Illumination Models and Surface Rendering Methods

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Illmato Illmato Models ad Srface Rederg Methods L dffse reflecto φ R V P lght sorces basc model ambet lght dffse shadg speclar hghlghts shadg terpolato Gorad Shadg Phog Shadg Werer Prgathofer /

1 Illmato Illmato Models ad Srface Rederg Methods L dffse reflecto φ R V P lght sorces basc model ambet lght dffse shadg speclar hghlghts shadg terpolato Gorad Shadg Phog Shadg Werer Prgathofer / Comptergraph Lght Sorces drectoal lght pot lght sorce (sometmes drectoal) dstrbted lght sorce ( area lght sorce ) Srface Lghtg Effects dffse reflecto reflectos from other srfaces speclar reflecto trasparecy Werer Prgathofer / Comptergraph Werer Prgathofer / Comptergraph 3 Basc Illmato Models Ambet Lght Reflecto emprcal models lghtg calclatos srface propertes (glossy, matte, opaqe, ) bacgrod lghtg codtos lght-sorce specfcato reflecto, absorpto ambet lght (bacgrod lght) I a appromato of global dffse lghtg effects costat over a srface depedet of vewg drecto dffse-reflecto coeffcet d (0 d ) I I ambdff d a Werer Prgathofer / Comptergraph 4 Werer Prgathofer / Comptergraph 5

Illmato ad Shadg Lambert's Law shaded srfaces geerate a spatal mpresso l the flatter lght falls o a srface,

cos whe cosderg the materal: I d I l cos Werer Prgathofer / Comptergraph 6 Werer Prgathofer / Comptergraph 7

Dffse Reflecto Coeffcet varyg d reslt for varyg vales of d, I a 0 Lambert s cose law L cos L I l,dff d I l

Dffse Reflecto total dffse reflecto I I I ( L) l,dff a a d l Ambet pls Dffse Reflecto total dffse reflecto I

2 Illmato ad Shadg Lambert's Law shaded srfaces geerate a spatal mpresso l the flatter lght falls o a srface, the darer t wll appear l therefore: we eed the cdet lght drecto or the posto of the (pot) lght sorce I I l cos whe cosderg the materal: I d I l cos Werer Prgathofer / Comptergraph 6 Werer Prgathofer / Comptergraph 7 Lamberta (Dffse) Reflecto deal dffse reflectors (Lamberta reflectors) brghtess depeds o oretato of srface Dffse Reflecto Coeffcet varyg d reslt for varyg vales of d, I a 0 Lambert s cose law L cos L I l,dff d I l (L ) L cos L Werer Prgathofer / Comptergraph 8 Werer Prgathofer / Comptergraph 9 Ambet pls Dffse Reflecto total dffse reflecto I I I ( L) l,dff a a d l Ambet pls Dffse Reflecto total dffse reflecto I I I ( L) l,dff a a d l (sometmes a for ambet lght) Werer Prgathofer / Comptergraph 0 Werer Prgathofer / Comptergraph

Speclar Hghlghts ths area mst be lghter tha the shadg model calclates, becase the lght sorce s reflected drectly to the vewer's eye Speclar Reflecto Model reflecto of cdet lght arod speclarreflecto

Phog model s large shy srface s small dll srface I l,spec s I l cos s φ cos 64 φ L R L R cos 56 φ Werer Prgathofer / Comptergraph 4 shy srface (large s ) Werer Prgathofer / Comptergraph 5 dll srface

3 Speclar Hghlghts ths area mst be lghter tha the shadg model calclates, becase the lght sorce s reflected drectly to the vewer's eye Speclar Reflecto Model reflecto of cdet lght arod speclarreflecto agle L R φ V emprcal Phog model I l,spec s I l cos s φ Werer Prgathofer / Comptergraph Werer Prgathofer / Comptergraph 3 Speclar Reflecto Coeffcet s cos s φ cos φ Speclar Reflecto Coeffcet emprcal Phog model s large shy srface s small dll srface I l,spec s I l cos s φ cos 64 φ L R L R cos 56 φ Werer Prgathofer / Comptergraph 4 shy srface (large s ) Werer Prgathofer / Comptergraph 5 dll srface (small s ) Fresel Speclar Reflecto Coeffcet Fresel s laws of reflecto speclar reflecto coeffcet W() I W( ) Werer Prgathofer / Comptergraph 6 l,spec I l cos s speclar reflecto coeffcet as a fcto of agle of cdece for dfferet materals φ Smple Speclar Reflecto W() costat for may opaqe materals ( s ) L L R R φ L V L calclato of R: I s l,spec si l ( V R) R L ( L) R ( L) L Werer Prgathofer / Comptergraph 7 3

Speclar Reflecto Reslts I I ( V R) l,spec s l s Smplfed Speclar Reflecto smplfed Phog model wth halfway vector H

Prgathofer / Comptergraph 9 Dffse ad Speclar Reflecto I I a a l I l s [ ( L ) ( H ) ] d ambet ambet dffse l s l

law) atmospherc effects shadows Werer Prgathofer / Comptergraph 0 Werer Prgathofer / Comptergraph Polygo-Rederg

Gorad Polygo Shadg: Iterpolato the shadg of a polygo s ot costat, becase t ormally s oly a appromato of the real

4 Speclar Reflecto Reslts I I ( V R) l,spec s l s Smplfed Speclar Reflecto smplfed Phog model wth halfway vector H I I ( V R) s s I I ( H ) spec s l spec s l L H α φ R V H L V L V Werer Prgathofer / Comptergraph 8 Werer Prgathofer / Comptergraph 9 Dffse ad Speclar Reflecto I I a a l I l s [ ( L ) ( H ) ] d ambet ambet dffse l s l ambet dffse speclar Other Aspects testy atteato wth dstace asotropc lght sorces (War model) trasparecy (Sell s law) atmospherc effects shadows Werer Prgathofer / Comptergraph 0 Werer Prgathofer / Comptergraph Polygo-Rederg Methods applcato of llmato model to polygo rederg costat-testy shadg (flat shadg) sgle testy for each polygo flat Gorad Polygo Shadg: Iterpolato the shadg of a polygo s ot costat, becase t ormally s oly a appromato of the real srface terpolato Gorad shadg: testes Phog shadg: ormal vectors Werer Prgathofer / Comptergraph Werer Prgathofer / Comptergraph 3 4

Gorad Shadg Overvew testy-terpolato determe average t ormal vector at each polygo verte apply llmato model to each verte learly terpolate verte testes 4 V V 3 V Gorad

testes alog scales learly: I p I I 3 Werer Prgathofer / Comptergraph 4 Werer Prgathofer / Comptergraph 5 Gorad Shadg terpolatg testes 3 Gorad Shadg cremetal pdate y y

Prgathofer / Comptergraph 7 Problems of Gorad Shadg hghlghts ca get lost or grow dar lght dar dar dar dar corers o slhoette rema Gorad Shadg Reslts o testy dscottes

5 Gorad Shadg Overvew testy-terpolato determe average t ormal vector at each polygo verte apply llmato model to each verte learly terpolate verte testes 4 V V 3 V Gorad Shadg I v I ( v) I ' It I (-t) I I' I (-) I 3 fd ormal vectors at corers ad calclate shadg (testes) there: I terpolate testes alog the edges learly: I, I 3 terpolate testes alog scales learly: I p I I 3 Werer Prgathofer / Comptergraph 4 Werer Prgathofer / Comptergraph 5 Gorad Shadg terpolatg testes 3 Gorad Shadg cremetal pdate y y y y p p 4 4 I I y y y I I p 4 I5 y I sca le 4 p 5 I y y- y y y y I I I y y y y I I I sca les I I I I y y Werer Prgathofer / Comptergraph 6 Werer Prgathofer / Comptergraph 7 Problems of Gorad Shadg hghlghts ca get lost or grow dar lght dar dar dar dar corers o slhoette rema Gorad Shadg Reslts o testy dscottes Mach bads de to lear testy terpolato problems wth hghlghts flat Gorad Mach bad effect s vsble at some edges Werer Prgathofer / Comptergraph 8 Werer Prgathofer / Comptergraph 9 5

Phog Shadg stead of testes the ormal vectors are terpolated, ad for every pot the shadg calclato s performed separately dar lght dar Phog Shadg Prcple ormal-vector terpolato determe average t ormal

6 Phog Shadg stead of testes the ormal vectors are terpolated, ad for every pot the shadg calclato s performed separately dar lght dar Phog Shadg Prcple ormal-vector terpolato determe average t ormal vector at each polygo verte learly terpolate verte ormals apply llmato model alog each sca le Werer Prgathofer / Comptergraph 30 Werer Prgathofer / Comptergraph 3 Phog Shadg Overvew Phog Shadg ormal Vectors ormal-vector terpolato P ormal vectors at corer pots terpolate ormal vectors alog the edges 3 terpolate ormal vectors alog scales & calclate shadg (testes) for every pel y sca le y y y y y y y y Werer Prgathofer / Comptergraph 3 Werer Prgathofer / Comptergraph 33 Phog Shadg cremetal ormal vector pdate alog ad betwee sca les comparso to Gorad shadg better hghlghts less Mach badg more costly Flat/Gorad/Phog Comparso Werer Prgathofer / Comptergraph 34 Werer Prgathofer / Comptergraph 35 Pal Hecbert 6

Srface-Rederg Methods polygo rederg methods ray-tracg radosty evromet mappg tetre mappg bmp mappg Ray-Tracg Cocepts L lght sorce shadg α α Werer Prgathofer / Comptergraph 36 L Werer Prgathofer /

7 Srface-Rederg Methods polygo rederg methods ray-tracg radosty evromet mappg tetre mappg bmp mappg Ray-Tracg Cocepts L lght sorce shadg α α Werer Prgathofer / Comptergraph 36 L Werer Prgathofer / Comptergraph 37 vsblty calclato d lght sorce Ray-Tracg Cocepts Ray-Tracg Cocepts shadg of the reflected obect L shadows reflecto for perspectve proecto: eye pot shadows shadg reflecto trasparecy L Werer Prgathofer / Comptergraph 39 trasparecy vsblty calclato Werer Prgathofer / Comptergraph 38 Ray-Tracg Propertes hghly realstc mages very tme cosmg global reflecto, trasmsso vsble-srface detecto shadows trasparecy mltple lght sorces Ray-Tracg prcples of geometrc optcs proecto referece pot z ray-tracg coordate referece frame y Werer Prgathofer / Comptergraph 40 prmary ray eyepot s (pel eyepot) WBarth Werer Prgathofer / Comptergraph 4 7

8 Shadg: Dffse Shadg I d I d llmato cased by dffse shadg ay shadg model (Phog, Bl, Coo/Torrace, ) Ray-Tracg: Shadows ray tersecto pot s vector to lght sorce P ray P s (L P) P tersecto pot L lght sorce posto L a lght sorce fleces the reslt oly f there s o tersecto wth 0 < s < Werer Prgathofer / Comptergraph 4 Werer Prgathofer / Comptergraph 43 Ray-Tracg: Shadows ad Shadg shadow ray alog L I d d I a d ( L) ambet lght a I a s (H ) s dffse reflecto d ( L) speclar reflecto s (H ) s t vectors at a obect srface tersected by a comg ray from drecto V R L H V Ray-Tracg: Reflecto I r r X r I r llmato cased by reflecto r reflecto coeffcet of the materal X r shadg the reflected drecto α β X r α β Werer Prgathofer / Comptergraph 44 Werer Prgathofer / Comptergraph 45 Ray-Tracg: Reflecto Ray calclato of reflecto ray R V ( V) R R ( V) V V R V f V R ( ) [boo]: Ray-Tracg: Trasparecy I t t X t I t llmato cased by trasparecy t trasparecy coeffcet of the materal X t shadg the trasparecy drecto r r X t s :s r η r :η Werer Prgathofer / Comptergraph 46 Werer Prgathofer / Comptergraph 47 8

$Comptergraph 48 Werer Prgathofer / Comptergraph 49 Ray-Tracg: Rays & Ray Tree prmary, secodary rays R 3 T T P R R reflecto ad refracto ray paths for oe pel Werer Prgathofer / Comptergraph 50 R 3 R T$ P R T correspodg bary ray-tracg tree Ray-Tracg: Basc Algorthm FOR all pels P 0 DO trace prmary ray eye -> P 0 fd closest tersecto P FOR all lght sorces L DO trace shadow feeler P -> L IF o ters

P R T correspodg bary ray-tracg tree Ray-Tracg: Basc Algorthm FOR all pels P 0 DO trace prmary ray eye -> P 0 fd closest tersecto P FOR all lght sorces L DO trace shadow feeler P -> L IF o ters

9 Ray-Tracg: Trasparecy Ray Ray-Tracg: A Complete Shadg Method calclato of trasparecy ray η s r s η r T r V I I d I r I t addtoal reqremet: d r t η η T V (cos r cos ) η η r r Werer Prgathofer / Comptergraph 48 Werer Prgathofer / Comptergraph 49 Ray-Tracg: Rays & Ray Tree prmary, secodary rays R 3 T T P R R reflecto ad refracto ray paths for oe pel Werer Prgathofer / Comptergraph 50 R 3 R T P R T correspodg bary ray-tracg tree Ray-Tracg: Basc Algorthm FOR all pels P 0 DO trace prmary ray eye -> P 0 fd closest tersecto P FOR all lght sorces L DO trace shadow feeler P -> L IF o ters betwee P, L THE shadgflece of L 3IF srface of P s reflectve THE trace secodary ray; shadgflece of refl 4IF srface of P s trasparet THE trace secodary ray; shadgflece of trasp Werer Prgathofer / Comptergraph 5 Ray-Tracg Eamples Ray-Tracg Eamples Werer Prgathofer / Comptergraph 5 Werer Prgathofer / Comptergraph 53 9

Tre Global Illmato Eample Reqremets for Obect Data (to se them for ray-tracg) tersecto

Werer Prgathofer / Comptergraph 54 Werer Prgathofer / Comptergraph 55 Ray-Srface Itersecto

/ Comptergraph 56 z y P 0 descrbg a ray wth a tal-posto vector P 0 ad t drecto vector

s) c Pc r 0 Δ P P c P 0 z s ( ΔP) s ( ΔP r ) s ΔP ± ΔP) ΔP ( r Werer Prgathofer /

± Δ Δ becase P P (to avod rodoff errors whe r << ΔP ) r sphereflae ( P) Ray-Polyhedro

10 Tre Global Illmato Eample Reqremets for Obect Data (to se them for ray-tracg) tersecto calclato ray - obect possble srface ormal calclato possble B-Rep: smple CSG: recrsve evalato Werer Prgathofer / Comptergraph 54 Werer Prgathofer / Comptergraph 55 Ray-Srface Itersecto ray eqato P P s 0 for prmary rays P p P P P p for secodary rays R T prp prp Werer Prgathofer / Comptergraph 56 z y P 0 descrbg a ray wth a tal-posto vector P 0 ad t drecto vector Ray-Sphere Itersecto parametrc ray eqato serted to sphere eqato y P P P r c 0 P r 0 P ( P 0 s) c Pc r 0 Δ P P c P 0 z s ( ΔP) s ( ΔP r ) s ΔP ± ΔP) ΔP ( r Werer Prgathofer / Comptergraph 57 0 (² ) Ray-Sphere Itersecto dscrmat egatve o tersectos s ΔP ± ΔP) ΔP s ( r Δ ± Δ Δ becase P P (to avod rodoff errors whe r << ΔP ) r sphereflae ( P) Ray-Polyhedro Itersecto se bodg sphere to elmate easy cases P 0 Werer Prgathofer / Comptergraph 58 Werer Prgathofer / Comptergraph 59 0

Ray-Polyhedro Itersecto se bodg sphere to elmate easy cases locate frot faces solvg plae eqato A By Cz D 0 (A, B, C) P D (P 0 s) D D P0 s P 0 < 0 P P Ray-Polyhedro Itersecto tersecto pot sde polygo

11 Ray-Polyhedro Itersecto se bodg sphere to elmate easy cases locate frot faces solvg plae eqato A By Cz D 0 (A, B, C) P D (P 0 s) D D P0 s P 0 < 0 P P Ray-Polyhedro Itersecto tersecto pot sde polygo bodares? sde-otsde test smallest s to sde pot s frst tersecto otsde? pot of polyhedro P 0 P 0 polygo plae? sde? Werer Prgathofer / Comptergraph 60 Werer Prgathofer / Comptergraph 6 Ray-Srface Itersecto qadrc, sple srfaces: parametrc ray eqato serted to srface defto methods le mercal root-fdg, cremetal calclatos ray-traced scee wth URBS srfaces ad mltple reflecto / refracto Werer Prgathofer / Comptergraph 6 Redcg Obect-Itersecto Calclatos bodg volmes bodg volme herarches 3 rd herarchy bodg spheres Werer Prgathofer / Comptergraph 63 bodg sphere d herarchy bodg spheres Redcg Obect-Itersecto Calclatos space-sbdvso methods reglar grd octree Redcg Obect-Itersecto Calclatos space-sbdvso methods reglar grd octree P 0 P 0 Werer Prgathofer / Comptergraph 64 Werer Prgathofer / Comptergraph 65

12 Redcg Obect-Itersecto Calclatos space-sbdvso methods cremetal grd traversal 3D Breseham processg of potetal et faces Icremetal Grd Traversal ray drecto / ray etry posto P potetal et faces > 0 ormal vectors 3 P 0 P 3 P ot ray traversal throgh a sbrego of a cbe eclosg a scee ( ±,0,0) (0, ±,0) (0,0, ± ) chec sgs of compoets of P 0 P P ot Werer Prgathofer / Comptergraph 66 Werer Prgathofer / Comptergraph 67 Icremetal Grd Traversal calclato of et postos, select smallest s P P s ot, s Pot, D eample: (,0,0) Werer Prgathofer / Comptergraph 68 D P s P 0 0 P 3 P ot Icremetal Grd Traversal varato: tral et plae perpedclar to largest compoet of et pot 0 > doe {,, 3, 4} 6 > sde clear {5, 6, 7, 8} > etra calc P sectors of the tral et plae Werer Prgathofer / Comptergraph Srface-Rederg Methods polygo rederg methods ray-tracg radosty evromet mappg tetre mappg bmp mappg Radosty Method descrbes the physcal process of lght dstrbto a dffse reflectg evromet areas that are ot llmated drectly are also ot completely dar every obect acts as a secodary lght sorce Werer Prgathofer / Comptergraph 70 Werer Prgathofer / Comptergraph 7

13 Radosty Radosty B s the radat fl per t area that s leavg a srface Werer Prgathofer / Comptergraph 7 Radosty Eqato comg lght from the evromet radosty of the pot Werer Prgathofer / Comptergraph 73 self emsso (oly for lght sorces) reflected lght from evromet BE I() d db hem hem db db hem hem E Radosty Eqato Radosty Propertes to calclate the lght flece betwee srfaces Radosty total lght leavg a srface pot B E d B hem B radosty hem half space over pot E self emsso reflecto coeffcet dffse terreflectos a scee radat eergy trasfers z coservato of eergy, closed evromets sbdvso of scee to patches wth φ costat radosty B dω ds db Werer Prgathofer / Comptergraph 74 Werer Prgathofer / Comptergraph 75 y Radosty: Sbdvso to Patches the scee s dscretzed to "patches" (plae polygos) P, for each of these patches a costat radosty B s assmed: BE d B hem B E Σ B dffse reflecto coeffcet of patch F formfactor : descrbes how mch % of the flece o patch comes from patch ; geometrc sze F Radosty Model B radosty of patch E self-emsso of patch ΣB F cotrbto of other patches F form factor, defes cotrbto of B o patch whch s eqal to cotrbto of patch to B reflectvty coeffcet of patch ( albedo ) B E Σ B F Werer Prgathofer / Comptergraph 76 Werer Prgathofer / Comptergraph 77 3

14 Radosty Eqato solvg the radosty eqato F F B E BF B BF E F F F F B E B E B E Radosty Eqato: Form Factors srface propertes F F form factors (costats) F F radostes (ows) F F srface propertes B E B E B E Werer Prgathofer / Comptergraph 78 Werer Prgathofer / Comptergraph 79 Proecto of a Polygo Radosty: Form Factors a A form factor F : cotrbto of patch P to B cotrbto of B to patch P P a cos A cos eergy reachg patch from patch total eergy leavg patch P Werer Prgathofer / Comptergraph 80 Werer Prgathofer / Comptergraph 8 Radosty: Form Factors Radosty: Form Factors form factor F : cotrbto of patch P to B cotrbto of B to patch P cosφ cosφ A F P A πr φ r φ becase P A ' F P P Werer Prgathofer / Comptergraph 8 F form factor F : cotrbto of patch P to B cotrbto of B to patch P cosφ cosφ F πr more precsely: form factor s sm over cotrbtos from P averaged over area A A cosφ F A A πr Werer Prgathofer / Comptergraph 83 cosφ da da A 4

15 5 Werer Prgathofer / Comptergraph 84 Radosty: Form Factors form factor propertes coservato of eergy form lght reflecto o self-cdece F 0 F A F A F Werer Prgathofer / Comptergraph 85 Radosty: Form Factors form factor calclato most epesve step radosty calclato mercal tegrato (Mote Carlo methods) hemcbe approach (replaces hemsphere) P P P P Werer Prgathofer / Comptergraph 86 Radosty Eqato solvg the radosty eqato Gassa elmato Gass-Sedel terato very tme ad storage tesve E E E B B B F F F F F F Werer Prgathofer / Comptergraph 87 Radosty Eqato solvg the radosty eqato Gass-Sedel terato gatherg P B B F E B Werer Prgathofer / Comptergraph 88 Radosty Eqato gatherg vs shootg B F E B P B P B Werer Prgathofer / Comptergraph 89 shootg select brghtest patch ad dstrbte ts radosty B BF E B BF B to B de BF B de to B B A A F B to B de F A F A Progressve Refemet Radosty ()

Progressve Refemet Radosty () [oe refemet step] select patch wth hghest A *ΔB for selected patch { set

0 Werer Prgathofer / Comptergraph 90 Progressve Refemet Radosty (3) tally ΔB B E, select patch wth

methods Werer Prgathofer / Comptergraph 9 Radosty Eample Images () Radosty Eample Images () mage of a

wth progressve refemet radosty Werer Prgathofer / Comptergraph 9 Werer Prgathofer / Comptergraph 93

Prgathofer / Comptergraph 94 Radosty Aspects () radosty s vewpot-depedet eeds a rederg step to dsplay

16 Progressve Refemet Radosty () [oe refemet step] select patch wth hghest A *ΔB for selected patch { set p hemcbe calclate form factors F } for each patch { Δrad : *ΔB *F *A /A ΔB : ΔB Δrad B : B Δrad } ΔB : 0 Werer Prgathofer / Comptergraph 90 Progressve Refemet Radosty (3) tally ΔB B E, select patch wth hghest ΔB A cathedral redered wth progressve refemet radosty form factors compted wth ray-tracg methods Werer Prgathofer / Comptergraph 9 Radosty Eample Images () Radosty Eample Images () mage of a costrctvst msem redered wth progressve refemet radosty star tower of a bldg at Corell Uversty redered wth progressve refemet radosty Werer Prgathofer / Comptergraph 9 Werer Prgathofer / Comptergraph 93 Radosty Eample Images (3) lghtg schemes for a opera prodcto: (left) day vew (rght) ght vew Werer Prgathofer / Comptergraph 94 Radosty Aspects () radosty s vewpot-depedet eeds a rederg step to dsplay polygo rederg Gorad shadg ray-tracg combato wth ray-tracg eables reflectos shadows Werer Prgathofer / Comptergraph 95 6

Radosty Aspects () herarchcal radosty to

methods to calclate form factors to solve

terpolato Radosty Reslts Werer Prgathofer

Sphercal Evromet Map leghmachcom Evromet

17 Radosty Aspects () herarchcal radosty to redce mber of form factors stochastc methods to calclate form factors to solve radosty eqato system path tracg trace lght rays (forward tracg!) store effect of lght httg a patch terpolato Radosty Reslts Werer Prgathofer / Comptergraph 96 Werer Prgathofer / Comptergraph 97 Radosty Reslts Srface-Rederg Methods polygo rederg methods ray-tracg radosty evromet mappg tetre mappg bmp mappg Werer Prgathofer / Comptergraph 98 Werer Prgathofer / Comptergraph 99 Evromet Mappg Prcple reflecto mappg defed over srface of a eclosg verse (sphere, cbe, cylder) Sphercal Evromet Map leghmachcom Evromet Mappg Eample Bl, CACM 76 Obects Scee Werer Prgathofer / Comptergraph 00 Werer Prgathofer / Comptergraph 0 Haeberl/Segal 7

Evromet Mappg Calclato formato the evromet map testy vales

srface reflected oto evromet map Evromet Mappg Eample Werer

03 Evromet Mappg Flterg evromet maps may be fltered for ot so

Comptergraph 04 Werer Prgathofer / Comptergraph 05 Addg

gravel roads shag carpets DMolyea srface tetre reqred Addg

facets (eg, checerboard sqares) facets overlad o srface

sed for llmato calclatos mpractcal for complcated srface

18 Evromet Mappg Calclato formato the evromet map testy vales for lght sorces sy bacgrod obects pel area proected oto srface reflected oto evromet map Evromet Mappg Eample Werer Prgathofer / Comptergraph 0 Werer Prgathofer / Comptergraph 03 Evromet Mappg Flterg evromet maps may be fltered for ot so reflectve srfaces Evromet Mappg Eample Werer Prgathofer / Comptergraph 04 Werer Prgathofer / Comptergraph 05 Addg Srface Detal most obects do ot have smooth srfaces brc walls gravel roads shag carpets DMolyea srface tetre reqred Addg Srface Detal modelg srface detal wth polygos small polygo facets (eg, checerboard sqares) facets overlad o srface polygo (paret) paret srface sed for vsblty calclatos facets sed for llmato calclatos mpractcal for complcated srface strctre Artfcal Stdos Werer Prgathofer / Comptergraph 06 Staford Werer Prgathofer / Comptergraph 07 8

Tetre Mappg: Prcple tetre patters mapped oto srfaces tetre patter: raster mage or procedre (modfes srface

Space: (,v) Srface Parameters Vewg & Proecto Trasformato Image Space: (,y) Pel Coordates Tetre Mappg: Samples

Trasformato tetre mappg tetre scag (s,t) (,y) verse scag (,y) (s,t) Tetre Mappg (dt) Tetre Space: (s,t) Array

Prgathofer / Comptergraph 0 Obect Space: (,v) Srface Parameters v Vewg & Proecto Trasformato M VP v v Image

Obet-Ram: (,v) Fläche- Parameter Bld-Ram: (,y) Pel Koordate Vewg & Proetos- Trasformato Tetre Mappg: Iverse

Werer Prgathofer / Comptergraph M - M - T Tetre-Mappg: Cyldrcal Srface M VP, wth 0 π/ v z wth 0 z h r cos, y r

19 Tetre Mappg: Prcple tetre patters mapped oto srfaces tetre patter: raster mage or procedre (modfes srface testes) Tetre Space: (s,t) Array Coordates Tetre-Srface Trasformato Werer Prgathofer / Comptergraph 08 Obect Space: (,v) Srface Parameters Vewg & Proecto Trasformato Image Space: (,y) Pel Coordates Tetre Mappg: Samples marble leather tetle fr wood water drops Werer Prgathofer / Comptergraph 09 cobblestoes sad grass Tetre Mappg: Trasformato tetre mappg tetre scag (s,t) (,y) verse scag (,y) (s,t) Tetre Mappg (dt) Tetre Space: (s,t) Array Coordates Tetre-Srface Trasformato M T tetre-srface trasformato ( s, t) as b t c v v ( s, t) a s b t c Werer Prgathofer / Comptergraph 0 Obect Space: (,v) Srface Parameters v Vewg & Proecto Trasformato M VP v v Image Space: (,y) Pel Coordates Tetr-Ram: (s,t) Array Koordate Tetr-Obet Trasformato Werer Prgathofer / Comptergraph Obet-Ram: (,v) Fläche- Parameter Bld-Ram: (,y) Pel Koordate Vewg & Proetos- Trasformato Tetre Mappg: Iverse Trasformato proectg pel areas to tetre space verse scag (,y) (s,t) calclato of VP at-alasg wth flter operatos Werer Prgathofer / Comptergraph M - M - T Tetre-Mappg: Cyldrcal Srface M VP, wth 0 π/ v z wth 0 z h r cos, y r s, z v M - VP Werer Prgathofer / Comptergraph 3 ²y²r²,,y 0, 0 z h h pel srface pot (,y,z) (,y,z) (,v): cos - (/r), v z z r (,v) y 9

Tetre-Mappg: Cyldrcal Srface M T M - T 0 0 t s π/, v t h s s /π, t

proect pel area to tetre space ad tae average tetre vale speed ps:

Prgathofer / Comptergraph 4 Werer Prgathofer / Comptergraph 5 Sold

across corers Sold Tetrg Eamples eamples for applcato of 3D tetres

Prgathofer / Comptergraph 7 UvSwasea Procedral Tetrg procedral

or 3D (sold tetrg) stochastc varatos (ose fcto) eamples wood gras

Wavefrot Bmp Mappg Prcple bmps are vsble becase of shadg modelg of

20 Tetre-Mappg: Cyldrcal Srface M T M - T 0 0 t s π/, v t h s s /π, t v/h h z r (,v) y Tetre Mappg: At-alasg at-alasg wth flter operatos proect pel area to tetre space ad tae average tetre vale speed ps: mp-mappg smmed-area table method bacproected pel tetre space Werer Prgathofer / Comptergraph 4 Werer Prgathofer / Comptergraph 5 Sold Tetrg tetre defed 3D every posto space has a color coheret tetres across corers Sold Tetrg Eamples eamples for applcato of 3D tetres o a scll ad a face UvSwasea Werer Prgathofer / Comptergraph 6 Werer Prgathofer / Comptergraph 7 UvSwasea Procedral Tetrg procedral tetre defto tetre-fcto (,y,z) retrs testy avod M T D (srface tetrg) or 3D (sold tetrg) stochastc varatos (ose fcto) eamples wood gras marble foam Werer Prgathofer / Comptergraph 8 Copyrght Alas Wavefrot Bmp Mappg Prcple bmps are vsble becase of shadg modelg of bmps s very costly trc: sert a detal strctre T: v T Werer Prgathofer / Comptergraph 9 0

Bmp Mappg Eamples Bmp Mappg Calclato srface roghess smlated

v) srface pot Perl, SIGGRAPH85 Bl, SIGGRAPH78 Bl, SIGGRAPH78

Comptergraph 0 Staford P (, v) P(, v) b(, v) modfed srface

v) P(, v) b(, v) P P v P ( P b) P b b P P b, P P b, v v P P b

/ Comptergraph v v( v Alas Wavefrot Bmp Mappg Represetato bmp

dffereces Werer Prgathofer / Comptergraph Alas Wavefrot3 Bmp

Bmp Mappg: Grazg Agles red bttos appear too flat, althogh

21 Bmp Mappg Eamples Bmp Mappg Calclato srface roghess smlated pertrbato fcto vares srface ormal locally bmp map b(,v) P (, v) srface pot Perl, SIGGRAPH85 Bl, SIGGRAPH78 Bl, SIGGRAPH78 Bl, SIGGRAPH78 P P v / srface ormal Werer Prgathofer / Comptergraph 0 Staford P (, v) P(, v) b(, v) modfed srface pot Werer Prgathofer / Comptergraph Bmp Mappg Calclato P (, v) P(, v) b(, v) P P v P ( P b) P b b P P b, P P b, v v P P b ( P ) b ( P ) v v v bbv ( ) 0 b P ) b ( P ) Werer Prgathofer / Comptergraph v v( v Alas Wavefrot Bmp Mappg Represetato bmp map b(,v) defed as raster mage b, b v : appromated wth fte dffereces Werer Prgathofer / Comptergraph Alas Wavefrot3 Bmp Mappg Problems sorces of error dstortos at grazg agles wrog slhoette (geometry s ot chaged!) wrog shadows mssg shadows of bmps lght effects o bac sde Bmp Mappg: Grazg Agles red bttos appear too flat, althogh they are shaded 3D Werer Prgathofer / Comptergraph Copyrght Alas Wavefrot 4 Werer Prgathofer / Comptergraph 5

Bmp Mappg Problems sorces of error dstortos at grazg agles wrog slhoette (geometry s ot chaged!

Lfeg Wag Werer Prgathofer / Comptergraph Copyrght Alas Wavefrot 6 Werer Prgathofer / Comptergraph Copyrght Alas Wavefrot 7

Lfeg Wag Werer Prgathofer / Comptergraph Copyrght Alas Wavefrot 8 Werer Prgathofer / Comptergraph Copyrght Alas Wavefrot 9

22 Bmp Mappg Problems sorces of error dstortos at grazg agles wrog slhoette (geometry s ot chaged!) wrog shadows mssg shadows of bmps lght effects o bac sde Bmp Mappg: Wrog Slhoette bmp mappg correct geometry Lfeg Wag Lfeg Wag Werer Prgathofer / Comptergraph Copyrght Alas Wavefrot 6 Werer Prgathofer / Comptergraph Copyrght Alas Wavefrot 7 Bmp Mappg Problems sorces of error dstortos at grazg agles wrog slhoette (geometry s ot chaged!) wrog shadows mssg shadows of bmps lght effects o bac sde Bmp Mappg: Mssg Bmp Shadows bmp mappg correct shadows Lfeg Wag Lfeg Wag Werer Prgathofer / Comptergraph Copyrght Alas Wavefrot 8 Werer Prgathofer / Comptergraph Copyrght Alas Wavefrot 9 Bmp Mappg Problems Bmp Mappg: Bac Sde Lght Effects sorces of error dstortos at grazg agles wrog slhoette (geometry s ot chaged!) wrog shadows mssg shadows of bmps lght effects o bac sde Werer Prgathofer / Comptergraph Copyrght Alas Wavefrot 30 Werer Prgathofer / Comptergraph Copyrght Alas Wavefrot 3

) wrog shadows mssg shadows of bmps lght effects o bac sde specal

srface pots are moved from ther orgal posto otle of obect chages mch

spports t Werer Prgathofer / Comptergraph Copyrght Alas Wavefrot 3 Werer

appled to a srface eamples: tetre drt tetre lght map tetre bmp map photo

23 Bmp Mappg Problems sorces of error dstortos at grazg agles wrog slhoette (geometry s ot chaged!) wrog shadows mssg shadows of bmps lght effects o bac sde specal algorthms to repar each error Dsplacemet Mappg correct verso of bmp mappg srface pots are moved from ther orgal posto otle of obect chages mch harder to mplemet tha bmp mappg rare practce latest hardware partally spports t Werer Prgathofer / Comptergraph Copyrght Alas Wavefrot 3 Werer Prgathofer / Comptergraph 33 Mlttetrg: Combato of Mappgs or more tetres appled to a srface eamples: tetre drt tetre lght map tetre bmp map photo aotatos Mlttetrg: Combato of Mappgs bmp mappg & evromet mappg & tetre mappg Werer Prgathofer / Comptergraph 34 Werer Prgathofer / Comptergraph 35 Mare Mza 3

Object Modeling for Multicamera Correspondence Using Fuzzy Region Color Adjacency Graphs

Object Modeling for Multicamera Correspondence Using Fuzzy Region Color Adjacency Graphs Obect Modelg for Mltcamera Correspodece Usg Fzzy Rego Color Adacecy Graphs Amr Hosse Khall 1 ad Shohreh Kasae 2 1 Sharf Uersty of Techology, Tehra, Ira a_khall@ce.sharf.ed 2 Sharf Uersty of Techology,