S ? s t ?

1
6
S ? s t ? µ a t a a ? a f ? ? ? ? ? a ? ? ? ?
? ? ? Ge?da?t??? datum ?a? d??t?a
2
Ge?da?t???? s??teta?µ??e? ?a? ?e?da?t??? datum
?e?da?t??? µ???? ?, ?e?da?t??? p??t?? ?,
?e?da?t??? ???? h.
??e???e?d?? a?af???? ap? pe??st??f? ???e????
???? ap? t? µ???? ?µ?????a
3
Ge?da?t???? s??teta?µ??e? ?a? ?e?da?t??? datum
?e?da?t??? µ???? ?, ?e?da?t??? p??t?? ?,
?e?da?t??? ???? h.
??e???e?d?? a?af???? ap? pe??st??f? ???e????
???? ap? t? µ???? ?µ?????a
?a?tes?a?? s?st?µa a?af???? a??? ???t??
e??e???e?d??? a?af???? 3?? ????a? st??
?ate????s? t?? µ????? ?µ?????a 1?? ????a? ?a
pe????eta? st? µes?µß???? t?? Greenwitch.
4
Ge?da?t???? s??teta?µ??e? ?a? ?e?da?t??? datum
?e?da?t??? µ???? ?, ?e?da?t??? p??t?? ?,
?e?da?t??? ???? h.
??e???e?d?? a?af???? ap? pe??st??f? ???e????
???? ap? t? µ???? ?µ?????a
?a?tes?a?? s?st?µa a?af???? a??? ???t??
e??e???e?d??? a?af???? 3?? ????a? st??
?ate????s? t?? µ????? ?µ?????a 1?? ????a? ?a
pe????eta? st? µes?µß???? t?? Greenwitch.
?a??µet??? e??e???e?d??? a?af???? ?µ?????e? a
?a? b, (? a ?a? e??e?t??t?ta e??e???e?d???
)
5
Ge?da?t???? s??teta?µ??e? ?a? ?e?da?t??? datum
?e?da?t??? µ???? ?, ?e?da?t??? p??t?? ?,
?e?da?t??? ???? h.
??e???e?d?? a?af???? ap? pe??st??f? ???e????
???? ap? t? µ???? ?µ?????a
?a?tes?a?? s?st?µa a?af???? a??? ???t??
e??e???e?d??? a?af???? 3?? ????a? st??
?ate????s? t?? µ????? ?µ?????a 1?? ????a? ?a
pe????eta? st? µes?µß???? t?? Greenwitch.
?a??µet??? e??e???e?d??? a?af???? ?µ?????e? a
?a? b, (? a ?a? e??e?t??t?ta e??e???e?d???
)
?e?da?t??? datum s?st?µa a?af???? pa??µ?t???
e??e???e?d??? a ?a? b (?????a e???te??
ap? t? s?st?µa a?af????)
?? ?e?da?t???? s??teta?µ??e? ?, ?, h
e?a?t??ta? ap? t? ep????? t?? ?e?da?t???? datum
6
S??s? ?a?tes?a??? ?a? ?e?da?t???? s??teta?µ????
P
7
S??s? ?a?tes?a??? ?a? ?e?da?t???? s??teta?µ????
P
P0
P0 ???et? p??ß??? t?? P st? e??e???e?d??
a?af???? (h?? 0)
a?t??a ?aµp???t?ta? t?? ???et?? t?µ?? st? P0
µ??ad?a?? d????sµa ???et? st? e??e???e?d??
a?af???? st? P
8
S??s? ?a?tes?a??? ?a? ?e?da?t???? s??teta?µ????
P
m
x0
P0
S???st?se? t??
x0 s??teta?µ??e? t?? p??ß???? P0 (h 0)
9
S??s? ?a?tes?a??? ?a? ?e?da?t???? s??teta?µ????
P
m
x0
P0
S???st?se? t??
x0 s??teta?µ??e? t?? p??ß???? P0 (h 0)
S??teta?µ??e? x t?? P
10
S??s? ?a?tes?a??? ?a? ?e?da?t???? s??teta?µ????
P
m
x0
P0
S???st?se? t??
x0 s??teta?µ??e? t?? p??ß???? P0 (h 0)
S??teta?µ??e? x t?? P
????t?s? t?? ?a?tes?a??? s??teta?µ???? ap? t??
?e?da?t???? q ? ? hT a??? ?a? ap? t??
pa?aµ?t???? t?? e??e???e?d??? a?af???? a ?a? b
11
A?t?st??f? s??s?
de? ?p?????? ap??? a?a??t???? s??se??!
12
A?t?st??f? s??s?
de? ?p?????? ap??? a?a??t???? s??se??!
13
A?t?st??f? s??s?
de? ?p?????? ap??? a?a??t???? s??se??!
14
A?t?st??f? s??s?
de? ?p?????? ap??? a?a??t???? s??se??!
µ???? ?
???? h (a? p??????e? ? ?p?????sµ??
t?? ? )
(p??ß??µata st?? pe????? t?? ?e?da?t????
?s?µe????? ?p?? x3 ? 0, sin? ? 0 )
15
A?t?st??f? s??s?
de? ?p?????? ap??? a?a??t???? s??se??!
µ???? ?
???? h (a? p??????e? ? ?p?????sµ??
t?? ? )
(p??ß??µata st?? pe????? t?? ?e?da?t????
?s?µe????? ?p?? x3 ? 0, sin? ? 0 )
p??t?? ? ep?????ta? µe d?ad??????
p??se???se?? t? s??s?
µe a????? t?µ? st? de??? s?????
?p?? e? de?te?? e??e?t??t?ta
16
A?t?st??f? s??s?
A??????µ?? F?t???
17
??ast?µ??? ep??? e??at?stas? pa???sµ???
s?st?µ?t?? a?af????.
18
??ast?µ??? ep??? e??at?stas? pa???sµ???
s?st?µ?t?? a?af????.
????f????? s?st?µa p??sd????sµ?? ??s?? GPS
?e?da?t??? s?st?µa WGS84 datum WGS84 a??? ?
???t?? µ??a? t?? ???, 3o? ????a? ? µ?s? ??s?
????a pe??st??f?? t?? ???
19
??ast?µ??? ep??? e??at?stas? pa???sµ???
s?st?µ?t?? a?af????.
????f????? s?st?µa p??sd????sµ?? ??s?? GPS
?e?da?t??? s?st?µa WGS84 datum WGS84 a??? ?
???t?? µ??a? t?? ???, 3o? ????a? ? µ?s? ??s?
????a pe??st??f?? t?? ???
IERS Interational Earth Rotation and Reference
System Service ????? ?p??es?a t?? IAG
(International Association of Geodesy) IAU
(International Astronomical Union)
20
??ast?µ??? ep??? e??at?stas? pa???sµ???
s?st?µ?t?? a?af????.
????f????? s?st?µa p??sd????sµ?? ??s?? GPS
?e?da?t??? s?st?µa WGS84 datum WGS84 a??? ?
???t?? µ??a? t?? ???, 3o? ????a? ? µ?s? ??s?
????a pe??st??f?? t?? ???
IERS Interational Earth Rotation and Reference
System Service ????? ?p??es?a t?? IAG
(International Association of Geodesy) IAU
(International Astronomical Union)
ITRF International Terrestrial Reference
Frame S??teta?µ??e? xi(t0) se µ?a ep??? a?af????
t0 ?a? s???st?se? ta??t?ta? vi ??a ??a s?????
ep??e?µ???? sta?µ?? i 1, 2, , N. To ITRF e??a?
???p???s? t?? ITRS International Terrestrial
Reference System.
21
?a?a??te?a t?p???-pe??fe?e?a?? ?e?da?t???
datum µe t? ß???e?a ast????µ???? pa?at???se??.
???sd????sµ?? t?p???? datum (1) ?????sµa
ßa??t?ta? (d?e????s? t?? ?ata????f??) se ??a
ep??e?µ??? s?µe?? P ?ate????s? t?? ?a??t??
PP? st? e??e???e?d??
(2) T?s? t?? s?µe??? st?? ?ata????f?
?e?da?t??? ???? h PP? t?µ? ap?
????st??µ?s? ?e?????ta? ap? t? ep?ped? t??
???assa?.
(3) T?s? t?? e??e???e?d??? a?af???? se s??s? µe
t? st??f? t?? ???? ap? t?? ????a PP?
?e?da?t??? a??µ????? aPQ e??? ????? s?µe???
Q ast????µ??? a??µ????? APQ (ap?
ast????µ???? pa?at???se??).
22
Ge?da?t??? (?e?µet????) ?a? ????µet???? ???µet??
St?? efa?µ???? de? e?d?af??e? t? ?e?da?t???
???µet?? h ( ???? p??? ap? t? e??e???e?d??
a?af????), a??? t? ???? p??? ap? t?? ep?f??e?a
t?? ???assa?.
23
Ge?da?t??? (?e?µet????) ?a? ????µet???? ???µet??
St?? efa?µ???? de? e?d?af??e? t? ?e?da?t???
???µet?? h ( ???? p??? ap? t? e??e???e?d??
a?af????), a??? t? ???? p??? ap? t?? ep?f??e?a
t?? ???assa?.
?e?e?d?? ep??tas? t?? ep?f??e?a? t?? ???assa?
st? ste??? (?s?d??aµ??? ep?f??e?a t?? ped???
ßa??t?ta? st??µ? ?e??? se ??eµ?a)
d?a??µa?s? t?? ?e?e?d??? ? ???? t??
?e?e?d??? (G) p??? ap? t? e??e???e?d?? a?af????
(?)
????µet???? ???µet?? ap? t? s?µe?? P µ????
t? ?e?e?d?? ?at? µ???? µ?a? ?ata????f??
?aµp???? (?aµp???? µe t? d????sµa t??
ßa??t?ta? efapt?µe?? se ???e s?µe?? t??)
24
?? t?p??? ?e?da?t??? s?st?µa a?af????
t?p??? ?e?da?t??? s?st?µa a?af???? se ???e
s?µe?? P, µe ?e?da?t???? s??teta?µ??e? ?, ?, h
S?st?µa ?????a??????
????a? ???et?? st? e??e???e?d??
(?et??? f??? p??? ta p???),
????a? ???et?? p??? t? ep?ped? t??
?a? t?? ????a t?? ?e?da?t???? datum
(?ate????s? a?at?????)
????a? s?µp?????e? t?? ?????a??????
t???da (?ate????s? ß?????).
25
Met?ßas? ap? t? ß?s? t?? ?e?da?t???? datum st??
t?p??? ?e?da?t??? ß?s?

• pa??????? µet??es? ap? t?? a??? O
  st? s?µe?? P
• st??f? ???? ap? t?? 3? ????a ?at? ????a 90??
• (?ste ? 1?? ????a? ?a p??e? t?? ?ate????s? t??
  )
• st??f? ???? ap? t?? 1? ????a ?at? ????a 90?-?
• (?ste ? 3?? ????a? ?a p??e? t?? ?ate????s? t??
  )

???a?a? pe??st??f??
S???st?se? d?a??sµat?? µet??es??
?a?tes?a??? s??teta?µ??e? t?? P ?? p??? t?
?e?da?t??? datum (c xP)
Ka?tes?a??? s??teta?µ??e? x? t????t?? s?µe??? st?
t?p??? ?e?da?t??? s?st?µa
( x s??teta?µ??e? st? ?e?da?t??? datum)
26
?? t?p??? ast????µ??? s?st?µa a?af????
????eta? se ???e s?µe?? P µe t? ß???e?a d??
d?a??sµ?t?? (1) d????sµa t?? ßa??t?ta?
(s???staµ??? t?? ????? t?? ??? ?a? t??
f????e?t??? d??aµ??), (2) d????sµa pe??st??f??
t?? ??? (st?? ?ate????s? t?? st??µ?a??? ????a
pe??st??f?? t?? ???) µe µ??e??? ? ?s? µe t?
st??µ?a?a ta??t?ta pe??st??f?? t?? ???
??p??? ??????t?? ep?ped? ???et? st? t?p???
d????sµa t?? ßa??t?ta?
??p??? ast????µ??? µes?µß???? ep?ped? ep?ped?
t?? ?a? t?? t?p???? pa???????? p??? t?
27
?? t?p??? ast????µ??? s?st?µa a?af????
3?? ????a? (?e???) t?p??? d?e????s? t??
?ata????f?? (?et??? p??? ta p???) -
a?t??et? ap? t? d?e????s? t?? d?a??sµat?? t??
ßa??t?ta?
2?? ????a? (ß????) t?µ? ??????t??? ?a?
ast????µ???? µes?µß????? ep?ped??
1?? ????a? (a?at???) s?µp?????e? t? de???st??f?
?????a?????? t???da (a?at???, ß????, ?e???)
S?st?µa ?????a??????
28
??a??sµata ß?s??
?e???
a?at???
ß????
?st????µ??? µ???? ?P ?a? ast????µ??? p??t?? FP
S??se?? µetas??µat?sµ?? ap? t? ?e?da?t??? st?
t?p??? ast????µ??? s?st?µa
29
?st????µ???? pa?at???se?? st? s?µe?? P p??? ??a
???? s?µe?? Q
?e????a ????a ZPQ a??µ????? APQ ap?stas?
sPQ
x?Q s??teta?µ??e? t?? Q st? t?p???
ast????µ??? s?st?µa t?? s?µe??? P
30
?a?t???af???? p??ß????
?a?t???af??? p??ß??? µa??µat??? ape?????s?
t?? ep?f??e?a? tµ?µat?? t?? e??e???e?d???
a?af???? se ep?ped? (µe a?ap?fe??t? µ????
pa?aµ??f?s?) s?µe?? (?, ? ) st?? ep?f??e?a t??
e??e???e?d??? ? s?µe?? (x, y ) st? ep?ped?
????eta? ap? µa??µat???? s??se?? t?? µ??f??
t??t? d??stas? ????µet???? ???µet?? H
(ap?d?d?deta? st? ???t? µe t? µ??f? ?s?????
?aµp????).
31
?a?t???af???? p??ß????
?a?t???af??? p??ß??? µa??µat??? ape?????s?
t?? ep?f??e?a? tµ?µat?? t?? e??e???e?d???
a?af???? se ep?ped? (µe a?ap?fe??t? µ????
pa?aµ??f?s?) s?µe?? (?, ? ) st?? ep?f??e?a t??
e??e???e?d??? ? s?µe?? (x, y ) st? ep?ped?
????eta? ap? µa??µat???? s??se?? t?? µ??f??
t??t? d??stas? ????µet???? ???µet?? H
(ap?d?d?deta? st? ???t? µe t? µ??f? ?s?????
?aµp????).
Met?ßas? ap? t?? ?a?t???af???? s??teta?µ??e?
x, y, H st?? ?e?da?t???? ?, ?, h
(a?t?st??fe? s??se?? t?? ?a?t???af???? p??ß????)
(apa?te? ???s? t?? ????? t?? ?e?e?d??? ? )
32
?a?t???af???? p??ß????
?a?t???af??? p??ß??? µa??µat??? ape?????s?
t?? ep?f??e?a? tµ?µat?? t?? e??e???e?d???
a?af???? se ep?ped? (µe a?ap?fe??t? µ????
pa?aµ??f?s?) s?µe?? (?, ? ) st?? ep?f??e?a t??
e??e???e?d??? ? s?µe?? (x, y ) st? ep?ped?
????eta? ap? µa??µat???? s??se?? t?? µ??f??
t??t? d??stas? ????µet???? ???µet?? H
(ap?d?d?deta? st? ???t? µe t? µ??f? ?s?????
?aµp????).
Met?ßas? ap? t?? ?a?t???af???? s??teta?µ??e?
x, y, H st?? ?e?da?t???? ?, ?, h
(a?t?st??fe? s??se?? t?? ?a?t???af???? p??ß????)
(apa?te? ???s? t?? ????? t?? ?e?e?d??? ? )
x, y, H ?aµp?????aµµe? s??teta?µ??e? (??a
t?? pe????? ?p?? ???s?µ?p??e?ta? ? ?a?t???af???
p??ß???)
33
??a??st?p???s? pa?aµ??f?s?? ???? ?a?t???af????
p??ß????
??? µ?a, a??? µ?a ???????e?a ?a?t???af????
p??ß???? µe ????? µ??f?
K??e µ?a efa?µ??eta? se tµ?µa p?? ????eta? ap?
ep??e?µ??a s?µe?a P.
???????e?e? p??ß???? f???a ???t?? µ?a?
?????? p??ß????, K??e s?µe?? P ???t?? t??
f????? ???t??.
34
??a??st?p???s? pa?aµ??f?s?? ???? ?a?t???af????
p??ß????
??? µ?a, a??? µ?a ???????e?a ?a?t???af????
p??ß???? µe ????? µ??f?
K??e µ?a efa?µ??eta? se tµ?µa p?? ????eta? ap?
ep??e?µ??a s?µe?a P.
???????e?e? p??ß???? f???a ???t?? µ?a?
?????? p??ß????, K??e s?µe?? P ???t?? t??
f????? ???t??.
?a?ade??µata - p??ß??? Hatt (?p???e ? ep?s?µ?
???????? p??ß???) - p??ß??? UTM (Universal
Transverse Mercator) se ???e? µe d?af??et?????
?e?t?????? µes?µß?????? ?P. ep?s?µ? ????????
p??ß??? µ?a ???? t?? UTM ??a ??? t?? ????da.
35
??a??st?p???s? pa?aµ??f?s?? ???? ?a?t???af????
p??ß????
??? µ?a, a??? µ?a ???????e?a ?a?t???af????
p??ß???? µe ????? µ??f?
K??e µ?a efa?µ??eta? se tµ?µa p?? ????eta? ap?
ep??e?µ??a s?µe?a P.
???????e?e? p??ß???? f???a ???t?? µ?a?
?????? p??ß????, K??e s?µe?? P ???t?? t??
f????? ???t??.
36
??a??st?p???s? pa?aµ??f?s?? ???? ?a?t???af????
p??ß????
??? µ?a, a??? µ?a ???????e?a ?a?t???af????
p??ß???? µe ????? µ??f?
K??e µ?a efa?µ??eta? se tµ?µa p?? ????eta? ap?
ep??e?µ??a s?µe?a P.
???????e?e? p??ß???? f???a ???t?? µ?a?
?????? p??ß????, K??e s?µe?? P ???t?? t??
f????? ???t??.
O? s??teta?µ??e? x, y µ?a? ?a?t???af???? p??ß????
e?a?t??ta? ap? (a) t? e?d?? t?? p??ß????, d??ad?
ap? t?? µa??µat???? s??se?? x x(?,?), y
y(?,?), (ß) t? ???s?µ?p????µe?? ?e?da?t???
datum st? ?p??? efa?µ??eta? ? p??ß???.
37
??a??st?p???s? pa?aµ??f?s?? ???? ?a?t???af????
p??ß????
??? µ?a, a??? µ?a ???????e?a ?a?t???af????
p??ß???? µe ????? µ??f?
K??e µ?a efa?µ??eta? se tµ?µa p?? ????eta? ap?
ep??e?µ??a s?µe?a P.
???????e?e? p??ß???? f???a ???t?? µ?a?
?????? p??ß????, K??e s?µe?? P ???t?? t??
f????? ???t??.
O? s??teta?µ??e? x, y µ?a? ?a?t???af???? p??ß????
e?a?t??ta? ap? (a) t? e?d?? t?? p??ß????, d??ad?
ap? t?? µa??µat???? s??se?? x x(?,?), y
y(?,?), (ß) t? ???s?µ?p????µe?? ?e?da?t???
datum st? ?p??? efa?µ??eta? ? p??ß???.
Metat??p? ap? µ?a ?a?t???af??? p??ß??? se µ?a
???? (se d?af??et??? datum) - µetat??p? t??
?e?da?t???? s??teta?µ???? ap? ??a pa???sµ??
s?st?µa (?,?. h) se ??a ???? (??,??, h?). -
µetat??p? t?? ?a?tes?a??? s??teta?µ???? ap? ??a
pa???sµ?? s?st?µa (X, Y, Z) se ??a ???? (X?,
Y?, Z?) .
38
S????? t?? µetat??p??, ap? µ?a ?a?t???af???
p??ß??? se µ?a ????
?a??µet??? µetat??p?? p?? ??e?????ta? se ???e
ß?µa pa?aµ?t??i µet??es?? ??X, ?Y, ?Z ?a?
st??f?? ?1, ?2, ?3, ap? datum se
datum pa??µet??? t?? e??e???e?d?? t?? d?? datum
(a, e ?a? a?, e? ), d?af??et??? ???µet?a t??
?e?e?d??? (? ?a? ?? ).
39
S??s? ?a?tes?a??? s??teta?µ???? µe t?? s????e??
s??teta?µ??e? t?? efa?µ???? - ??????t?e?
s??teta?µ??e? x, y, ?a?t???af???? p??ß???? -
????µet???? ???µet?? ? (p??? ap? t? ?e?e?d??)
s??teta?µ??e? ?a?t???af???? p??ß???? x,
y o???µet???? ???µet?? ?
?a?tes?a??? s??teta?µ??e? st? s?st?µa
a?af???? t?? ?e?da?t???? datum ?, ?, ?
?e?da?t???? s??teta?µ??e? ?, f, h
h ?e?da?t??? ???µet?? (p??? ap? t? e?e???e?d??)
? ???µet?? ?e?e?d???
?a?t???af??? p??ß???
40
?etat??p? ap? µ?a ?a?t???af??? p??ß??? se ??a
datum, se µ?a ???? ?a?t???af??? p??ß??? se ??a
???? datum
P
41
?etat??p? ap? µ?a ?a?t???af??? p??ß??? se ??a
datum, se µ?a ???? ?a?t???af??? p??ß??? se ??a
???? datum
P
42
?etat??p? ap? µ?a ?a?t???af??? p??ß??? se ??a
datum, se µ?a ???? ?a?t???af??? p??ß??? se ??a
???? datum
P
43
?etat??p? ap? µ?a ?a?t???af??? p??ß??? se ??a
datum, se µ?a ???? ?a?t???af??? p??ß??? se ??a
???? datum
datum ? ?a?t???af??? p??ß??? ?
datum A ?a?t???af??? p??ß??? ?
44
S??s?
???se???se?? ??a µ????? ????e? st??f?? ?i (sin?i
?i, cos?i 1, ?i ?k 0)
45
????f????? s?st?µa GPS d??e? ?e?da?t????
s??teta?µ??e? st? s?st?µa (datum) WGS84
Ep?s?µe? t?µ?? s??teta?µ???? se e?????
s?st?µa a?af???? (s???e???µ??? ?e?da?t???
datum, s???e???µ??? ?a?t???af??? p??ß???, ?
???????e?a ?µ?e?d?? p??ß???? se d?af??et??? f???a
? ???e?).
46
????f????? s?st?µa GPS d??e? ?e?da?t????
s??teta?µ??e? st? s?st?µa (datum) WGS84
Ep?s?µe? t?µ?? s??teta?µ???? se e?????
s?st?µa a?af???? (s???e???µ??? ?e?da?t???
datum, s???e???µ??? ?a?t???af??? p??ß???, ?
???????e?a ?µ?e?d?? p??ß???? se d?af??et??? f???a
? ???e?).
?pa?t???ta? - pa??µet??? µetat??p?? ap? ??a
s?st?µa a?af???? st? ????, - pa??µet??? t??
e??e???e?d?? a?af???? sta d?? s?st?µata - t?p???
?e?e?d?? (??a t?? µetat??p? t?? ?e?da?t????
???µ?t??? h se ????µet???? H ). ??a??s?µ?
?e?e?d??, p.?. µe t? µ??f? p????? d?a???t?? t?µ??
?ik ?(?i,?k) se ???aß? ? ????st??µ?s?
µe GPS (µe s?µp????µat??? ???s? ded?µ????
ßa??t?ta?)
47
?? p??ß??µa t?? a??a??? ???µa?a?
?a?a??te?a ape??e?a? µet??se?? µ???? (s??µata
INVAR) ßa?µ???µ?µ??a µe ??a p??t?p? µ?t??.
S?µe?a ap?st?se?? ap? µet??se?? t?? ????????
d?af???? ?t p?? ??e???eta? ? ??e?t??µa???t???
a?t???ß???a ??a ?a d?as??se? µ?a ap?stas? s
M?t??s? t?? ap?stas?? s c ?t (c ta??t?ta
f?t??)
48
?? p??ß??µa t?? a??a??? ???µa?a?
?a?a??te?a ape??e?a? µet??se?? µ???? (s??µata
INVAR) ßa?µ???µ?µ??a µe ??a p??t?p? µ?t??.
S?µe?a ap?st?se?? ap? µet??se?? t?? ????????
d?af???? ?t p?? ??e???eta? ? ??e?t??µa???t???
a?t???ß???a ??a ?a d?as??se? µ?a ap?stas? s
M?t??s? t?? ap?stas?? s c ?t (c ta??t?ta
f?t??)
K??µa?a d??t??? ??? ap? ???sµ? µ???da? µ?????,
a??? ap? t?? ???sµ? t?? µ???da? ??????, p?a?t???
???p???s? p?????e? epe?d? st????eta? se ??a
s???e???µ??? s?st?µa ?????µ?t??? (????????).
???t?a µe EDM µ???da ?????? ap? ta ?????µet?a
t?? ??????? ???t?a µe pa?at???se?? GPS µ???da
t?? ?????? GPS, (s???e???µ??? d??t??
????????)
49
?? p??ß??µa t?? a??a??? ???µa?a?
?et?ßas? ap? s?st?µa a?af???? se ???? µe
d?af??et??? ???µa?a s??te?est?? µetaß????
???µa?a? s 1 ? (s ? 1, ? ? 0)
µetas??µat?sµ?? ?µ???t?ta? (similarity
transformation) µet??es?, a??a?? ???µa?a? ?a?
pe??st??f? (µe ?p??ad?p?te se???)
50
?? p??ß??µa t?? a??a??? ???µa?a?
?et?ßas? ap? s?st?µa a?af???? se ???? µe
d?af??et??? ???µa?a s??te?est?? µetaß????
???µa?a? s 1 ? (s ? 1, ? ? 0)
µetas??µat?sµ?? ?µ???t?ta? (similarity
transformation) µet??es?, a??a?? ???µa?a? ?a?
pe??st??f? (µe ?p??ad?p?te se???)
6 d?af??et??? µ??t??a µetas??µat?sµ?? ?µ???t?ta?
a?????a µe t? se??? t?? pe??st??f?? (R),
µetaß???? ???µa?a? (S) ?a? pa???????? µet??es??
(T).
?e se??? efa?µ???? ap? a??ste?? p??? ta de???
(p.?. RST se??? pe??st??f?, ???µa?a,
µet??es?)
6 µ??t??a (RST, RTS, SRT, STR, TRS, TSR).
51
?? p??ß??µa t?? a??a??? ???µa?a?
?????? 6 µ??t??a (RST, RTS, SRT, STR, TRS, TSR).
?d?? ap?t??esµa s (R x) R (s x) a?
µetaß???e? aµ??ßa?a ? se??? d?ad??????
pe??st??f?? ?a? ???µa?a? (RS SR) ta?t?s? t??
µ??t???? RST SRT ?a? TRS TSR.
52
?? p??ß??µa t?? a??a??? ???µa?a?
?????? 6 µ??t??a (RST, RTS, SRT, STR, TRS, TSR).
?d?? ap?t??esµa s (R x) R (s x) a?
µetaß???e? aµ??ßa?a ? se??? d?ad??????
pe??st??f?? ?a? ???µa?a? (RS SR) ta?t?s? t??
µ??t???? RST SRT ?a? TRS TSR.
?e???? µ??? 4 µ??t??a µetas??µat?sµ?? ?µ???t?ta?
RST SRT
RTS
STR
TRS TSR
53
?? p??ß??µa t?? a??a??? ???µa?a?
?????? 6 µ??t??a (RST, RTS, SRT, STR, TRS, TSR).
?d?? ap?t??esµa s (R x) R (s x) a?
µetaß???e? aµ??ßa?a ? se??? d?ad??????
pe??st??f?? ?a? ???µa?a? (RS SR) ta?t?s? t??
µ??t???? RST SRT ?a? TRS TSR.
?e???? µ??? 4 µ??t??a µetas??µat?sµ?? ?µ???t?ta?
RST SRT
RTS
STR
TRS TSR
54
?? p??ß??µa t?? a??a??? ???µa?a?
?????? 6 µ??t??a (RST, RTS, SRT, STR, TRS, TSR).
?d?? ap?t??esµa s (R x) R (s x) a?
µetaß???e? aµ??ßa?a ? se??? d?ad??????
pe??st??f?? ?a? ???µa?a? (RS SR) ta?t?s? t??
µ??t???? RST SRT ?a? TRS TSR.
?e???? µ??? 4 µ??t??a µetas??µat?sµ?? ?µ???t?ta?
RST SRT
RTS
STR
TRS TSR
??af????? µ??? ?? ???? µet??es??
s?????? ???s?µ?p??e?ta? t? p??t? µ??t??? (RST
SRT)