In: Wagner W., Szekely, B. (eds.): ISPRS TC VII Symposium - 100 Years ISPRS, Vienna, Austria, July 5-7, 2010, IAPRS, Vol. XXXVIII, Part 7B 
number is changed to l-> 129, the mod(129,129)=0. 
X = (N + H) cos B cos L 
Y = [jV(l -e 2 ) + //]sin B 
Z = (N + H) cos B sin L 
a 
( i ) 
where 
N = 
vr 
e 2 sin 2 B 
a 
a = 1738000m, b = 1737400m 
a 
Figure 6 (a): Before a change in viewpoint 
Moving direction Updated zone 
Visible zone 
lunar long radius, and b is short radius. For reducing 
the CPU’ burden and optimizing efficiency, we can 
implement the equation by GPU. 
3.3 Spherical view range culling 
As shown in Figure 7, for optimizing efficiency, 
we use view range culling and back face culling 
algorithm to eliminate invalid data. 
Updating zone 
Figure 6 (b): After a change in viewpoint to the 
southeast 
Figure 6: An example of the data in the heightmap 
(top) and toroidal array (bottom).before and after a 
change in viewpoint. The position of the viewer in the 
heightmap is shown by the red dot. 
3.2 Transformation of planar terrain to 
spherical terrain 
The test data is Lunar DEM and image in WGS84 
coordinate system. If the coordinate of a grid point is 
(B, L, H) , w h ere B is longitude, L is latitude, 
and H is elevation. We must transform the WGS84 
coordinate system to OpenGL world space coordinate 
system for spherical terrain rendering. 
According to Eq.(3), we can transform the WGS84 
coordinate system to OpenGL world space coordinate 
system. 
Figure 7: Data culling based on viewpoint and 
visible face 
As shown in Figure 8, the spherical terrain can be 
divided into two parts. One part is face to viewpoint 
n'h' 
and one part is back to viewpoint. The a ° in back 
to viewpoint part is in view cone, but it is invisible to 
viewer. So we must eliminate it with spherical view 
range culling algorithm: 
Figure 8: spherical view range culling