Normals. In OpenGL the normal vector is part of the state Set by glnormal*()

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1 Ray Tracig 1

2 Normals OpeG the ormal vector is part of the state Set by glnormal*() -glnormal3f(x, y, z); -glnormal3fv(p); Usually we wat to set the ormal to have uit legth so cosie calculatios are correct - egth ca be affected by trasformatios - Note that scalig does ot preserve legth -gleable(g_normaze) allows for autoormalizatio at a performace pealty 2

3 Normal for Triagle plae (p - p 0 ) = 0 p 2 = (p 2 - p 0 ) (p 1 - p 0 ) ormalize / p p 0 p 1 Note that right-had rule determies outward face 3

4 Polygoal Shadig Shade a polygoal mesh - flat shadig - iterpolative or Gouraud shadig - Phog shadig polygoal mesh 4

5 Flat Shadig (1/2) Costat shadig - flat polygo : costat - distat light source l: costat - distat viewer v: costat Oe shadig calculatio for each polygo OpeG glshademodel(g_fat); distat source ad viewer 5

6 Flat Shadig (2/2) Always be 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!! 6

7 Polygo Normals Polygos have a sigle ormal - Shades at the vertices as computed by the Phog model ca be almost same - detical for a distat viewer (default) or if there is o specular compoet Cosider model of sphere Wat differet ormals at each vertex eve though this cocept is ot quite correct mathematically 7

8 Mesh Shadig The previous example is ot geeral because we kew the ormal at each vertex aalytically For polygoal models, Gouraud proposed we use the average of the ormals aroud a mesh vertex = ( )/

9 Gouraud Shadig OpeG glshademodel(g_smooth); Oe lightig calculatio for each vertex - biliearly iterpolate colors Vertex ormal could be defied through iterpolatio ormals ear iterior vertex 9

10 Smooth Shadig We ca set a ew ormal at each vertex Easy for sphere model - f cetered at origi = p Now smooth shadig works (color value iterpolatio iside the mesh) Note silhouette edge 10

11 Wireframe 11

12 Flat Shadig 12

13 Gouraud Shadig 13

14 Phog Shadig (1/2) May ot prevet the appearace of Mach bads What 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 Compute vertex ormal at each poit 1 A B, 1 C D edge ormals iterpolatio of ormals 14

15 Phog Shadig (2/2) Wireframe Flat Gouraud Phog 15

16 Gouraud ad Phog Shadig Gouraud Shadig - Fid average ormal at each vertex (vertex ormals) - Apply modified Phog model at each vertex - terpolate vertex shades across each polygo Phog shadig - Fid vertex ormals - terpolate vertex ormals across edges - terpolate edge ormals across polygo - Apply modified Phog model at each fragmet 16

17 Compariso f the polygo mesh approximates surfaces with a high curvatures, Phog shadig may look smooth while Gouraud shadig may show edges Phog shadig requires much more work tha Gouraud shadig - Util recetly ot available i real time systems Both eed data structures to represet meshes so we ca obtai vertex ormals 17

18 Shadows Shadow terms tell which light sources are blocked - Cast ray towards each light source i - S i = 0 if ray is blocked, S i = 1 otherwise Shadow Term E A A ( D N V R S ) S 18

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28 28 Ray Castig Trace primary rays from camera - Direct illumiatio from ublocked lights oly S D A A E S N ) R V (

29 29 Recursive Ray Tracig Also trace secodary rays from hit surfaces - Global illumiatio from mirror reflectio ad trasparecy T T R S S D A A E S N ) R V (

30 30 Mirror Reflectio Trace secodary ray i directio of mirror reflectio T T R S S D A A E S N ) R V ( Radiace for mirror reflectio ray

31 31 Trasparecy (1/2) Trace secodary ray i directio of refractio T T R S S D A A E S N ) R V ( Radiace for refractio ray

32 Trasparecy (2/2) Trasparecy coefficiet is fractio trasmitted - T = 1 if object is trasparet - T = 0 if object is opaque - 0 < T < 1 if object is traslucet Trasparecy Coefficiet E A A D N S V R S S R T T ( ) 32

33 33 Ray Tracig Extesio of ray castig - ook for the visible surface for each pixel - Cotiue to bouce the ray aroud the scee T T R S S D A A E S N ) R V (

34 Ray Tracig Global illumiatio - Shadows - Refractios - ter-object reflectios Highly realistic vs. computatio time Shadow Reflectace Trasparecy E A A D N S V R S S R T T ( ) 34

35 Radiosity Goal Simulate diffuse iter-object reflectios ad shadows for a scee cosistig of oly perfectly diffused surface i the closed space 35

36 Basic idea Radiosity - Treat every polygo as light source 36

37 Radiosity Advatages - Physically models shadows ad idirect diffuse illumiatio - depedet of ay viewpoit Equatio B i E i ρ i B j F ij B i = Radiosity of patch i E i = Emissio of patch i ρ i = Reflectivity of patch i F i = Form-factor betwee patches i ad j 37

38 Form Factors Defiitio - Fractio of eergy leavig patch j that arrives at patch i Computatio - Hemishere Project a patch oto uit hemisphere Divide the area of the patch o the hemisphere with the total area - Hemi-cube Project oto uit hemisphere Project oto Hemi-cube 38

39 Matrix Solutio Methods 1 iteratio 2 iteratios 24 iteratios 100 iteratios 39