Digital Elevation Models and TIN Algorithms

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Digital Elevation Models and TIN Algorithms
Marc van Kreveld

• ????? ?????
• ?????? ?????

2
????? ?? ????? ?-

1. ?????? ????? ?????? ???-???? (terrain).
2. ????????? ???? ?-TIN.
3. ????????? ???? ??? ??????? ??????.

3
? ? ? ? ?

• GIS- Geographic Information System (????? ????
  ????????)- ????? ??????? ??????, ????? ?????
  ?????? ????? ?????????.
• ??? ???????? ??????? ????-?????, ??? ?? ????
  ?????? ?? ????? ????? ???-??????.
• fA?RR?R ??????? ?????? ???? ??? ????? p?A,
  (A- ??? ???-????? ????????.
• ???? ??????? ???? ?? ???? ??????, ??? ????? ????
  ?? ?????? ?????? ?? ?????? ????? (?????
  ?????-????? ??? ?????? ?????).

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??? ?? ????? ?-

1. ?????? ????? ?????? ???-???? (terrain).
2. ????????? ???? ?-TIN.
3. ????????? ???? ??? ??????? ??????.

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?????? ??????? ?????? ???-????

1. The regular square grid.
2. The contour line.
3. The triangulated irregular network.

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The regular square grid

• ???? ????? ?? ???? ?-n ?????? ????.
• ?????? ????? ????? ??-????? ????? nn.
• ???? ?? ????, ???? ????? ??? ???? ??? (?????
  ?????? ?????? ????? ??? ???? ?? ??????? ??????
  ????? ?????? ?????? ????? ?????).

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Sample of regular square grid
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????? ???? ????? p

• ???? ?????? ???? ?????? ??? ???? ????? ??
  ?????? ?????.
• ?????? ??????? f ?? ?????, ????? ????? ?? ????
  ????? ?????.

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?????? ???????? ?????

• ?????? ?????? ?? ????? ??? ????? ????? ??? ??? ??
  ????.
• ??????? ?????? ?? ????? ??? ???? ???? ?????? ???
  ?? ?????? ?????.

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The Contour line model

• Contour line - ???? ?????? ??????? ???? ????
  ????.
• ????? ????? ????? ?? contour lines.
• ?? contour line ?????? ????? ?? ?????? ??
  ???????????? x, y ??? ??? ????.
• Contour line ??? ?? ???? ????, ?? ?? ??????? ????
  ??? ?????? ?? ?????? ????, ??? ???? ?????
  ??????????.

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Sample of Contour line model
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Perspective view of an Elevation model and the
contour line map of it
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????? ???? ????? p

• ?? ?????? ????? ?? ????, ??? ????? ?? p ??? ????
  ?- contour line ????? ???? ??.
• ????, ?????? ?? ???????? ?? ?????? ?????, ???????
  ?? ????? ???? ??????? ?? ?? ?- contour lines
  ??????? ??????? ??.

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????? ?????

• ???? ???? ????? ?????? ?- contour lines
• Doubly connected edge list (DCEL).
• The adjacency structure.

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The adjacency structure

• ???? ??? ????? ?? ????????
• ?????? ????? ??????? (??? ???? ???-?????)- ??????
  ?? ????????. (????? ?- ).
• ?????? ????? contour line- ???????? ??????? ????
  ??? ???? ??????. (????? ?- ).
• ?? ??? ??? ??????? ?-contour line ?? ?? ?? ?????
  ???? ????? ????????.
• ?????? ?-contour line ???? ????? ?? ?? ?? ???
  ????? ????? ??? ?? ??? contour line ??? ???? ??
  ??? ????????? ?????.

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The adjacency structure
t8
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????? contour lines

• ??? ?????? ????? ?????? ?-contour lines.
• ?????????
• ?????? ??????????? ?? ?????? ????? (??????
  ??????????? ?????). (????- ??? ??????? ???????).
• ???? ?? ???? ?????? ??? ???? ???? ??? ???
  ?????????, ??? ???? ?? ?????? ?? ????? ??????.

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???????????, ?????? contour lines ????? 24
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The Triangulated Irregular Network model (TIN)

• ????? ????? ????? ?? ?????? ??????? ??? ?????.
• ????? ???????? ??? ??????? ?????? ??????? (??????
  ?- grid).
• ?????? ??????????? ?? ?????? ???? ???.
• ?? ????? ????? ????? ????, ?? ??? ?? ?? ?????
  ?? ?????.

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Sample of TIN model
Perspective view of a triangulated irregular
network
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????? ???? ????? p

• ?? ?????? ????? ?? ????? ?? ??????, ??? ???? ????
  ?? ????? ????? ?????? (????? ????).
• ?? ?????? ????? ?? ??? ?? ????? ???????????
  ???????? ??? ??? ??????? ??????? ??? ??.
• ?? ?????? ????? ???? ??????- ??????????? ????????
  ??? ????? ??????? ??????? ????? ??.

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????? ????? Network structure

• ???? ?? ????? t, ??? e ??????? v ???? ???????.
• ???????? ????? ???? ????? ???? ?? ??? ?????
  ???? ?? ??????.
• ???????? ??? ???? ????? ????-
• ??? ???? ??? ??? ??? ????? ?????? ????? ???? ??.
• ??? ???? ??? ??? ??? ????? ??????? ?? ????.
• ???????? ?????? ???? ????? ???? ??????? ?? ????
  ????????????? ?????? ?? ???????.

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The TIN and the network structure for it. The
three values of each vertex are not shown.
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???? ?????-Hierarchical models

• ???? ?????? ????? ??? ????? ?? ??? ????? ?????
  ???? ?? ??-????.
• ??? ??????? ????????? ??????? ?? TIN.
• ??? ????? ?????? ????? ????, ?? ???? ????? ??
  ?-TIN ??? ????? ????, ???? ?????? ??? ??? ????.
• ???? ????????? ????? ?????? ??? ???? ????? ????
  ???? ?????? ?-TIN ?? ???? ?????? ????.
• ????? ??????? ????? ?????? ????? ??? ???? ???? ??
  ?????, ????? ??????.

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????? ?????? ?????? ???-????

• ??????? ????????
• Grid- ???? ?????? ???? ????? ?????? ??????.
  ?????? ?????? ????? ?????. ??????? ????? ?? ?????
  ???????? ?? ??? ?????.
• Contour line- ???? ????? ?? ???? ??????????,
  ????? ????? ???? ???????. ???? ?? ???? ?????
  ??????????. ????? ?????? ???? ??? ???????.
• TIN- ???? ????? ?? ???? ????????. ??? ???? ?????
  ?????? ?????? ??????? ?????? ????? ????? ???????.
  ??????? ????? ?? ????? ???????? ?? ??? ?????.
• ???? ????? (????? ???????)- ???? ?????? ????? ??
  ??? ????? ????? ?????? ?????? ??????.

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??? ?? ????? ?-

1. ?????? ????? ?????? ???-???? (terrain).
2. ????????? ???? ?-TIN.
3. ????????? ???? ??? ??????? ??????.

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Access to TIN

• ???? ??? ????? ???? ?-TIN
• Traversal of a TIN
• Efficient access to a TIN

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Traversal of a TIN

• ???? ????, ?????? ???? ?? TIN, ?????? ???
  ?????????, ?????? ???????? ?? ?????.
• ????? ?????- ??? ???? ?????? ???? ??? ?????? ???
  ?????? ?-TIN.

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Traversal of a TIN cont ...
????? ????? -

• ??? T TIN, ??????? ????? network structure. ??? v
  ??????? ?????? ?????? ?? T.
• ??? ????? t ?-T ???? ????? ??? ???.
• ??? t ????? ????? ?-T. ???? ???? e ?? t ?? ??????
  in ?? ??? ????? ??? e ???? ?? ?????? ???? ?????
  ?? ????? ??? ???? t ????? ???? v, ???? ???? ??
  ?????? out.

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Traversal of a TIN cont ...

• ?? ??? ????? ??? e ???? ?? v, ??? ?? t ???? ?????
  ???, ???? ?-e ????? out, ???? ???? ?-e ?????
  in.
• ??? ????? ?? ????? ??? ??? ?? ????? in ?????? ???
  ??? ?? ????? out.
• ???? ????? ?? TIN ???? ???? ?? ????? in, ????? ??
  ?????? ?????? ??????.

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????? ??? ??? ????? ?? ?????? in-

• ??? ?????? ????? ?????? ????? v. ???? ?-in ??
  ???? ?????? ????? ???? ????? ??? ???? (v,v),
  ??-in-and-back ?? ???? ?????.
• ???? ?????? ???? ?? ????? in-and-back ???? ?????
  ?????? ??? ??? ??, ???? ??? ???-?? ???? ????
  (?????) ??? ??? ??.

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????? ??? ??? ????? ?? ????? out-

• ???? ?? ?????? ?-first-out ?-second-out.
• ???? ?? ?????? first-out, ???? ???? ?????? ?????
  ??? ????? ??? ???? (v,v) ???? v ??? ???????
  ?????? ???? ??????.
• ?????? ?????, ??? ??????? ?????? ????? ???? ????.

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?????????

• ???
• ????? t.
• ??? e.
• ????? ?????? ?????? t ???????? v ??? ???
  ????????? ???, ???? ??? e ?????? ?? ????? ??????
  ?? ????.
• ????????? ???? ?????? ?????? ??-??? ???? ?? ?????
  ?????? ???? ??? ????? ???? ???.
• ?????? ?????? ?? ??? ???? e ???? ?????? t.

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????????? -
35
(No Transcript)
36
?????
Traversing a TIN numbers at arrows correspond to
the algorithm
37
???????? ?? ?????????
5
18
out
in
In-and-back
first-out
first-out
10
Second-out
Second-out
in
in
in
first-out
first-out
in
Second-out
Second-out
25
20
10