International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B-YF. Istanbul 2004
2
(X KG) Fr
x
ye -x)-KE( xr o
r- (x =X) tQ = voi.
b. Computing the joint points
Fig.5 shows the projection of a building in a photo. In principle,
all the lines that respectively parallel X, Y and Z coordinate axis
should join in three points 7, J and K. If we pick some points
along /3 and get the coordinate sets ((x,.yj). (X5). ... (XY).
then we can get the line 4x + By = / using the formula below.
Tr Tw
Ty yy Tutt
Be EX Y sts
yx av y y
And by the same means, we can get the description of line 24,
then compute the coordinate of point / using the following
formula.
(3)
Us Nat B3 —VB*N AB
CS 449 8° —S AR*S AR
NB*YV 4^ V 4* Y 4B
SAL*S B Y AB" Y dB
/
Y=
And the coordinates of point / and K can be computed using the
formula 3and 4. To ensure the precision of results, in practice,
we usually take redundant points and compute the average.
Fig.5 The Joint Points in A Image
c. Computing the angle elements
After the determination of the three joint points, next we will
compute the three exterior angle elements 4, aandk. Taking one
side face A of the building showed in Fig.5 as an example, we
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calculate the three elements. Fig.6 shows the detail. The angle a
is photo obliquity, and the range is from 0°to 90°. 4 is attitude
angle, and it also ranges from 0°to 90°. And K is the angle from
x coordinate axis counter-clockwise to the u coordinate axis
with the range from 0°to 360°.
Fig.6 The Angle Elements in A Image
From the geometric relation of special Points, Lines and Faces
in photogrammetry, obviously So: o/K and ov! /K, so we can
draw the conclusion that oaS, Isa, “SaK, loa and Koa
are all right-angled triangles. Based on relations of the right-
angle and the coordinate axis, we can deduce the following
formula.
A= £ISa
a = LSao (5)
K= Zxu= Zxu = io! + dou = 2xol + Zola
And the anglekis determined by the quadrant of the point a
which is the cross of /K and Sv. Using coordinates of the points
I, J. K, o and f, we can compute the length of oa, Sa, Jo and SI,
then we can calculate the three exterior angle elements 4, dandk
by the formula 6.
+100
A = arcsin(—
C
s, f.
& = arcsın(— (6)
yı'=) Joa
Ku are ( + arcsin(—)
X; 7X9 lo
d. Computing the scale
Based on the above parameters xy, yy, f, 4,Q and K, we can found
the model of building in object space. But without any
coordinate and length information of reality, we can't
determinate the size of the model. There are a few kinds of
means could be used to get the scale between thé model and
reality. For that we have already possessed plenty of digital
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