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In: Wagner W., Székely, B. (eds.): ISPRS TC VII Symposium - 100 Years ISPRS, Vienna, Austria, July 5-7, 2010, IAPRS, Vol. XXXVIII, Part 7B 
sc • ec> 0 , invisible 
sc • ec< 0 , visible 
(2) 
Where, s is the center point of earth, e is 
viewpoint, and c is a point on spherical surface in 
view range. If the angle a from vector sc to vector 
ec <90° 
is visible. 
, point s is invisible. Whereas point 
. P, P 2 . AP x P 2 A' t , . P, 
point 1 to 2 is 12 . Translating 1 
P OP 
to 2 , we can rotate vector 1 about great 
OY 
circle’s normal ^ 1 . As shown in Figure 10, A 
@ rotation of vector ^ about vector ^ should 
TT? 
produce the vector v . The Equation is [ 121 
V' = V. cos#+ V.n.(l-cos0)Ji+(V xn).sinO 
(3) 
As shown in Figure 9, We implement Geometry 
Clipmaps algorithm with spherical culling, the 
efficiency be shown by blue dashed. The red dashed 
show the efficiency of Geometry Clipmaps algorithm 
without spherical culling. The x-coordinate is the 
deferent viewpoint and the y-coordinate is render fps. 
Compared the result, we can find the Geometry 
Clipmaps algorithm with spherical culling is more 
efficient than Geometry Clipmaps algorithm without 
spherical culling. The average frame of Geometry 
Clipmaps algorithm with spherical culling is 23 fps 
and the average frame of Geometry Clipmaps 
algorithm without spherical culling is 9 fps. 
Analyzing the test result, the render efficiency of 
Geometry Clipmaps is steady. Using Geometry 
Clipmaps algorithm with spherical culling, because 
we must read different data file in hard disk, when 
viewpoint ramble to boundary of data block, the 
rendering efficiency is low. For example, a point in 
Figure 9. Because the efficiency of Geometry 
Clipmaps algorithm without spherical culling is low, 
so the data file’s searching and reading don’t 
influence the rendering efficiency. 
Figure 9: Comparing the rendering frame of view 
range culling 
3.4 Viewpoint control 
Rambling in spherical surface, the controlling of 
view point is more complex than ramble in plane. As 
shown in Figure 10, if we rotate the line of sight n 
in viewpoint P , we can rotate the line of sight n 
(IP 
about vector . Defining the great circle from 
Figure 10: Transformation of spherical view point 
Figure 11: Rotating vector about pointed axis 
4 RESULTS AND DISCUSSION 
4.1 Test Data and Results 
The test data was from USGS’s web. The global lunar 
digital elevation models (DEMs) is at a resolution of 
16 pixels/degree (e.g. about 1.895 km resolution). As 
shown in Figure 12, the size of DEM grid is 
5760x2880, created from a triangle irregular network 
(TIN) of the original points-Unified Lunar Control 
Network (ULCN2005). See Tables 1 for statistics on 
this and the other networks. 
The global lunar image data is Clementine 
UWIS(5 bands, 1 OOm/pixel). The size of data is 
163840x81920. In addition, there are high resolution 
Appolol5 image and DEM in the zone of Appolol5 
land in moon. The resolution of Appolol5 image is 
1.5m/pixel, the size of data is 3319x3226 and grid cell 
size is 50m.