Interactive Graphical Systems HT2003

Transcription

1 Inerive Grphil Ssems H Lesson 2 : Grphis Primer Sefn Seipel Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi Wh is Inerive Compuer Grphis Compuer ided Design (CD) inerive modeling (simple visul represenions) merill orre onsruions s sis for uomed mnufuring resuls : ehnil sehes, 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 Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi Wh is Inerive Compuer Grphis Emple : Compuer ided Design (CD) Wh is Inerive Compuer Grphis Emple : Compuer Grphis nimion Rihrd Nordhus Shool of rhieure nd Plnning Universi of New Meio in o Coprigh Pir nimion Sudios Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi Wh is Inerive Compuer Grphis Inerive Grphil Ssems: Sruure Emple : Inerive Compuer Grphis Mulimedi Feed Compuersimulion Relime Mulimodl Inpu Design nd Simulion of Roo Cell Coprigh Sndi Nionl Lirries Repliion Rel world Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi

2 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 ) resin o-ordine ssem { ; i, j, } - orhogonl - orhonorml j P(,,) i Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi 2) polr o-ordine ssem { ; r, λ, φ } Relions eween polr nd resin o-ordines definiion of,, nd λ r P(r, λ, φ ) φ π < λ < π π/2 < φ < π/ r nλ n ϕ 2 2 rosϕosλ r sinϕ r osϕ sinλ Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi Veor lger (qui rehersl of useful formuls) Inner produ / do produ of wo veors α os α Used for ) lulion of lengh nd disnes ) ngle mesuremens Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi ppliion of he do produ - Bfe 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 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 v~ N Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi

3 ppliion of he do produ - Bfe Culling Veor lger (qui rehersl of useful formuls) Le: P ; N 3; N Cse: Le V 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 2 Veor produ or ross produ of wo veors i j ( ) ( ) ( ) is veor perpendiulr o nd Used for ) lulion of surfe norml veors ) es for ollineri of wo veors ( ) ) lulion of referene frmes Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi ppliion of he ross produ - Polgon Norml Seup Given: ringle given veries,b nd C Quesion: How does he polgons norml veor loo lie 2 ; B 5 ; C 2 Spn veors: 2 B C 5 5 ; 2 C N B Conenion of rnsforms : Mri Mulipliion Mri ; n elemens Mri B ; l elemens > C B defined; nd he resuling mri C hs n l elemens > generll : B no equl B! N 5 5 ( ) 5 ( ) 5 Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi ; < i < n, < j < l ij s is sj Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi rnsformion of Poins : Mri-Veor Mulipliion rnsformion represened s M n, where n4, 4 Poin represened homogeneous oordines {,,, } s olumn veor P where 4, l he resuling mri hs n4 rows nd l olumns m m 2 m 3 m 4 m 3 m m m m 4 m m m P M m P 2 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 Mri represenion of si geomeri rnsforms Sle rnslion Roions s os ϑ sin ϑ s S sin ϑ os ϑ s R () ϑ osϑ sin ϑ R () ϑ sinϑ os ϑ os ϑ sin ϑ R ( ϑ) sinϑ os ϑ Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi

4 Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi 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 Emple : R Emple : R 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 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 (,,,) 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) Hene: nloguousl, rnsformion mri rnsles he origin of he se ssem (,,,) ino he new rigin (,,,) 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 rnsle he origin, regrdles of he roionl omponens Hene, he omined rnsformion mri n e denoed s: Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi 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

5 How re grphil ojes defined Mhemil funions : Emple MLB How re grphil ojes defined Finie se of volume poins (voels) : Voelviewer Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi 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) Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi 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 Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi rgniion of geomer d: v2 v p v7 p4 v3 p2 p3 v4 v6 v5 jes referene frme Vere Lis,,,u,v 2,,,u,v 3,,,u,v 4,,,u,v 5,,,u,v 6,,,u,v Polgon Lis n,,,u,v 4 {, 2, 3, 4 } { } Vere Inde Vere D 2 3 { 6, 4, 3 } { } Cresin Coordines 3 3 { 5, 4, 6 } { } 4 4 { 3, 2, 7, 6 } { } Norml Veors eure Coordines Color Vlues 3 { l, m, n } Polgon Inde Numer of Veries Lis of Vere Indies { } her d eg eure Referene Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi

6 Rendering Mehods Rendering Mehods Poin Clouds Emples: je 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) 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 Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi 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 looing 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) Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi 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 n4 n 4 Phong-Shding: Surfe norml veors per vere Usull luled from surrounding polgon norml veors fn 3 fn n fn2 fn4 n2 n n 2 Emple : n (fn fn 2 fn 3 fn 4 )/4 Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi

7 Gourud Shding nd Phong Shding Differenes : Gourud Shding vs Phong Shding l n 2 n n 2 n n α(n) v C n 2 2 α(n) v C 2 2 C v C n C v C n Gourud C ( n l) λ ξ C n l ( ) λ ξ 2 2 v 3 Illuminion nd olor lulion veries: Color lulion eween veries (i)liner inerpolion: C C C [ ] ( α ) α α n 2 More on illuminion : see Fole, hper 6 Phong l Illuminion nd olor lulion for eh piel nlil: For vere piels: C ( n l) λ ξ C n l ( ) λ ξ 2 2 For piels eween veries, inerpolion of norml veor nd lulion of illuminion nd olor: v 3 [ ] ( α ) α α n 2 ( n l) ξ Emple: I ( n l) λ ξ λ ; ξ 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 ) Inensi ross spn,2,8,6,4, I(phong) I(gourud) Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi 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,,,u,v 2,,,u,v 3,,,u,v 4,,,u,v 5,,,u,v 6,,,u,v Polgon Lis n,,,u,v 4 {, 2, 3, 4 } { } Vere Inde Vere D 2 3 { 6, 4, 3 } { } Cresin Coordines 3 3 { 5, 4, 6 } { } 4 4 { 3, 2, 7, 6 } { } Norml Veors eure Coordines Color Vlues 3 { l, m, n } Polgon Inde Numer of Veries Lis of Vere Indies { } her d eg eure Referene Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi Hierrhil modeling Purposes: Consru omple ojes in modulr fshion reusili of uilding los 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 run 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

8 Creing he Model Hierrh Creing he Geomeri Cone Bse run Hed Lef_rm Righ_rm ree of involved insnes Generi ojes se VR_NodeNew(roo,"Roo Bse"); run VR_NodeNew(se,"Roo run"); hed VR_NodeNew(run,"Roo Hed"); lef_rm VR_NodeNew(run,"Lef rm"); righ_rm VR_NodeNew(run,"Righ rm"); linder VR_Cone(,,,2); ue VR_Cue(); o VR_Bo(2,,2); VR_NodeSeGeomer(se,linder); VR_NodeSeGeomer(run,ue); VR_NodeSeGeomer(hed,ue); VR_NodeSeGeomer(lef_rm,o); VR_NodeSeGeomer(righ_rm,o); VR_NodeSle(se,,2,); VR_Nodernsle(run,,2,); VR_NodeSle(run,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 run hed lef_rm righ_rm Sefn Seipel, Deprmen of Informion ehnolog, Uppsl Universi