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Photon Mapping Reference Material The slides have used/adapted - - PowerPoint PPT Presentation

Photon Mapping Reference Material The slides have used/adapted material from the following references: Slides on Photon Mapping by Jan Kautz (web4.cs.ucl.ac.uk/teaching/4074/archive/.../04_ photon _ maps .pdf) Slides on Photon Mapping by Bill


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SLIDE 1

Photon Mapping

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SLIDE 2

Reference Material

The slides have used/adapted material from the following references: Slides on Photon Mapping by Jan Kautz (web4.cs.ucl.ac.uk/teaching/4074/archive/.../04_photon_maps.pdf) Slides on Photon Mapping by Bill Clark (http://penguin.ewu.edu/cscd570/2011/PDFNotes/PhotonMapping.pdf)

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SLIDE 3

Photon Mapping

()*+,&-+$&.*/0-/$&"#,)1#+,23)-$#+,

!"#$%&'(!)&"**)+(!&)(,-&,)*",&,'./!'(.&$00$*!% 1'2$*!&$00$*!%&02)3&,'./!&!)&)45$*!&!)&$-$&6&0)2&4)!/& 1'00+%$&"(1&%7$*+,"2&,'./!'(.8

4-5&60-7#+,

0)2&1'00+%$&,'./!&+%$%&)(,-&,)*",&$00$*!%&()&.,)4",& ,'./!'(.8 0)2&%7$*+,"2&,'./!&1)$%&1)&%)3$&.,)4",&,'./!'(.&%'(*$& 2$0,$*!$1&2"-%&*"(&42'(.&4"*#&,'./!&02)3&)!/$2&)45$*!%&6& !/+%&'(&!/$&%7$*+,"2&*)37)($(!&.,)4",&,'./!'(.&'%& 72)9'1$18

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SLIDE 4

Photon Mapping

Ray Tracing

  • Cast a ray from the eye through each pixel
  • Trace secondary rays (light, reflection, refraction)
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SLIDE 5

Photon Mapping

()$#*+#,-

!"#$%"&!''"()#*%+"#*!#"&,)-!.-/.!#)'".01*#",)!-*021" %2)",)10%2"3,%("!.."%#*),",)10%2'" (%+).'"%2.4"+033/')".01*#021 '&)-/.!,".01*#021"-!2"5)"&,%60+)+"60!"!"*45,0+",)2+),)," #*!#"/')'"5%#*",!+0%'0#4"3%,"#*)"+033/')"#),("!2+",!4" #,!-021"3%,"#*)"'&)-/.!,"#),(7

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SLIDE 6

Photon Mapping

The Rendering Equation (Kajiya '86) x' x'' x

  • L(x'->x'') is the total radiance from x'

L x x E x x f x x x L x x V x x G x x dx

r x

( ' '' ) ( ' '' ) ( , ' , '' ) ( ' ) ( , ' ) ( , ' ) " = " + "

#

  • f is the BRDF
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SLIDE 7

Photon Mapping

./0123$123$&/4560

><2409?/49<2$?@$ 06E56>49F94@$ CG8.HD$<E$476$=/0E1>6$14$AB

  • BDICA-DLCA-ABDMCA-ABD$3N

! " "

r

n

i r

!i

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SLIDE 8

Photon Mapping

!"#$%#&%#'()*"+'(*,#-&#.(/"+(+%0+%)%#'&#.(*"1(2&.*'( )3,''%+)(,2"#.($,+&"4)(0,'*)(&#(,()3%#%(/+"5('*%( 2&.*'()"4+3%('"('*%(%6%7 8%/&#&'&"#)(9('*%($%+'&3%)("/(,(2&.*'(0,'*(3,#(:%;

<(;(,(2&.*'()"4+3% =(;('*%(%6% >(;(,()0%342,+(+%/2%3'&"# 8(;(,(-&//4)%(+%/2%3'&"#

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SLIDE 9

Photon Mapping

CS

!"#$%&&' ("#$%&' )"#$&&%'

! " #

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SLIDE 10

Photon Mapping

()*+#,-.#),&/).-.#),!"#$%&'(#!$)*#$++,-.! .-/(/,-.0

"102!3!-.$!-#!4-#$!-5!1!$6$./+ "107!3!8$#-!-#!4-#$!-5!1$6$./+ "109!3!8$#-!-#!-.$!1!$6$./ "1:1;0!3!(!1!-#!(!1;!$6$./

<)(4*'$!3!=">:?02?<!@@!*(/A!5#-4!',%A/!B,/A!-.$!-#! 4-#$!C,55&+$!-#!+*$D&'(#!#$5'$D/,-.+!E$5-#$!E$,.%! C,55&+$'F!#$5'$D/$C!/-!/A$!$F$G

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SLIDE 11

Photon Mapping

(<=#%&#7&(&>(.4=<&

(<*%+&

Caustic Reflection

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SLIDE 12

Photon Mapping

Introduction

  • ! ,1%41%&JT;:&UVK&UW&
  • ! G*3.@($14&$"1&$2(%4)#2$&#7&*%6*P*6.(@&

)"#$#%4&

  • ! !"#$#%4&13*X16&72#3&@*+"$&4#.2<14&
  • ! !"#$#%4&L#.%<1&#Y&#7&4)1<.@(2&

4.27(<14&

  • ! !"#$#%4&61)#4*$16&#%&6*Y.41&4.27(<14&

–! 81@6&*%&(&Z?E&4)(=(@&6($(&4$2.<$.21& –! G.27(<14&%116&%#$&L1&)(2(31$12*/16&

  • ! !"#$#%4&!"##$!%$&'()'*+%,'%-+!./0'72#3&

1A1&

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SLIDE 13

Photon Mapping

Introduction

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SLIDE 14

Photon Mapping

Introduction

  • Store photons

– position + light power + incoming direction

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SLIDE 15

Photon Mapping

Introduction

  • Efficiently store photons for fast access
  • Use hierarchical spatial structure (kd-tree)
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SLIDE 16

Photon Mapping

Introduction

  • Cast primary rays
  • For secondary rays

– reconstruct irradiance using k closest photons

  • Combine with irradiance caching and other techniques
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SLIDE 17

Photon Mapping

Introduction

Photon Mapping - Caustics

  • Special photon map for specular reflection and

refraction

Glass sphere

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SLIDE 18

Photon Mapping

What is a Photon?

!p !"p xp

  • ! _&)"#$#%&*&*4&(&)(2=<@1&#7&@*+"$&

$"($&<(22*14&S.^&!"*D!*K&!*H&

–! !#512B&!"*&c&3(+%*$.61&D*%& :(X4H&(%6&<#@#2&#7&$"1&S.^&*$& <(22*14K&4$#216&(4&(%&;TR&$2*)@1& –! !#4*=#%B&!*&c&@#<(=#%&#7&$"1& )"#$#%& –! E*21<=#%B&!*&c&$"1&*%<*61%$& 6*21<=#%&!.&.416&$#&<#3).$1& *22(6*(%<1&

  • ! !"#$#%4&P4O&2(A4&

–! !"#$#%4&)2#)#+($1&S.^& –! ;(A4&+($"12&2(6*(%<1&

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SLIDE 19

Photon Mapping

Sources

  • ! !#*%$&4#.2<1&

–! !"#$#%4&13*X16&.%*7#23@A&*%&(@@& 6*21<=#%4&

  • ! !#512&#7&4#.2<1&D:H&6*4$2*L.$16&

1P1%@A&(3#%+&)"#$#%4&

  • ! 0@.^&#7&1(<"&)"#$#%&1M.(@&$#&4#.2<1&

)#512&6*P*616&LA&$#$(@&d&#7&)"#$#%4&

  • ! 0#2&1^(3)@1K&(&Wb:&@*+"$&L.@L&5#.@6&

41%6&#.$&(&$#$(@&#7&ebb-&)"#$#%4K& 1(<"&<(22A*%+&(&S.^&!"&#7&bOW&3:&

  • ! !"#$#%4&41%$&#.$&#%<1&)12&4*3.@(=#%K&

%#$&<#%=%.#.4@A&(4&*%&2(6*#4*$A&

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SLIDE 20

Photon Mapping

Mixed Surfaces

!d = 50% !s = 30%

  • ! '()*+,$-&.+/$&-0$,(1+)&+2%&

%"3(-$&,45042$26-&

–! &!!&7&%"3(-$&)$8$,6+2,$& –! &!"&7&-0$,(1+)&)$8$,6+2,$& –! &!!&9&!"&:&;&<,42-$)/+=42&4*& $2$)>?@&

  • ! A$6&!&B$&+&(2"*4)5&)+2%45&/+1($&

*)45&C&64&;&

  • ! D*&!&:&!!&6.$2&)$8$,6&%"3(-$&
  • ! E1-$&"*&!&:&!!&9&!"&6.$2&)$8$,6&
  • 0$,(1+)&
  • ! F6.$)G"-$&+B-4)B&

Russian Roulette

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SLIDE 21

Photon Mapping

!"#$#%&'())*%+&*,&(&-&,$(+.&)/#0.,,1

!)%*&+,&-.#"$#/0&)1%&213)3/&45* 2'*$&)"#$#%,&3/#'&$".&4*+"$, 50($$./&)"#$#%,&*%&$".&,0.%.&6&)"#$#%&*%$./(0$*#%,& 7*$"&#89.0$, 5$#/.&)"#$#%,&*%&$".&)"#$#%&'() !)%*&',&67#/0&)1%&*13)3/&85*&#/&95:&)95;#/0&<&=#/5"& 9%/$%9#/0 :$&*%$./,.0$*#%&)#*%$,&;&*%,$.(<&#3&0(40=4($*%+&$".& <*33=,.&4*+"$*%+&0#')#%.%$&3/#'&$".&%#/'(4&>.0$#/?& $".&<*33=,.&4*+"$*%+&0#')#%.%$&0#'.,&3/#'&$".& )"#$#%&'()1

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SLIDE 22

Photon Mapping

LTW&])$$&

  • ! ^"/$2&+&1+)>$&2(5B$)&4*&04"26-&0;N_N02&"2&XW&
  • 0+,$&G$&G+26&64&,1+--"*?&6.$5&+2%&B$&+B1$&64&

5+M$&*+-6&U($)"$-`&

–!a"2%&+11&6.$&04"26-&G"6."2&+&,(B4"%& –!a"2%&+11&6.$&04"26-&G"6."2&+&2$">.B4().44%&4*&+& >"/$2&04"26&

  • ! ].$-$&04"26-&+)$&0.4642&04-"=42-&42&-()*+,$-R&
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SLIDE 23

Photon Mapping

LTW&])$$&

  • ! J&LTW&6)$$&"-&b(-6&+2&+#"-&+1">2$%&c'Q&6)$$R&
  • ! E+,.& 24%$& 4*& 6.$& 6)$$& -64)$-& +& -$0+)+=2>&

01+2$N&%$\2$%&B?&6.$&5$%"+2&/+1($&+142>&42$& 4*&6.$&,44)%"2+6$-R&&

  • ! ].$&1$+/$-&4*&6.$&6)$$&,426+"2&6.$&4)">"2+1&%+6+&

04"26-R&&

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SLIDE 24

Photon Mapping

LTW&])$$&

  • ! Y)"6$&0"&d&<#;"N&#V"N&#X"@&
  • ! A$6&#be&B$&6.$&5$%"+2&4*&6.$&/+1($-&4*&6.$&b6.&,44)%"2+6$&

<bd;NVNX@R&

  • ! '6+)6&G"6.&#;e&G.",.&G"11&0+)==42&6.$&4)">"2+1&-$6&4*&04"26-&

"264&6G4&-$6-&<%"/"%$%&+142>&6.$&f&+#"-@R&

  • ! Z4G&+001?&6.$&-+5$&0)4,$%()$&64&$+,.&4*&6.$&1$PT&+2%&)">.6T
  • $6-N&$#,$06&24G&-(B%"/"%$&42&#Ve&&
  • ! Z4G&+001?&6.$&-+5$&0)4,$%()$&)$,()-"/$1?&64&$+,.&4*&6.$-$&
  • (B-$6-&$#,$06&24G&-(B%"/"%$&42&#Xe&&
  • ! L$$0&+001?"2>&6."-&)$,()-"/$1?&(2=1&$+,.&1$+*&4*&6.$&6)$$&

,426+"2-&+&%+6+&04"26R&&

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SLIDE 25

Photon Mapping

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SLIDE 26

Photon Mapping

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SLIDE 27

Photon Mapping

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SLIDE 28

Photon Mapping

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SLIDE 29

Photon Mapping

  • ! H'>+..$5<'$&'I'>5'1$&+19+4>'$'E:+;04$
  • ! /043'&5$94>91'45$&+19+4>'$9450$94>91'45$I:*$
  • ! H'I'>5'1$&+19+4>'$94$5'&,7$0=$94>91'45$I:*$
  • ! J:,'&9>+..A$

+19+4>'$'E:+;04$

!A = !r2

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SLIDE 30

Photon Mapping

  • ! !"#$./0$/,$+*1$2/,3$4&2/5,$!-$
  • ! 6&401$1'"50*$+*&+$+*1$2/,3$

,544"5'2,$+*1$"$'1&41,+$ 7*"+"',8$

  • ! 9*1$'5:.14$";$7*"+"',$5,12$;"4$

&$4&2/&'<1$1,=:&+1$"$/,$5,5&>>($ .1+#11'$?@$&'2$?@@8$

!A = !r2

"',-$

A&2/&'<1$1,=:&+1$5,/'0$?@$7*"+"', $ A&2/&'<1$1,=:&+1$5,/'0$?@@$ 7*"+"', $

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SLIDE 31

Photon Mapping

  • ! 9""$;1#$7*"+"',$<&5,1$.>544($

41,5>+,$

  • ! C/:7>1$&D14&0/'0$74"25<1,$&$."E$

F>+14/'0$";$7*"+"',$

  • ! )*"+"',$'1&414$+"$+*1$,&:7>1$

,*"5>2$.1$#1/0*+12$:"41$*1&D/>($

  • ! A1,5>+,$/'$&$<"'1$F>+14/'0$";$

7*"+"',$

slide-32
SLIDE 32

Photon Mapping

%5>=7>1$)*"+"'$%&7,$

  • ! G>".&>$6HCIJKLJ$7*"+"'$:&7$

–! )*"+"'$,=<3,$+"$2/M5,1$,54;&<1$ #"$$."5'<1,$+"$'1E+$,54;&<1$H/;$ /+$,54D/D1,$A5,,/&'$4"5>1N1K$ –! )*"+"',$2"'O+$,=<3$+"$,71<5>&4$ ,54;&<1,$

  • ! P&5,=<$6CCLJ$7*"+"'$:&7$

–! !/0*$41,">5="'$ –! 6/0*+$,"54<1$5,5&>>($1:/+,$ 7*"+"',$"'>($/'$2/41<="',$+*&+$ */+$+*1$+*/'0$<41&='0$+*1$<&5,=<$

,$

&<1$

Caustic map photons Global map photons

slide-33
SLIDE 33

Photon Mapping

A1'214/'0$

  • ! A1'21412$.($0>",,(Q,54;&<1$

2/,+4/.5+12$4&($+4&</'0$

  • ! R*1'$4&($*/+,$F4,+$2/M5,1$

,54;&<1S$

–! P":75+1$2/41<+$/>>5:/'&="'$ –! P":75+1$41T1<+12$4&2/&'<1$ ";$<&5,=<$:&7$7*"+"',$ –! U0'"41$0>".&>$:&7$7*"+"',$ –! U:7"4+&'<1$,&:7>1$VAJB$%!$ &,$5,5&>& –! W,1$0>".&>$7*"+"'$:&7$+"$ /:7"4+&'<1$,&:7>1$/'</21'+$ 4&2/&'<1$;5'<="'$'(& –! XD&>5&+1$41T1<+&'<1$/'+104&>$ .($<&,='0$4&(,$&'2$ &<<5:5>&='0$4&2/&'<1,$;4":$ 0>".&>$7*"+"'$:&7$

B/4,+$2/M5,1$/'+14,1<="'8$ A1+54'$4&2/&'<1$";$<&5,=<$ :&7$7*"+"',$*141Y$.5+$ /0'"41$0>".&>$:&7$7*"+"', $ W,1$0>".&> $ :&7 $ 7*"+"',$+" $ 41+54' $ 4&2/&'<1 $ #*1' $ 1D&>5&='0 $ 6/$&+$F4,+ $ 2/M5,1 $ /'+14,1<="' 8 $

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SLIDE 34

Photon Mapping

J/41<+$U>>5:/'&="'$

www.bennolan.com

G>".&>$)*"+"'$%&7$

www.bennolan.com

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SLIDE 35

Photon Mapping

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SLIDE 36

Photon Mapping

Realistic Image Synthesis Using Photon Mapping Realistic Image Synthesis Using Photon Mapping

Realistic Image Synthesis Using Photon Mapping

Realistic Image Synthesis Using Photon Mapping

Foreword by Pat Hanrahan

Realistic Image Synthesis Using Photon Mapping

Henrik Wann Jensen Jensen

Foreword by Pat Hanrahan

The creation of realistic three-dimensional images is central to

computer graphics. Photon mapping, an extension of ray tracing, makes it possible to efficiently simulate global illumination in complex scenes. Photo mapping can simulate caustics (focused light, such as shimmering waves at the bottom of a swimming pool), diffuse inter-reflections (e.g., the `bleeding' of colored light from a red wall onto a white floor, giving the floor a reddish tint), and participating media (e.g., clouds or smoke). This book is a practical guide to photon mapping; it provides both the theory and the practical insight necessary to implement photon mapping and simulate all types of direct and indirect illumination efficiently. A K PETERS LTD.

A K PETERS

Henrik Wann Jensen