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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B3. Istanbul 2004
Once p,, p,. p, and p; are determined, the j-th rectangle
is formed as By; = {p, Pos Ps Pu} -
If the two lines starting from p, and p, cannot join
together at the same point p;, we temporarily create an
auxiliary point. p,(x,, y,) for rectangulation (Figure 2d).
685
680 +
675
670 +
665 -
660 -
655 +
650 +
645 +
640 J À À L 1 1 1 1 1 1 J
315. 320 325 330. ;:338 340. 345 3560 388 360: 2365: 370
Figure 2b). Roof points.
645 -
640 1 1 I L 1 1 1 L J L 1
15-320 325 330 .335.. 34D. 345. 3590 .355. 360. 365 370
Figure 2c). Intermediate points.
685
[
680 +
675 +
Pn Pj
670 +
660 -
B55 F
d &
B] .
)
p D; Pe
645}
J | 1 L 1 1 am]
315 30 35 33) 335 340 345 350 355 200 365 370
Figure 2d). Rectangulation.
If there is no auxiliary point created, repeat step 1 to step 5
555
to form the (j+/)-th rectangle on this level by
P uy 7 B; - B
i i
7. Once auxiliary points are created, repeat step 1 to step 5 by
Pan =F; —B; + Pag where F,; denotes auxiliary points
in the j-th round.
8. After the rectangulation process continually repeats, if the
number of the rest points is less than four, or if there are
points that cannot form a rectangle, what remains can be
classified as roof points.
2.2 Forming 3-D primitives
After finding rectangular bases of primitive roofs, the next step
is to reconstruct 3-D polyhedral roof primitives. This process is
working on the 3-D space. However, to reconstruct these
surfaces, we first apply a 2-D range query to find roof points for
each rectangular base. This is a 2-D check across different
levels. The range query is to check the x, y coordinates of roof
points P and base points. If the roof points lie inside the base in
the nearest level above the base, they can form a roof primitive.
The ^ rectangular bac can be represented by
B, =[x:x"]x[y:y"] and P. lying inside B, if
x, e[x:x'] and y, e[y: y]. 3)
The primitive is determined according to| P. |. If | P. |=1and 2,
it is a one-ridge point roof and two-ridge points roof,
respectively (Figure 2e). If an upper rectangular base B, ,., in
the nearest level exists, and satisfies
B, C B;. (4)
a four-ridge points roof can be formed. Then the 3-D polyhedral
surfaces of a roof primitive can be formed by connecting roof
points and base points (Figure 2f).
688r
B45
640 1 À LL. 1 1 1 À 1 1 L J
315.5320 325 5330. 3358. 340. 345 350. 385. 300 305 370
Figure 2e). Roof points inside bases.
2.3 Combining 3-D primitives
Since the primitive roof models have been reconstructed in the
previous step, the following steps are combining primitive
models by Boolean operators in order to obtain a complete
building. This process is first working on 2-D horizontal level
for rectangular bases and roof points separately.