????? ??????????????? (radiosity)

1
?????? ??????????? ??????? ???????????????

• ??????? ?????????
• ?????? 6
• 18 ??? 2009

2
??????????????? ?????????????? ??????????

• ?????? ???????, ?????????? ??????????? ?????????
  ???????
• ??????????? B (?)
• ??????? ????????? ??/?2

3
??????????? ? ???????????????

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

4
???????????
5
???????????????
6
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7
?????????????

• ????????? ??????????????? ?????? ?????????
  ??????????? ????????? ??? ?????? ??????????????
  ?????????????
• ??? ??????????? ?????????? (???????? ?????????)
• ??????????? ????? ???? ???????? ?? ???????
  (?????) ??????????? ???????????????
• ??????????????? ?????????????? ?????? ??
  ????????????
• ????????? ?????????????? ???????? ?? ??????????
  ???????????
• ?????? ???????????? ??? ????????? ???????
• ??????? ?? ?????????
• ??? ????????????? ????????? ??????? ?????????
  ??????????? ????????? ????????!

8
??????????????? ????????? ????????????

• ??????????????? ??? ????????? ????????????
• ????????? BRDF ? ???????? ???????????? ?????????
  ???????????

9
??????? ???????

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

10
?????? ??????? ???????????

• ??????????? ???????? ?? ????????? ???? ? ????????
  ?? ???? ?????? ???????????? ?????

11
????????????? ????????? ?????

• ???????????, ??? ????????? ??????? ?? N
  ???????????????? ???????????? (patches) Pi,
  i1..N
• ??????? Ai
• ???????????, ??? ??????????????? ?????????? ??
  ??????
• ???????

12
?????????? ??????

• ???????? ???????? ?? ?????? ????????? ?? ????? ??
  ????????????

13
????-??????
Fij - ????? ?????? ???????, ?????????? ????????
Pi ? ?????????? ????????? Pj
???????? j
???????? i
14
????-?????? ????? ????????????????? ??????????
???? ????? Normali ? r
?????????? ??????? ???????? I, j
???? ????? Normalj ? r
???????? j
?????? ?? dAi ? dAj
???????? i
15
?????? ????-??????
Surface j
Surface i
16
???????? ????-???????

• ??????? ?????? ?? ?????????
• ??????????? AiFijAjFji
• ???????????? Fi(j?k)Fij Fik
• ????? ????? ???????
• ??? ???????, ?????????? ????????, ?????? ????-??
  ??????

17
????????? ??? ?????????? ???????????????

• ??? ????!
• ??????? M NxN
• ??????? ??????? ?
• ?? ??????? M ????? ????????? ???????????,
  ?????????? ??????????

18
????????? ???????????????
Form Factor of surface j relative to surface i
Radiosity of surface i
Emissivity of surface i
Radiosity of surface j
Reflectivity of surface i
Surface j
Surface i
19
???????????????
????????? ????????? ?? ????????
????????? ????-???????
?????? ????
???????????? ? ????? ???????
20
???????????????
????????? ????????? ?? ????????
????????? ????-???????
?????? ????
???????????? ? ????? ???????
21
??? ????????? ??? ??????????
???????? j
????????? ?? j
????????? ?? i
???????? i
22
???????? ?????????

• ?????? ?????????? ????-??????? ?????? ???? ???
  ??????? ????????????!
• ???????? ?????????? ?????????????? ??????,
  ??????? ????????? ??????? ? ?????? ??????????
  ???? ??????? ????? ???????????? ? ?????? ??
  ?????? ???????????

23
????????? ?????????????? ???????? ?????????
??? ???? ????-?????? FdAiAj
Aj
dAi
24
???????? ?????????

1. Project Aj along its normalAj cos qj
2. Project result on sphereAj cos qj / r2
3. Project result on unit circleAj cos qj cos qi
   /r2
4. Divide by unit circle areaAj cos qj cos qi /
   pr2
5. Integrate for all points on Aj

???????? Aj
qj
r
qi
??????????? ???????? Aj cos qj/r2
?????? ???????? Aj cos qj cos qi /r2
????????? ??????? p
25
????? 1 ???????

• ????????????? ??????? ????????? ????? ?????? dAi
  ? ????????? Aj

????????????? ??????? (Aj)
??????????????????????? (dAi)
26
???????

• ??? ???????? ???????????? ??? ??????? 1 ? ???????
  ?????? 2x2. ??????? ????? 1x2
• ??? ??????????? ?? ?????? (????????, 512x512 ???
  ??????? ?????)

27
?????? ?????? ????????
28
????? ????????

1. ???????? ???? ???????? ????? ?? ???? ?????? ????
2. Z ????? ??? ?????????? ?????????
3. ???????????? ?????? ????-???????? ????? ????????
   ???????? ?????????
4. ??? ???? ????-?????? ????????? ???????? ?? ????
   ??????????

29
????? ????????

• ???????????
• ?????? ???????????? ?????
• ????? ???????????? ??????????
• ??????? ?????????? ???????? ??????????
  ????-????????
• ??????????
• - ????????? ???????????????-???????? ????-??????
• - ????????
• - ?????? ?????????
• - ????????????? ?? ??????????? ????????
• - ??????? ????????? ?????????? ??????
  ????-???????

30
????? ???????? ????????
31
????? 2 ????????? ?????????????

• ????? Aj ?? ????? ????? dAj
• 2. ??? ???? dAj
• ??? dAj-dAj ??? ?????? Vij
• ???? ?????? ????????? FdAidAj
• ?????????
• FdAiAj FdAidAj
• 3. ????? FdAiAj

Aj
dAj
???
dAi
32
???????????????
????????? ????????? ?? ????????
????????? ????-???????
?????? ????
???????????? ? ????? ???????
33
??????? ???????????????
Ei
Bi
34
??????? ???????????????

• ?????????????? ??????? ????????? ????-???????
  ???? ??? ???????? ? ????? ????????? ????
• ???? ???????? ??? ???? Bi
• ????????? (luminance) ????? ????? ???????????
  ?????????

35
??????? FB E

• ?????? ?????? O(n3)
• ???????? ??????????
• Goral, Torrance, Greenberg, Battaile, 1984
• ??????????? ?????? O(n2)
• ?????????? ???????
• ????????????-??????????? ? ?????? ?????????
• Gauss-Seidel, Jacobi ??????
• Nishita, Nakamae, 1985
• Cohen, Greenberg, 1985
• Southwell ????????
• Cohen, Chen, Wallace, Greenberg, 1988

36
??????

• ????, ?????????? ????????, ???????????? ? ???????
  ????? ????? ? ?????????

37
??????

• ?????? ????? ????? ??????? ????????? ????????
  ???? ????

38
??????
39
????????

• ???????? ????? ????? ??????? ?????????
  ???????????? ???????? ???????? ???????????????
  ??? ????? ?????????

??? ???? j
where
40
????????
41
????????????? ???????????????
42
??????? ???????? ????????
43
??????? ???????? ?????????
44
?????????? ??????????
45
?????????? ??????????
46
???????????????
????????? ????????? ?? ????????
????????? ????-???????
?????? ????
???????????? ? ????? ???????
47
?????????? ?????? ?????? ???????????????
48
?????????? ?????? ?????? ???????????????

• Cornell box
• Cindy M. Goral, Kenneth E. Torrance, and Donald
  P. Greenberg for the 1984 paper Modeling the
  interaction of Light Between Diffuse Surfaces,
  Computer Graphics (SIGGRAPH '84 Proceedings),
  Vol. 18, No. 3, July 1984, pp. 213-222.

49
The Cornell Box

• Michael F. Cohen and Donald P. Greenberg for the
  1985 paper The Hemi-Cube, A Radiosity Solution
  for Complex Environments, Vol. 19, No. 3, July
  1985, pp. 31-40.
• The hemi-cube

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