CS-184: Computer Graphics. Today

Transcription

1 CS-184: Computer Grphics Lecture #10: Clippin n Hien Surces Pro. Jmes O Brien University o Cliorni, Berkeley V2006-F Toy Clippin Clippin to view volume Clippin ritrry polyons Hien Surce Removl Z-Buer BSP Trees Others 2

2 Clippin Stu outsie view volume shoul not e rwn Too close: oscures view 3 Clippin Stu outsie view volume shoul not e rwn Too close: oscures view Too r: Complexity Z-uer prolems Too hih/low/riht/let: Memory errors Broken lorithms Complexity 4

3 Clippin Line to Line/Plne Line sement to e clippe x(t) = +t( ) Line/plne tht clips it ˆn x ˆn r = 0 ˆn r 5 Clippin Line to Line/Plne Line sement to e clippe x(t) = +t( ) Line/plne tht clips it ˆn x = 0 ˆn 6

4 Clippin Line to Line/Plne Line sement to e clippe x(t) = +t( ) } Line/plne tht clips it ˆn x = 0 ˆn ( +t( )) = 0 ˆn +t(ˆn ( )) = 0 ˆn t = ˆn ˆn 6 Clippin Line to Line/Plne Sement my e on one sie t [0...1] Lines my e prllel ˆn = 0 ˆn t = ˆn ˆn 7

5 Clippin Line to Line/Plne Sement my e on one sie t [0...1] ˆn Lines my e prllel ˆn = 0 ˆn! t = ˆn ˆn (Recll comments out numericl issues) 7 Polyon Clip to Convex Domin Convex omin eine y collection o plnes (or lines or hyper-plnes) Plnes hve outwr pointin normls Clip inst ech plne in turn Check or erly/trivil rejection 8

6 Polyon Clip to Convex Domin 9 Polyon Clip to Convex Domin Insie Outsie Insie Outsie Insie Outsie Insie Outsie s p p i s p s i p s Output p Output i No output Output i n p 10

7 Polyon Clip to Convex Domin Sutherln-Homn lorithm Bsiclly ee wlkin Clippin one oten... shoul e eicient Lin-Brsky prmetric spce lorithm See text or clippin in 4D homoenize coorintes 11 Generl Polyon Clippin A B A B B A A B A B 12

8 Generl Polyon Clippin Weiler Alorithm Doule ees 13 Hien Surce Removl True 3D to 2D projection woul put every thin overlppin into the view plne. We nee to etermine wht s in ront n isply only tht. 14

9 Z-Buers A extr epth chnnel to ime Write Z vlues when writin pixels Test Z vlues eore writin Imes rom Okn Arikn 15 Z-Buers Beneits Esy to implement Works or most ny eometric primitive Prllel opertion in hrwre Limittions Quntiztion n lisin rticts Overill Trnsprency oes not work well 16

10 Z-Buers Trnsprency requires prtil sortin: Prtilly trnsprent 3r Front Prtilly trnsprent 1st Opque 2n Opque 3r Opque 1st Opque 2n Goo Not Goo 17 Z-Buers Recll epth-vlue istortions. It s eture...! More resolution ner viewer! Best use o limite precision 18

11 A-Buers Store sorte list o rments t ech pixel Drw ll opque stu irst then trnsprent Stu ehin ull opcity ets inore Nice or ntilisin Scn-line Alorithm Assume polyons on t intersect Ech time n ee is crosse etermine who s on top 20

12 Pinter s Alorithm Sort Polyons Front-to-Bck Drw in orer Bck-to-Front works lso, ut wsteul How to sort quickly? Intersectin polyons? Cycles? 21 BSP-Trees Binry Spce Prtition Trees Split spce lon plnes Allows st queries o some sptil reltions Simple construction lorithm Select plne s su-tree root Everythin on one sie to one chil Everythin on the other sie to other chil Use rnom polyon or splittin plne 22

13 BSP-Trees,,c,,e,, e c 23 BSP-Trees e,, c 2,e,, c 2 24

14 BSP-Trees e c 2,e,, c 2 25 BSP-Trees e 1 e 2 c 2 c 2 e 1, e 2, 26

15 BSP-Trees e 1 e 2 c 2 c 2 e 1 e 2, 27 BSP-Trees e 1 e 2 c 2 c 2 e 1 e 2 28

16 BSP-Trees + e 1 e c c 2 e 1 e BSP-Trees Visiility Trversl Vrition o in-orer-trversl Chil one Su-tree root Chil two Select chil one se on loction o viewpoint Chil one on sme sie o su-tree root s viewpoint 29

17 BSP-Trees e 1 e 2 c 2 c 2 e 1 e 2 :::::e 1 :c 2 ::e 2 30 BSP-Trees e 1 e 2 c 2 c 2 e 1 e 2 :e 2 :c 2 ::e 1 :: :: 31