Ray Tracing II. Improving Raytracing Speed. Improving Computational Complexity. Raytracing Computational Complexity

Transcription

1 Ra Tracing II Iproving Raracing Speed Copuer Graphics Ra Tracing II 2005 Fabio Pellacini 1 Copuer Graphics Ra Tracing II 2005 Fabio Pellacini 2 Raracing Copuaional Coplei ra-scene inersecion is epensive iprove b low-level opiizaions iporan bu does no provide scalabili iprove b reducing copuaional coplei Iproving Copuaional Coplei ra-scene inersecion is an O(n) algorih, where n is he nuber of objecs loop over each objec, check inersecion noe ha i is fundaenall a search algorih use divide and conquer o urn i o O(log n) siilar principles of search algorihs divide objecs ino ses discard ses of objecs quickl es inside se onl when necessar no as eas since daa srucures becoe coplicaed which daa srucures o use? Copuer Graphics Ra Tracing II 2005 Fabio Pellacini 3 Copuer Graphics Ra Tracing II 2005 Fabio Pellacini 4

2 Acceleraion Srucures Eaples Bounding Volues [Shirle original fro Dearle] wrap groups of objecs in bounding volues all poins on he objecs are inside he bounding vol. if ra does no hi volue, han i does hi he objec if ra his he volue, es he objec [Shirle] Copuer Graphics Ra Tracing II 2005 Fabio Pellacini 5 Copuer Graphics Ra Tracing II 2005 Fabio Pellacini 6 Bounding Volues Ais-Aligned Bounding Boes worh if volue hi-esing cheaper han obejc s e.g. polgon esh inside a bounding sphere need o know if inersecion eiss, no where speed up b reoving copuaion use onl siple priiives sphere, ais-aligned boes (AABB), oriened boes (OBB) choose based on ighness of fi vs. inersecion speed increasing ighness: spheres, AABBs, OOBBs increasing speed: OOBBs, AABBs, spheres os coonl used inersecion wih uliple infinie slabs [Shirle] Copuer Graphics Ra Tracing II 2005 Fabio Pellacini 7 Copuer Graphics Ra Tracing II 2005 Fabio Pellacini 8

3 Ais-Aligned Boes in 2D Ais-Aligned Boes in 2D P = E + I poin on a ra P [, ] P [, ] poin in he bo assue > 0 I > 0 I copue for each plane = ( = ( inersec if = ( = ( since [, ] [, ] [Shirle] [Shirle] Copuer Graphics Ra Tracing II 2005 Fabio Pellacini 9 Copuer Graphics Ra Tracing II 2005 Fabio Pellacini 10 Ais-Aligned Boes eend o oher quadrans b redefining inersecions for I < 0 for I < 0 define define = ( = ( = ( = ( avoid division b zero as in Shirle 10.9 Hierarchical Bounding Volues group bounding volues hierarchicall his is wha gives us he epeced O(log n) no provable, srongl depends on inpu daa volues bound all surfaces inside he no a perfec spli: siblings volues can overlap hierarchical inersecion esing if paren does no inersec, hen no inersecion else inersec all children and pick he closes inersecion (if an) eend o 3D b including wo new planes Copuer Graphics Ra Tracing II 2005 Fabio Pellacini 11 Copuer Graphics Ra Tracing II 2005 Fabio Pellacini 12

4 Creaing Bounding Hierarchies effecive space pariioning is necessar following ransfor hierarch is no alwas efficien basic greed algorih for binar rees pick a direcion, sa along ais spli objecs ino wo groups, and bound he coninue spliing each group change ais a each ieraion:,,z,,,z goal 1: balanced nuber of children in subrees spli for sae nuber of priiive in each group goal 2: equal space for each subree spli he paren bounding bo in he iddle spaiall Copuer Graphics Ra Tracing II 2005 Fabio Pellacini 13 Binar Space Pariioning (BSP) Trees concepuall siilar o bounding hier. creaion node defined b spliing plane ofen pick a plane orhogonal o, hen, hen z, children conain objecs in one of wo half spaces objecs inersecing plane are in each child Copuer Graphics Ra Tracing II 2005 Fabio Pellacini 14 Inersecing BSP rees sars a he op and deerine which of case 1: es onl Lef case 2: es Lef; if no inersecions es Righ case 3: es Righ; if no inersecions es Lef case 4: es onl Righ Regular Space Subdivision non hierarchical acceleraion srucure uniforl spli scene in a volue grid sae objec can be in uliple grid cell bu a poin can onl be in one cell a a ie inersec b walking he grid increenall [Shirle] [Shirle] Copuer Graphics Ra Tracing II 2005 Fabio Pellacini 15 Copuer Graphics Ra Tracing II 2005 Fabio Pellacini 16

5 Hierarchical Regular Space Subdivision a each cell of a regular grid, sore a regular grid norall 2-3 levels deep O(kn) behavior, wih k << 1 epec o skip a consan fracion of all objecs ver fas increenal walk eas o updae no efficien for scenes wih big holes in he Acceleraion Srucures which one is he winner? depends on pe of inpu and if we need o updae for aniaion sar wih a hierarchical grid Copuer Graphics Ra Tracing II 2005 Fabio Pellacini 17 Copuer Graphics Ra Tracing II 2005 Fabio Pellacini 18 Sofware Engineering Consideraions acceleraion srucs are subclasses of Surface high-level raracing code should no know abou he can swich daa srucures can cobine daa srucures hierarchical grids as grids of grids hierarchical bounding volues as volues of surfaces hierarchical boes wih a grid per bo in he leaves regular grid: sores Surface[n][n][n] bounding volue: sores Surface[n] ofen binar for siplici BSP node: sores Surface[2] Teure apping for Raracing Copuer Graphics Ra Tracing II 2005 Fabio Pellacini 19 Copuer Graphics Ra Tracing II 2005 Fabio Pellacini 20

6 Teure apping Consideraions especiall efficien in raracing since ra-objec inersecion is ver epensive rivial suppor for eure and bup apping unclear how o efficienl do displaceen aps akes us loose raracing nice properies Deerining apping Funcion sphere: given inersecion poin P, reurn angles fro spherical coordinaes riangle: change inersecion code o use baricenric coordinaes Shirle, Ch apping funcion: objec-inersecion code reurns uv paraeers Copuer Graphics Ra Tracing II 2005 Fabio Pellacini 21 Copuer Graphics Ra Tracing II 2005 Fabio Pellacini 22 Filering Teures Filering Teure Coparison copue average of eure subended b piel in general quie hard for reflecion/refracion ra differenials new and elegan discover: Igeh, SIGGRAPH 1999 propagae differenials ogeher wih ras no filering [Igeh, 1999] [Igeh, 1999] bad for view ras Copuer Graphics Ra Tracing II 2005 Fabio Pellacini 23 Copuer Graphics Ra Tracing II 2005 Fabio Pellacini 24

7 Filering Teure Coparison ip-ap filering based on disance Filering Teure Coparison ip-ap filering based on ra differenials [Igeh, 1999] [Igeh, 1999] ok for view ra, bad for reflecion/refracions ok in os cases, jus a bi of overblur Copuer Graphics Ra Tracing II 2005 Fabio Pellacini 25 Copuer Graphics Ra Tracing II 2005 Fabio Pellacini 26 Filering Teure Coparison accurae filering based on ra differenials [Igeh, 1999] works grea Copuer Graphics Ra Tracing II 2005 Fabio Pellacini 27