1. Photorealism Reflection, Refraction Bump maps
Ray-tracing
Photorealism
Reflection, Refraction
Bump maps

2. Overview Textures review Lighting re-visited
Photorealism + Global Illumination
Reflection
Refraction
Bump Maps / Normal maps
Lab

3. © Gilles Tran

4. The Phong Illumination algorithm cannot generate images like these

5. The Rendering Equation
A physicists representation of light transport in the scene, describing the amount of light going from any point x to another point x’:
I(x, x’) = intensity of light passing from x to x’
(two point transport)
g(x, x’) =
(geometry factor)
e (x, x’) = intensity of light emitted by x and passing to x’
ρ (x, x’, x”) = bi-directional reflectance scaling factor for light passing from x” to x by reflecting off x’
S = all surfaces in the scene
[Kajiya 1986]
0 if x and x’ are not mutually visible
1/r2 where
Attenuation (distance from x to x’)

6. Light_transport_from B to A:
Emmitance of B
Visibility of B from A
Distance to B from A
Also:
Reflectance of B
Light_transport_from Ci to B
Emmitance of C
Visibility of C from B
Distance to C from B A B C2 C1 C3 D1

7. Assumptions
I on both sides of the equation suggests an infinitely recursive path of light transfer.
We need to make some simplifying assumptions in order to solve this equation
Local Illumination algorithms assume light only “bounces” once travelling from light source to a point in the scene and then to the eye
Global Illumination algorithms account for light transport between several points on the scene before reaching the eye (several bounces)
Thus can account for refraction, shadows, reflections etc.
Less realistic, usually used in real-time rendering
More expensive, usually used in off-line rendering

8. Local vs. Global Illumination
Illumination depends on local object &
light sources only
Illumination at a point can depend
on any other point in the scene

9. Ray Tracing A photo-realistic rendering algorithm
Current ray tracing methods are attributed to Turner Whitted (Bell Labs. 1980)  Whitted Illumination Model
First implementation of ray tracing in computer graphics = Appel (IBM 1968)
Recursive Raytracing, 1979
Recorded in “An Improved Illumination Model for Shaded Display” (Bell Labs, 1980).

10. Albrecht Dürer ( )
Ray-tracing based on ideas employed since early Renaissance artists e.g. daVinci & Dürer

11. Ray Tracing I(P) = Ilocal(P) + krgI(Pr) + ktgI(Pt) Local term
(as in Phong)
Reflected
Transmitted
The Direct Diffuse Term Ilocal is calculated empirically (using Phong illumination)
In the global ray-traced terms, diffusion of light due to surface imperfections is totally ignored.

12. Ray Tracing from Eye
Tracing from light source
Traditional ray-tracing
We are only interested in light rays that reach the viewplane from the light source
If we begin at the light source only a small proportion of the rays we trace will reach the viewer
More efficient to start at viewer and trace in reverse – traditional ray tracing
Some implementations start at the light source and trace the actually light path – backwards raytracing
Starting at the light position traces many rays that never reach the eye. Thus the traditional ray-tracing method is to start at the eye and trace rays back-wards to the source.

13. Eye Ray and Object Intersection
Cast a ray from camera position through each pixel into the scene.
Calculate where this intersects with objects in the scene. Get the first intersection.

14. Diffuse Term
Extend a “Shadow Feeler” (or light ray) and see if it is occluded by an object in the scene
If so the object is in shadow from this light source
Otherwise solve the phong model to calculate the contribution of this point to the colour of the pixel.
If object is diffuse stop here.

15. Reflection
If object is specular THEN create a ray in the direction of perfect specular reflection.
For this new ray, we will again check whether…
it intersects an object,
if so is this object in shadow
what is the contribution of this object to the colour of the pixel?
Each ray contributes to the colour of the pixel it originated from

16. Refraction
Similarly if the object is transmissive (not-opaque) then generate a transmitted (or refracted) ray and repeat…

17. The Angle of Refraction
When light passes from a material of one optical density to another it changes direction.
The amount by which the direction changes is determined by the optical densities of the two media.
Optical density (and thus the amount of bending is related to a value we call the refractive index of the material.
Diamond
Air
Glass
Water

18. Index of Refraction (ior)
Material
Index of Refraction
Vacuum
1.0000
<--lowest optical density
Air
1.0003
Ice
1.31
Water
1.333
Ethyl Alcohol
1.36
Plexiglas
1.51
Crown Glass
1.52
Light Flint Glass
1.58
Dense Flint Glass
1.66
Zircon
1.923
Diamond
2.417
Rutile
2.907
Gallium phosphide
3.50
<--highest optical density
You can try these refracted index values in POVRay.

19. Ray Tracing Summary

20. Ray Tracing Issues I(P) = Ilocal(P) + krgI(Pr) + ktgI(Pt) Cast a ray
Determine Intersections
For closest Intersection:
Extend light(shadow feeler) ray + calculate local term
Spawn Transmitted Ray (step 1)
Spawn Reflected Ray (step 1)

21. Ray Tree
The spawning of reflected and refracted rays can be represented in tree structure.

22. Terminating Recursion
All of the spawned rays contribute to the pixel that the tree originated from.
However each new ray contributes less and less to the pixel.
Unlike in the real-world, we can’t keep bouncing around for ever so we stop the recursion at some stage  recursion clipping.
Stop after a set number of bounces.
Or stop when the contribution becomes less than a certain value.

23. Very high maximum recursion level
Recursion Clipping
max level = 1
max level = 2
Very high maximum recursion level
max level = 3
max level = 4

24. Object Intersection
Intersection testing is solved mathematically. But is an inherently expensive geometrical problem. (out of the scope of current lecture)
Where does ray intersect object?
Where does ray intersect scene?

25. The Ray Tracing Algorithm
for each pixel in viewport {
determine eye ray for pixel
intersection = trace(ray, objects)
colour = shade(ray, intersection) }
Intersection trace(ray, objects) {
for each object in scene
intersect(ray, object)
sort intersections
return closest intersection }

26. The Ray Tracing Algorithm
colour shade(ray, intersection) {
if no intersection
return background colour
for each light source
if(visible)
colour += Phong contribution
if(recursion level < maxlevel)
ray = reflected ray
intersection = trace(ray, objects)
colour += refl*shade(ray, intersection)
ray = transmitted ray
colour += trans* shade(ray, intersection) }
return colour

27. Reflection
finish {
reflection 0.5
//phong etc… }

28. Translucency
texture {
pigment
rgbf <1, 1, 1, .8> }
Filter value of 0 is fully opaque, 1 is fully transparent.

29. Refraction
texture {
pigment
rgbf <1, 1, 1, .8> }
interior
ior 3

30. Caustics texture { pigment rgbf <1, 1, 1, .8> } interior ior 3

31. A bump-map texture applied to a flat polygon.
Bump Mapping
A “real” bump distorts the directions of the normals (this effects calculations of light reflectance)
“Fake” bumps created by distorting the normals although the geometry is still flat.
A bump-map texture applied to a flat polygon.

34. Sample Scene (no normal maps)
We can add bumps, dents, wrinkles, ripples and waves to our objects.
box {
< -4, -.25, -4 > < 4, .25, 4 >
pigment { White }
finish
reflection .4 }
normal
//add normal pattern here ****
Sample Scene (no normal maps)

35. Bumps
normal {
bumps 1 }

36. Dents
normal {
dents 1 }

37. Wrinkles
normal {
wrinkles 1 }

38. Ripples
normal {
ripples 1 }

39. Waves
normal {
waves 1 }

40. Bump Map normal { bump_map gif "bumpmap.gif" }
rotate 90*<1, 0, 0>
scale 8

41. Lab
Reflection in POV-Ray: use the reflection parameter in the finish statement to generate photorealistic reflective surfaces
Refraction in POV-Ray: use the interior definition and ior values to generate photorealistic refraction
Use a bump map/ normal map to generate some of the following effects:

42. Normal Maps
ripples
bumps
dents
wrinkles

43. Bump Map
Insert Images
Bump Map image file
(or use your own)

44. POV-Ray Objects
If you want to create more interesting scenes with real world objects, you can find POV-Ray objects on several sites including: