Computer Graphics. Surface Rendering Methods. Content. Polygonal rendering. Global rendering. November 14, 2005

Transcription

1 Computer Graphics urface Rederig Methods November 4, 2005 Cotet Polygoal rederig flat shadig Gouraud shadig Phog shadig Global rederig ray tracig radiosity

2 Polygoal Rederig hadig a polygoal mesh flat or costat shadig iterpolative, smooth, or Gouraud shadig Phog shadig polygoal mesh lat hadig () Costat shadig flat polygo : costat distat light source l: costat distat viewer v: costat Oe shadig calculatio for each polygo I OpeG glhademodel(g_t); distat source ad viewer

3 lat hadig (2) Disappoitig for a smooth surface lateral ihibitio huma visual system has a remarkable sesitivity Mach bads perceive the icreases i brightess alog the edges flat shadig of polygoal mesh perceived ad actual itesities at a edge We eed smoother shadig techiques to avoid it!! Gouraud hadig I OpeG glhademodel(g_mooth); Oe lightig calculatio for each vertex biliear iterpolatio of colors Defiig vertex ormal through iterpolatio = ormals ear iterior vertex

4 xample: Wireframe xample: lat hadig

5 xample: Gouraud hadig xample: Bump Mappig

6 xample: virometal Mappig Phog hadig Not prevetig the appearace of Mach bads If polygoal mesh is too coarse to capture illumiatio effects i polygo iteriors? iterpolate ormals across each polygo Oe shadig calculatio for each pixel off-lie Computig vertex ormal at each poit ( α ) = ( α ) + α B ( α, β ) = ( β ) C + β D ormals o a edge iterpolatio of ormals

7 xample: Phog hadig Wireframe lat Gouraud Phog xample: hadig & ubdivisio Cotrol Mesh oop ubdivisio evel evel 2 lat Gouraud Phog

8 Global Rederig () ocal lightig model caot hadle: blockig some of the light from the source from reachig the other spheres scatterig some light amog spheres global lightig model local lightig model Global Rederig (2) Global effects shadows refractios iter-object reflectios Methods ray tracig radiosity

9 hadows hadow == light sources are blocked castig ray towards each light source i i = 0 if ray is blocked, i = otherwise ( N ) + K ( V R) I = I + K I + ( K ) D hadow Term I Ray Castig Tracig primary rays from camera direct illumiatio from ublocked lights oly ( N ) + K ( V R) I = I + K I + ( K ) D I

10 Recursive Ray Tracig lso tracig secodary rays from hit surfaces global illumiatio from mirror reflectio ad trasparecy D ( N ) + K ( V R) I + K I R KT IT I = I + K I + ( K ) + Mirror Reflectio Tracig secodary ray i directio of mirror reflectio radiace for mirror reflectio ray D ( N ) + K ( V R) I + K I R KT IT I = I + K I + ( K ) +

11 Trasparecy () Trace secodary ray i directio of refractio radiace for refractio ray D ( N ) + K ( V R) I + K I R KT IT I = I + K I + ( K ) + Trasparecy (2) Trasparecy coefficiet is fractio trasmitted K T = if object is traslucet K T = 0 if object is opaque 0 < K T < if object is semi-traslucet Trasparecy Coefficiet D ( N ) + K ( V R) I + K I R KT IT I = I + K I + ( K ) +

12 Refractive Trasparecy () or thi surfaces igorig chage i directio assumig light travels straight through surface T Refractive Trasparecy (2) or solid objects applyig ell s law: η r si Θ r = η i si Θ i η T = ( η i r cosθ i cosθ r )N η η i r

13 Ray Tracig () xtesio of ray castig lookig for the visible surface for each pixel cotiuig to bouce the ray aroud the scee D ( N ) + K ( V R) I + K I R KT IT I = I + K I + ( K ) + Ray Tracig (2) Global effects shadows refractios iter-object reflectios Highly realistic vs. computatio time Trasparecy Reflectace hadow D ( N ) + K ( V R) I + K I R KT IT I = I + K I + ( K ) +

14 Basic Ray Tracig lgorithm or each pixel primary ray testig each surface if it is itersected Itersected secodary ray reflectio ray trasparet refractio ray Basic Ray Tracig lgorithm or each pixel primary ray testig each surface if it is itersected Itersected secodary ray reflectio ray trasparet refractio ray

15 Ray Tracig Tree () Represetig illumiatio computatio oe brach reflectio the other brach trasmissio termiated reachig the preset maximum or strikig a light source cee Ray Tree Ray Tracig Tree (2) Pixel itesity sum of itesities at root ode startig at termial ode If o surfaces are itersected, the itesity of backgroud cee I pixel Ray Tree I back I back I back

16 Radiosity () Goal simulatig diffuse iter-object reflectios ad shadows Radiosity (2) Basic idea treatig every polygo as light source

17 Radiosity (3) dvatages physical modelig of shadows ad idirect diffuse illumiatio idepedet of ay viewpoit quatio B i = i + i B jij B i = Radiosity of patch i i = missio of patch i i = Reflectivity of patch i i = orm-factor betwee patches i ad j orm actors Defiitio fractio of eergy leavig patch j that arrives at patch i Computatio projectig oto uit hemisphere projectig oto uit circle base dividig by area of circle projectig scee oto hemi-cube projectig oto uit hemisphere projectig oto Hemi-cube

18 Matrix olutio Methods Matrix formulatio Progressive refiemet iteratig shoot radiosity from patches O( 2 ) computatio gettig pretty good solutios more quickly = B B B B Matrix olutio Methods 24 iteratios iteratio 00 iteratios 2 iteratios

19 ummary Polygoal rederig flat Gouraud Phog Global rederig ray Tracig less expesive more accurate radiosity Visible-ie Determiatio

20 Visible-urface Determiatio with mbiet Illumiatio Oly lat haded Polygos with Diffuse Reflectio

21 Gouraud haded Polygos with Diffuse Reflectio Gouraud haded Polygos with pecular Reflectio

22 Phog haded Polygos with pecular Reflectio Phog hadig of Curved urfaces with pecular Reflectio

23 Improved Illumiatio Model ad Multiple ights Texture Mappig