Key issues of this lecture. Interactive Graphical Systems HT2006. Interactive Graphical Systems: Structure. 3D Graphical Rendering Approaches

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1 Ke issues of his leure Inerive Grphil Ssems H26 Lesson 2 : Grphis Bsis Sefn Seipel he wo-fold world of 3D grphil rendering Illuminion models nd progrmmle shding models he fied funion rendering pipeline Repeiion of si nd useful mh for use in ICG Referene frmes nd rnsformion eween referene frmes Hndling of 3D models he ppliion developer Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi Inerive Grphil Ssems: Sruure 3D Grphil Rendering pprohes Grphil Oupu Glol Rendering Grphil Rendering Drwing Illumined Ojes Lol Rendering Mulimedi Feedk Relime Mulimodl Inpu Simuling ligh propgion in sene ring rs Simuling he shding of ojes ppling lol illuminion models Compuersimulion Illuminion ffeed lol oje properies nd relions eween ojes in sene Illuminion ffeed lol oje properies nd ssumed ligh soures Repliion Rel world Rendering order: From Sreen-spe o World Spe Imge formion proess: Pielwise r-ring Rendering order: Oje wise drwing o Sreen Imge formion proess: Polgonwise Pielision (Rseriion) Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi

2 Glol Rendering Simuling he phsis of ligh propgion Glol Rendering Simuling he phsis of ligh propgion In heor: Sring from ligh soure follow ligh rnspor 2 Idenif inerion wih ojes 3 Clule ligh sorion In heor: Sring from ligh soure follow ligh rnspor 2 Idenif inerion wih ojes 3 Clule ligh sorpion 4 Clule refleed ligh R 5 Clule rnsmied ligh R R R Cener of projeion (COP) Cener of projeion (COP) Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi Glol Rendering Simuling he phsis of ligh propgion Glol Rendering In prie: In heor: Sring from ligh soure follow ligh rnspor 2 Idenif inerion wih ojes 3 Clule ligh sorpion 4 Clule refleed ligh R 5 Clule rnsmied ligh 6 Colle ligh sreen piel R R R R-sing from COP hrough piels ino sene Reursive r-ring wih given reursion deph Ligh ph lulion nd olleion of refleed nd rnsmied ligh per piel dvned iner-oje illuminion effes possile - shdow sing - self-shdowing - oje iner reflene - rnspren nd mospheri effes R-oje inerseion esing ver epensive Cener of projeion (COP) Cener of projeion (COP) Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi

3 Glol rendering emple Glol rendering emple Illusrion of visul effes omplished wih phsill sed rendering mehodes (glol rendering) he Cornell Bo Oserve he refleion of he red nd green wll s olor on he oes sides Illusrion of visul effes omplished wih phsill sed rendering mehodes (glol rendering) he Cornell Bo Oserve he refleion of he red nd green wll s olor on he oes sides Design nd Simulion of Roo Cell Coprigh Sndi Nionl Lirries Oserve he sof shdows due o rel ligh soure Design nd Simulion of Roo Cell Coprigh Sndi Nionl Lirries hp://wwwgrphisornelledu/online/o/ojpg Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi Lol Rendering Lol Rendering Generl pproh: Drw he sene like piner proeed in n oje order when rendering he sene For he urren oje: Idenifiion of visile surfes/fees For eh oje Deermine su-surfes (fes) visile o he oserver 2 Deermine projeion of fe on sreen 3 Rserie fe ino frme uffer Cener of projeion (COP) Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi

4 Lol Rendering Lol Rendering For he urren fe: rnsformion nd projeion upon sreen Rseriion of urren polgon/fe Sn-line onversion of polgon Ie rversl of ll piels overed urren polgon Drwing piels wih some shded olor one sed on some illuminion model Cener of projeion (COP) Cener of projeion (COP) Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi Lol Rendering - Illuminion nd shding When polgons re olored during rseriion, erin illuminion models or shding ehniques re used o deermine he olor of he urren piel Illuminion models re mhemil epressions h pproime rel illuminion of ojes nd refleion of ligh Mos illuminion models re simplified pproimions of phsil orre inerion eween ligh nd mer Oher shding ehniques do no inend o mimi phsil ehvior of ligh ll (onsn shding, roon-rendering) Prolems Lol Rendering = Rendering in Oje Spe Order Corre Olusion nd Visiili is reled o o Sreen Spe ie in Viewing Spe How n we ssure h he mer sees fronmos oje surfe in lol rendering Cener of projeion (COP) Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi

5 Hidden Surfe ehniques Hidden Surfe ehniques Deph Sor / Piners lgorihm -Buffer Sors ojes wih deresing -disne o he sreen Render sene from k o fron Prolems, if ojes overlp in heir eens long nd in he -, nd -plne (piering) Ojes re rendered wihou speifi order Deph es is performed in he rseriion proess Deph ompre for n piel h is rendered piel loion (s,s) Prolems if ojes -rnge is full inluded in noher ojes -rnge Prolems n e overome wih ddiionl geomeri ess Mehod is ver effiien for senes wih few ojes (-> fs rendering) (used in some gme engines) Oserver Frme Buffer (Piel Colors) -Buffer sores he loses disne of n oje h een drwn piel posiion Implemens orre olusion Is eing implemened more nd more in hrdwre => quie fs Oserver -Buffer ( - vlue) Frme Buffer (Piel Colors) Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi Hidden Surfe ehniques -Buffer lgorihm oninued -Buffer lgorihm (deph uffer lgorihm) Frme Buffer - keeps he olor piels of he rendered piure piel loion (s,s) -Buffer - keeps deph vlues for eh piure elemen Iniiliion (normll): Frme uffer is se o kground olor -Buffer elemens re se o ero ie fr lipping plne disne igges vlid -vlue represens fron lipping plne disne Oserver -Buffer ( - vlue) Frme Buffer (Piel Colors) Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi

6 -Buffer lgorihm oninued Olusion esing is performed during rseriion for piels No oje-oje esing, no pre soring fer rnsformion of frgmens Piels of frgmen re rseried inl deph inerpolion For ever piel, urren deph is ompred wih -uffer onen Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi -Buffer lgorihm : Pseudo-Code vr p : ineger // iniiliion for = o m do for = o m do egin WriePiel(,,BkgroundColor) WrieZ(,,) end // polgon rseriion for eh polgon do for eh piel in polgon s projeion do egin p = polgon s vlue piel oords (,) if p > RedZ(,) do egin // he urren poin is loser WrieZ(,,p) WriePiel(,,polgons_olor ) end end end Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi Deph-Rnge -Buffer lgorihm oninued: -rnge onsiderions MXIN (virul) sreen fr lipping plne = _fr ner lipping plne = _ner Deph uffer elemens hve limied numer of is => ineger vlue represenion Modeling oordines re oninuous floing poin vlues FP -Rnge mus e lmped o disree ineger vlue rnge => disreiion is suje o lising rifs Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi

7 Z-uffer rseriion emple = = Minining urren -vlues per piel Sn-Line Rseriion of ringles s p p 3 ( 2 ) ( 3) p ( ) s 2 s 3 s Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi -Buffer oninued lising rifs: visul emple Lol Rendering & Fied Funion Rendering Pipeline Geomeri Oje Primiives: Poins, Lines nd ringles riues: Color, Normls, eure Coordines rnsformion Lighing nd Illuminion Culling nd Clipping Projeion Rseriion Inerpolion eel & Piel Buffer Operions progrmmle Displ fied funions ie hrdwre oded Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi

8 Rendering Mehods in he Fied Funion Pipeline renissne of poin sed rendering Poin Clouds Emples: Oje veries re drwn s piels Color of he piels n e onsn (oje olor) or e shded (depending on lighs nd oje olors) Deerminion of disree sreen-oordines from model vere oordines Ver fs rendering mehod Ver populr for densel smpled surfes (3D sns) Reen ppliions of Poin-Bsed Rendering ehniques le e l, Poin Se Surfes, Visuliion 2 - voiding millions of polgons - Drw surfes s densel populed poin ses - Inrese speed of rendering - Oserve: Poin sed drwings hve omple visul sruure => good for 3D perepion when rendered dnmill Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi Rendering Mehods in he Fied Funion Pipeline Rendering Mehods in he Fied Funion Pipeline Wire Frmes Emples: Edges of oje polgons re drwn s lines Color of he lines n e onsn (oje olor) or e shded (depending on lighs nd oje olors) Deerminion of disree sreen-oordines for model veries 2D line drwing (sn onversion) eween he veries Ver fs rendering mehod if used wihou hidden surfe removl Solid Shding Emples: Oje polgons re drwn s filled res Color of he polgons n e onsn (oje olor) or e shded (depending on lighs nd oje olors) (onsn or mien shding, diffuse shding) Deerminion of disree sreen-oordines for model veries 2D line drwing (sn onversion) of he edges 2D re fill inside he polgon Cn e ver slow depending on shding mehod Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi

9 Solid Shding Models Emple: Fl Shding vs Gourud Shding Consn / Fl Shding one shding vlue is luled per polgon enire polgon is filled onl wih h olor vlue fs u no nie looking Color Inerpolion (Gourud Shding) shding vlues re luled for eh vere olor vlues for eh piel inside polgon re linerl inerpoled good visul pperne os of redued rendering speed Norml Veor Inerpolion (eg Phong or Blinn) for eh piel he surfe norml veor is inerpoled from he given vere norml veor definiions shding lulion is performed for eh piel slow rendering, ver good visul resuls (speulr higlighs) Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi Requiremens: Fl Shding vs Gourud Shding Gourud Shding nd Phong Shding Fl-Shding: One surfe norml veor per fe/polgon n n 3 n 4 n2 n 4 n 2 n (n) v C n 2 2 (n) v C 2 2 C C n C v l l v n n 2 n C n Gourud v 3 Phong v 3 Gourud-Shding: Surfe norml veors per vere Usull luled from surrounding polgon norml veors fn fn2 n fn 3 fn 4 n2 n n 2 Illuminion nd olor lulion veries: C ( n l) C ( n l) 2 2 Color lulion eween veries (i)liner inerpolion: C ( ) C C n 2 Illuminion nd olor lulion for eh piel nlil: For vere piels: C ( n l) C ( n l) 2 2 For piels eween veries, inerpolion of norml veor nd lulion of illuminion nd olor: n ( ) n n n 2 ( n l) n k Emple : n = (fn +fn 2 +fn 3 +fn 4 )/4 More on illuminion : see Fole, hper 6 Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi

10 Differenes : Gourud Shding vs Phong Shding How n ou hieve eer shding hn Gourud Emple: I ( n l) k k ; 2 2 n 4 ; n2 4 ; l 4 5 Using he fied funion pipeline: n ros(nl) I(phong)I(gourud), -, 4, -, -,7752,7757,7757, -,85 4, -,93 -,793,793,78 2, -,7 4, -,85 -,8264,82638,79 3, -,55 4, -,78 -,8398,83983,8 4, -,4 4, -,7 -,85,8536,8 5, -,25 4, -,63 -,86749,867493,82 6, -, 4, -,55 -,888,888,82 7,,5 4, -,48 -,89786,897862,83 8,,2 4, -,4 -,984,984,84 9,,35 4, -, -,9,99,85,,5 4, -,25 -,9,97,86,,65 4, -,8 -,9,9,87 2,,8 4, -, -,94658,946578,88 3,,95 4, -,3 -,954,9546,88 4,, 4,,5 -,95465,954652,89 5,,25 4,,3 -,95638,956382,9 6,,4 4,,2 -,95668,95668,9 7,,55 4,,28 -,95564,955645,92 8,,7 4,,35 -,958,9579,93 9,,85 4,, -,95,949997,94 2, 2, 4,,5 -,9456,9456,9456 I(n ),2,8,6,4 Inensi ross spn I(phong) I(gourud) Inresing he esselion -> Inrese he numers of polgons in our oje -> Inrese he numer of norml veors -> on-sreen fooprin of polgon equivlen wih one piel Consequene: Per-Piel Evluion of he Illuminion Equions -> Phong Shding l -2-4, k Drwk: -> Vere proessing overhed -> Bndwidh Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi Illuminion of surfes I ol I mien I diffuse I speulr Lighing Equion Diffuse refleion n idel Lmerin refleor: Refleion of iniden ligh equll owrds ll direionsll V I d I ol I mien = ol ligh inensi emmied from n illumined surfe = Conriuion from rndoml sered, mien ligh P he moun of ligh refleed o he oserver does no depend on he viewing direion V L N I diffuse I speulr = Conriuion modelled s diffuse refleion (Lmerin refleion) = Conriuion modelled s speulr refleion (ppriimive models Phong, Blinn) Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi he rdine energ of iniden ligh per surfe uni depends on he ngle eween he ligh direnion N nd he surfe orienion N I diffuse I k os ; d d L N I k N L d d Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi

11 Speulr refleion - Phong Speulr refleion - Blinn n perfe refleoor would s ll he ligh from he inoming ligh direion L owrds he refleed direion R Mos merils re no prefe mirrors nd herefore spred ligh round round som solid ngle round refleion veor (ligh lue re) N R L V he lulion of he refleion veor in Phong s model nd he ngel lulion for he weighing funion re epensive operions In Blinn s shding model, simplifiion of he illuminion lulions i sproposed h gives n eple pproimion of speulr refleion similr ophong L N H R V he moun of refleed ligh owrds he oserver depends lso on he osine of he ngle eween he idel refleion direion R nd he veor V owrds he oserver In ddiion, he degree of refleion depends lso on he ngle eween he he iniden ligh nd he surfe his is lled he refleion disriuion nd n e moduled wih weighing funion W() I spe _ linn I L os k spe k I N H spe L he illuminion formul in he Phong model n herefore e denoed s: I spe _ phong W k kspe I os W I R V spe L L Blinn sill reples he empiril os() wih noher jus noher equll empiril os() lulion he dvnge is h N*H is fser o lule hn V*R whih requires n ddiionl refleion lulion of L ou N lso, for siuions where oh he ligh soure nd he oserver re fr w from he oje, L nd V nd hene H n e onsidered onsn for he enire oje Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi Some veor mh Veor mh needed for - Illuminion lulions - Oje rnsformions nd deformion - Deerminion of spil relionships Veor lger (quik rehersl of useful formuls) Inner produ / do produ of wo veors os = Used for ) lulion of lengh nd disnes ) ngle mesuremens Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi

12 ppliion of he do produ - Bkfe Culling ppliion of he do produ - Bkfe Culling Given: polgon vere P, nd polgon norml veor N Users viewing posiion V Quesion: Is he polgon fing owrds he oserver Soluion: O P v~ N V V he polgon is fing owrds he oserver if he norml veor of h fe is fing owrds he oserver his is he se, if he lengh of he projeion of he veor V ono N is greer hn ero See ne slide for wo emples Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi Le: P ; N 3; N Cse: Le V 7 5 V' V P v~ N V' Cse2: Le V V' V P v~ N V' > -> he polgon is fing owrds V -8< -> he polgon is no fing owrds V Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi Veor lger (quik rehersl of useful formuls) ppliion of he ross produ - Polgon Norml Seup 2 Veor produ or ross produ of wo veors i j k is veor perpendiulr o nd Used for ) lulion of surfe norml veors ) es for o-lineri of wo veors ( = ) ) lulion of referene frmes Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi Given: ringle given veries,b nd C Quesion: How does he polgons norml veor look like 2 ; B 5 ; C 2 Spn veors: 2 B C 5 5 ; 2 N 5 5 ( ) 5 ( ) 5 O C Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi N B

13 Conenion of rnsforms : Mri Mulipliion rnsformion of Poins : Mri-Veor Mulipliion Mri ; n k elemens Mri B ; k l elemens => C = B defined; nd he resuling mri C hs n l elemens rnsformion represened s M n,k where n=4, k=4 Poin represened homogeneous oordines {,,, } s olumn veor P where k = 4, l = he resuling mri hs n=4 rows nd l= olumns => generll : B no equl B! ; i n, j l ij k s is sj m m 2 m 3 m 4 P = M m P = 2 m m m = m 3 m m m m 4 m m m m + m 2 + m 3 Z+ m 4 m 2 + m + m Z+ m m 3 + m + m Z+ m m 4 + m + m Z+ m Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi Mri represenion of si geomeri rnsforms Sle rnslion Roions s os sin s S sin os s R () umuled/omposie rnsformions n iude of n oje n e epressed/deomposed s n onenion of elemenr rnsforms Emple : = R S Oserve : Mri onenion order (rnsformion sequene) is imporn os sin R () sin os Emple : = R Emple : = R os sin R ( ) sin os Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi

14 Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi umuled/omposie rnsformions X Y Z ) Roe ou Z, 5 deg 2 rnsle long X, 5 3 Roe ou X, 25 deg B) Roe ou X, 25 deg 2 rnsle long X, 5 3 Roe ou Z, 5 deg Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi Clulion of Referene Frmes (iude Mri) Given: hree poins in spe idenif he spil iude of n oje s referene frme O B C O, B, nd C n e used o lule new orhonorml sis {;,,} B B C C ) ( ) (,, nd normlied veors! rnsformion mri roes he uni veor (,,,) ino he new se veor =(,,,) * Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi Clulion of Referene Frmes (iude Mri) * Hene: * Hene: * Hene: Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi Clulion of Referene Frmes (iude Mri) * O O Hene: O nloguousl, rnsformion mri O rnsles he origin of he se ssem O=(,,,) ino he new Origin =(,,,) Sine,, nd opere independenl on he respeive se veors, he n e omined ino on single rnsformion mri, h roes ll se veors simulneousl he rnslion mi operes independenl on O o rnsle he origin, regrdles of he roionl omponens Hene, he omined rnsformion mri n e denoed s: desries new frme in erms of he oordines of he referene frme O, ie i desries he rnsformion from lol oordines wihin ino oordines wihin O In order o rnsform o-ordine from O ino relive oordines, C mus e rnsformed wih -

15 ppliion of Referene Frmes rnforms ppliion of Referene Frmes rnforms he dil red-nd-uer in liring rking devies o displ devies h2 Prolem: rking oordine ssem is no o-ligned wih displ oordine ssem S Cliring displ devies wih referene frme in he phsil world h s h nd h2 re posiions mesured in referene frme u re needed in he sreen s lol oordine frme S m s Soluion: Regiser hree referene poins on-sreen h define he origin nd se veors of S s Clule S - h s = S - * h h2 s = S - * h2 Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi Quesion: For rked displ nd given given lol oordine wihin DM, wh is he lol oordine wihin SM -> p SM =SM - *(DM*p) Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi Beer soluion: Progrmmle Grphis Hrdwre Vere- nd Frgmen Shder : D Flow Geomeri Oje Primiives: Poins, Lines nd ringles riues: Color, Normls, eure Coordines rnsformion Lighing nd Illuminion Culling nd Clipping Projeion Vere Progrm (user definle) Vere Shder: Some imporn essile riues (Inpu) ve4 glposiion ve3 glnorml ve4 glcolor ve3 glmuliecoord Oupu Vriles Rseriion Inerpolion eel & Piel Buffer Operions Frgmen Progrm (user defined) ve4 gl_posiion // mus e wrien o flo gl_poinsie // m e wrien o ve4 gl_clipvere // m e wrien o progrmmle Displ fied funions ie hrdwre oded Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi

16 Vere- nd Frgmen Shder : D Flow Emple: Progrmmle Grphis Hrdwre Frmgmen Shder: Some imporn essile riues (Inpu) ve4 gl_frgcoord user-defined vring vriles Oupu Vriles ve4 gl_frgcolor // mus e wrien o ve4 gl_frgd[gl_mdrwbuffers]; flo gl_frgdeph; simple shder progrm for Gourud Shding #ommon vring ve3 olor; vring ve3 norml,ligh; #vere void min() { gl_posiion = gl_modelviewprojeionmri * gl_vere; ve3 pos = ve3(gl_modelviewmri * gl_vere); norml = normlie(gl_normlmri * gl_norml); ligh = normlie(gl_lighsoure[]posiion - pos); flo diffuse = 5; flo phong = pow(m(, do(norml,ligh)), 5)*5; olor = ve3(gl_colorrg * (phong + diffuse)); } #frgmen void min() { gl_frgcolor = ve4(olor, ); } Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi Emple: Progrmmle Grphis Hrdwre Progrmmle Grphis Hrdwre simple shder progrm for Phong Shding #ommon vring ve3 olor,pos; vring ve3 norml,ligh; #vere void min() { gl_posiion = gl_modelviewprojeionmri * gl_vere; pos = ve3(gl_modelviewmri * gl_vere); norml = gl_norml; ligh = normlie(gl_lighsoure[]posiion - pos); olor = gl_colorrg; } Hnds-On Demo #frgmen void min() { flo diffuse = 5; flo phong = pow(m(, do(norml,ligh)), 25)*5; if (norml > 3) disrd; gl_frgcolor = ve4(olor * (phong + diffuse), ); } Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi

17 Eplii geomer represenions in inerive CG Orgniion of geomer d: v2 v p v7 p4 v3 p2 p3 v4 v6 v5 Ojes referene frme Vere Lis n Vere Inde,,,u,v,,,u,v,,,u,v,,,u,v,,,u,v,,,u,v,,,u,v Vere D Cresin Coordines Norml Veors eure Coordines Color Vlues Polgon Lis 4 {, 2, 3, 4 } 2 3 { 6, 4, 3 } 3 3 { 5, 4, 6 } 4 4 { 3, 2, 7, 6 } k 3 { l, m, n } Polgon Inde Numer of Veries Lis of Vere Indies { } { } { } { } { } Oher d eg eure Referene Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi Hierrhil modeling Purposes: Consru omple ojes in modulr fshion reusili of uilding loks ese of modeling Inrese sorge effiien uild one eeue/re-use mn imes (displ liss) llow es upde of omponens llow for esier nimion of ehvior Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi Hierrhil modeling Simple Roo : Modeling Hierrh Emple: simple roo Bse runk Hed Lef_rm Righ_rm hree differen generi ojes Severl insnes of ojes rrnged in hierrhil order ree of involved insnes Lis of generi ojes used Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi

18 Creing he Model Hierrh Creing he Geomeri Cone Bse Hed runk Lef_rm Righ_rm ree of involved insnes Generi ojes se = VR_NodeNew(roo,"Roo Bse"); runk = VR_NodeNew(se,"Roo runk"); hed = VR_NodeNew(runk,"Roo Hed"); lef_rm = VR_NodeNew(runk,"Lef rm"); righ_rm = VR_NodeNew(runk,"Righ rm"); linder = VR_Cone(,,,2); ue = VR_Cue(); o = VR_Bo(2,,2); VR_NodeSeGeomer(se,linder); VR_NodeSeGeomer(runk,ue); VR_NodeSeGeomer(hed,ue); VR_NodeSeGeomer(lef_rm,o); VR_NodeSeGeomer(righ_rm,o); VR_NodeSle(se,,2,); VR_Nodernsle(runk,,2,); VR_NodeSle(runk,5,,5); VR_Nodernsle(hed,,2,); VR_NodeSle(hed,5,5,5); VR_Nodernsle(righ_rm,-4,8,-2); VR_NodeSle(righ_rm,2,2,2); VR_NodeRoe(righ_rm,8,,); VR_Nodernsle(lef_rm,,8,-2); VR_NodeSle(lef_rm,2,2,2); VR_NodeRoe(lef_rm,8,,); Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi Simple Roo : he Sene Grph se Sr rooee runk hed lef_rm righ_rm Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi