Hudson Valley, near West 
point, VA, USA), with a 11 = 11 points 
grid with a spacing of 209.46 meters on 
the E-W direction, and 277.53 meters on 
the N-S direction. the altitude range in 
the real terrain is from 0 to 394 meters. 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B4. Vienna 1996