Interactive Graphical Systems HT2002

Transcription

1 Wh is Inerive Compuer Grphis Inerive Grphil Ssems H Lesson 2 : Grphis Primer Sefn Seipel Compuer ided Design (CD) inerive modeling (simple visul represenions) merill orre onsruions s sis for uomed mnufuring resuls : ehnil skehes, simple rendered sill imges Compuer Grphis nimion modeling & design of ojes modeling of dnmi ehvior resuls : HQ si piures nd si movies Inerive Compuer Grphis on-line rendering (rel-ime!) rendering s relisi s frme-re llows resuls: user driven non si 3D senrio Wh is Inerive Compuer Grphis Wh is Inerive Compuer Grphis Emple : Compuer ided Design (CD) Emple : Compuer Grphis nimion Rihrd Nordhus Shool of rhieure nd Plnning Universi of New Meio in o Coprigh Pir nimion Sudios

2 Wh is Inerive Compuer Grphis Inerive Grphil Ssems: Sruure Emple : Inerive Compuer Grphis Mulimedi Feedk Compuersimulion Relime Mulimodl Inpu Design nd Simulion of Roo Cell Coprigh Sndi Nionl Lirries Repliion Rel world How re grphil ojes defined Definiion of poins Surfe represenions => infinie numer of poins o form oje surfe (mhemil funions) Bsed on he definiion of referene o-ordine ssem heir omponens => finie se of surfe poins - rendered s poin louds - rendered s polgons given erin onneivi => finie se of volume poins (voels) - rendered s poin louds - rendered s solid volume ojes ) kresin o-ordine ssem { ; i, j, k } - orhogonl - orhonorml k j P(,,) i

3 2) polr o-ordine ssem { ; r, } Relions eween polr nd resin o-ordines definiion of,, nd r P(r, ) r n = n 2 2 =rosos = r sin = r os sin Veor lger (quik rehersl of useful formuls) Inner produ / do produ of wo veors os = Used for ) lulion of lengh nd disnes ) ngle mesuremens 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: 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

4 ppliion of he do produ - Bkfe Culling Veor lger (quik rehersl of useful formuls) 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 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 ollineri of wo veors ( = ) ) lulion of referene frmes ppliion of he ross produ - Polgon Norml Seup 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 C N B Conenion of rnsforms : Mri Mulipliion Mri ; n k elemens Mri B ; k l elemens => C = B defined; nd he resuling mri C hs n l elemens => generll : B no equl B! ; i n, j l ij k s is sj

5 rnsformion of Poins : Mri-Veor Mulipliion Mri represenion of si geomeri rnsforms 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 Sle rnslion Roions s os sin s S sin os s R () 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 os sin R () sin os os sin R ( ) sin os umuled/omposie rnsformions umuled/omposie rnsformions n iude of n oje n e epressed/deomposed s n umulion of elemenr rnsforms Emple : = R S serve : Mri onenion order (rnsformion sequene) is imporn Y ) Roe ou Z, 5 deg 2 rnsle long X, 5 3 Roe ou X, 25 deg Emple : = R Emple : = R Z X B) Roe ou X, 25 deg 2 rnsle long X, 5 3 Roe ou Z, 5 deg

6 Clulion of Referene Frmes (iude Mri) Given: hree poins in spe idenif he spil iude of n oje s referene frme B C, B, nd C n e used o lule new orhonorml sis {;,,} B C ) ( Noe:,, nd mus e normlied! rnsformion mri roes he uni veor (,,,) ino he new se veor =(,,,) * Clulion of Referene Frmes (iude Mri) * Hene: * Hene: * Hene: Clulion of Referene Frmes (iude Mri) * Hene: nloguousl, rnsformion mri rnsles he origin of he se ssem =(,,,) ino he new rigin =(,,,) Sine,, nd opere independnl 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 rnsle he origin, regrdles of he roionl omponens Hene, he omined rnsformion mri n e denoed s: Represenions of 3D Models Quniive Models Mhemil, phsil, hemil funion define vere d Proedurl Models Delrive or proedurl ssem desries vere d nd onneivi (rule sed, lnguge sed, reursive nd frl funions) Hierrhil Geomeri Models Eplii definiion of ojes vere d nd onneivi Re-Usge of geomeri proopes Defining hierrhies nd geomeri relions eween insnes

7 How re grphil ojes defined Mhemil funions : Emple MLB How re grphil ojes defined Finie se of volume poins (voels) : Voelviewer How re grphil ojes defined Finie se of surfe poins : Sumrine je represenions in inerive CG Grphi rendering engines re rdiionll opimied for drwing of 3D poins drwing of 3D veors drwing of 3D polgons (mosl ringles) (some n drw spheres eg SGI Ereme) => ojes re represened s omposie lumps of veries nd polgons => more dvned, nlil desripions of ojes re usull no found in inerive ompuer grphis (see 3D nimion progrms nd rring s/w)

8 je represenions in inerive CG Eplii geomer represenions in inerive CG Emple : Sene wih epo eplii definiion of veries&polgons rendered using fl shding Piures: Coprigh () 99 Pir 2 omined pproh: eplii vere d nd mhemil polnomil funions define urved surfes rgniion of geomer d: v2 v p v7 p4 v3 p2 p3 v4 v6 v5 jes 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 { } { } { } { } { } her d eg eure Referene Rendering Mehods Rendering Mehods Poin Clouds Emples: je veries re drwn s singulr 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 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

9 Rendering Mehods Surfe Shding Emples: je 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 Surfe Shding Models Consn / Fl Shding one shding vlue is luled per polgon enire polgon is filled onl wih h olor vlue fs u no nie looking Gourud Shding (Color Inerpolion) 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 Phong Shding (Norml Veor Inerpolion) for eh piel he surfe norml veor is inerpoled from he given vere normls shding lulion is performed for eh piel eremel slow rendering, ver good visul resuls (speulr properies) Emple: Fl Shding vs Gourud Shding Requiremens: Fl Shding vs Gourud Shding Fl-Shding: ne surfe norml veor per fe/polgon n n2 n 3 n 4 n 4 Phong-Shding: Surfe norml veors per vere Usull luled from surrounding polgon norml veors fn fn2 n fn 3 fn 4 n2 n n 2 Emple : n = (fn +fn 2 +fn 3 +fn 4 )/4

10 Gourud Shding nd Phong Shding Differenes : Gourud Shding vs Phong Shding n 2 n (n) v C n 2 2 (n) v C 2 2 C C n C v Gourud C ( n l) C ( n l) 2 2 l v 3 Illuminion nd olor lulion veries: Color lulion eween veries (i)liner inerpolion: C ( ) C C n 2 More on illuminion : see Fole, hper 6 v Phong l n n C n Illuminion nd olor lulion for eh piel nlil: For vere piels: C ( n l) C ( n l) v 3 n ( ) n n n 2 ( n l) n 2 2 For piels eween veries, inerpolion of norml veor nd lulion of illuminion nd olor: k n 2 Emple: I ( n l) k k ; 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 l n 4 ; n2 4 ; l 4 5 I(n),2,8,6,4,2 Inensi ross spn k I(phong) I(gourud) Eplii geomer represenions in inerive CG rgniion of geomer d: v2 v p v7 p4 v3 p2 p3 v4 v6 v5 jes 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 { } { } { } { } { } her d eg eure Referene 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

11 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 hierrhi order ree of involved insnes Lis of generi ojes used Creing he Model Hierrh Creing he Geomeri Cone Bse runk Hed 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,,);

12 Simple Roo : he Sene Grph se Sr rooee runk hed lef_rm righ_rm