is
...
=:
R
=:
'3 )
~
-,
(5)
s = R
= (
(4)
ot:,
+
)
(5
z
z : ;:
(
(6)
.... co
i
( )
cSt'
cos
=(
-1) d~
~
we can
d$
=:
=:
cos
Jt
fH
-J(l
s-
=--
111-"-"'. . . . . . .
0(
- 1) d<X.-
=---
(8 )
dp> and dO(... to be
$'" ::: ~~ clol.
.. Then it is
menta
:::
eOSd-
Z + z
cos ee:.
doL
Fig. 2
infitely small area
293 Deformation
AI
Length abreviation
in the radial direction
(11 )
the perpendicular direct
BI
Plane abreviation
S 6 p:::
~
0 S •
dsk
(13 )
-
Angles which are measured
the tangent plane cr:" /horizontal angles me:asured by theodoli tel are distorted when they are projected from
S to the plane 1:)., It was already stated that
the planes 1: ,1:1
:r'2., are parallel. Distort
of horizontal
angles is the same
the three planes. The easiest way to
analyt,e
ion
to
I~, which
going
B, where
horiz
angle:s are
measured.
intersection
of the planes cr a..'rld 1: 2d,oes
projec d from
S", Therefore it
is
aqgles
s i n g from the line p.
The measured
b- ,
proje
from S, change to 6'
The
author, when applying the laws of spherical trigonometry, has de-rived the relation between the angles 6" and 6' :;
4>
cotg
as well as it
-G" ::: arc cos
The distortion
~
::::
cotg6"
cos~
COS(04 t'
cos 6'"' cos
(0(. t)
0(...
r)
---::------::.-.:.:...---..:-~--:----S in3.G" cos 2.
+
+ cos2.() cos 2.0(
azimuth then is
111 ... 370
(14)
(14a)
( 7 ), ( 8), (9), (1 0) and (1 5) we can
, areas
azimuths.
When applying the equat
define distortion of
AI
Lengths distort
the rad
direct
6s'
m
or
( 1'-6a)
:::::
88
in the
mk
BI
0
m
0
IDk
Ss-
:::::
SS
on
)
( 1
:::::
8
Plane distort
or
17
:::
bs . ~Sk
p
::::
:::::
bs. «5
m.mk
cl Azimuth distortion
Il.fr
( 15)
402 Deformat
within defintely
In some cases
is important to know
mote sensed picture within
point Bi of informations collec
ned when equations derived
For the
abreviat
ly
area of the po
cos
~J'fA'" (R
the re-
0(.
+ Z\2.. . '1
R J S lnol.
Within the definitely small area
revi ion in Fsdial direction is
Ils~:::::
1
ab-
Jt-i'))1fR
-
1
dtJ.~ 0 )
~
the
direction the
areal
- .(
ion is /within
R + Z-' a .
R
")
2Sln~
Then the length abreviation Iwithin the
in the perpendicular direction is
III
1
ly small areal
i-~- r=====C=O=S==--
_
1) . . __
Z_
coso(
is
( 5)
III