P2-5-4 
Table 1 Visibility Check and Image Output 
Case 
View 
Shift 
Shadow 
Shift 
Image Output 
1 
Fore 
Fore 
Paint dark only in shadowed areas 
2 
Fore 
Aft 
Paint dark in all areas 
3 
Aft 
Fore 
Neglect 
4 
Aft 
Aft 
Neglect 
The concept of shadow analysis using the depth 
distance only in “Fore” sides of view and shadow shift 
spaces is shown in Fig. 7. The hatched areas show the 
case No.2 with “Fore” view shift and “Aft” shadow 
shift. 
The computation time required for the integration of 
the “View Shift” and “Shadow Shift” depends on the 
height of building, the unit of shift amount and the 
resolution of pixel spacing. As the shift amount and 
the resolution affect the computation time as a linear 
and quadruple function respectively, an experimental 
study was implemented to test the computation time 
with respect to the change of height. 
In order to simplify the experiment, seven buildings 
were given the same height in each case. Six cases 
with different height ranging from 10 to 60 pixels in 
the shift amount were implemented with a Pentium of 
200 MHz and 64 MB memory. A full-screen memory 
of 700x700 pixels x 3 color bands (1.47 MB) is used 
for the “depth distance” buffer in both “View” and 
“Shadow” shift. 
Fig. 8 shows four examples of 3D view map with 
different shadow shift for the same building plan that 
was used in the above case study. 
Fig. 9 shows the six case studies for generating 3D 
view maps with shadow using the polygon shift 
method. 
Table 2 shows the computation times with respect to 
the change of height and the sub-programs. 
As seen in the table, about 90 percent of the 
computation time was required for the shadow shift 
analysis and the integration with the view shift analysis 
because two full-screen buffers are to be checked. 
The total computation time can be represented as a 
function of quadruple equation with respect to the 
height as shown in Fig. 10. When the polygon shift 
method is applied only to the generation of a 3D view 
map without shadow, the computation time will be less 
than 90 seconds in the six case studies. 
Table 2. Computation times with respect to the change 
of height and the sub-programs, (unit : second) 
Sub Program 
Case 1 
H=10 
Case 2 
H=20 
Case 3 
H=30 
Case 4 
H=40 
Case 5 
H=50 
Case 
H=6 
View Shift 
11.42 
14.35 
16.69 
21.77 
25.86 
29.5 
Shadow Shift 
and Integration 
401.96 
423.30 
443.43 
469.93 
497 J 6 
540.': 
Image output 
and others 
31.87 
36.84 
38.84 
45.06 
50.17 
56.4 
Total 
445.25 
474.49 
498.96 
536.76 
573.20 
626.t 
7. CONCLUSIONS AND FURTHER STUDIES 
A polygon shift method was proposed and 
demonstrated as a powerful algorithm to generate 3D 
view of buildings with shadow without any complicate 
data structure. 
The concept of polygon shift including shift direction, 
shift amount, repetition, fore and aft polygon regions 
and depth distance was recognized to simplify the 
geometric, topologic and logical operations required 
for three-dimensional visualization. It can overcome 
the weakness of raster data structure with respect to 
topology by introducing the above concepts. 
The polygon shift method can be widely applied to 
other three dimensional objects, for example, 
topography represented by contour lines. 
Further studies should be made to extend the polygon 
shift method to apply to inclined roofs and perspective 
views. An improvement to reduce the computation 
time required for the shadow shift analysis and the 
integration with the view shift analysis has to be made. 
8. REFERENCES 
Chen, Xiayong and Ikeda, Kozo. ; Three Dimensional 
Modeling of GIS Based on Delaunay Tetrahedral 
Tessellations, ISPRS Comm. Ill Symposium, Munich, 
Germany, XXX B3/1, pp. 124-131. 
Harrington, Steven; Computer Graphics, A 
Programming Approach, International Edition 1987, 
McGraw-Hill Book Co. - Singapore, pp.3 12, 3 19-320. 
Molenaar, M.; A Formal Data Structure for Three 
Dimensional GIS in Geographic Information Systems: 
Proceeding of 4th International Symposium on Spatial 
Data Handling, Vol.2 pp.830-843, 1990. 
Murai, Shunji; GIS Work Book.- Technical Course, 
Japan Association of Surveyors, Jan. 1997 pp. 141 -149. 
Shibasaki, R. and Huan S.; A Digital Urban Space 
Model - A Three Dimensional Modeling Technique of