1. illumination
2016, Fall

2. Ray Casting
Image RayCast(Camera camera, Scene scene, int width, int height) {
Image image = new Image(width, height);
for (int i; i< width; i++)
for (int j=0; j<height; j++) {
Ray ray=ConstructRayThroughPixel(camera, i, j);
Intersection hit = FIndIntersection(ray, scene);
Image[i][j]=GetColor(scene, ray, hit); }
return image;

3. Illumination How do we compute radiance for a sample ray?
image[i][j]=GetColor(scene, ray, hit);

4. Goal Must derive computer models for … Desirable feature …
Emission at light source
Scattering at surface
Reception at the camera
Desirable feature …
Concise
Efficient to compute
“Accurate”

5. Overview Direct Illumination (=Local illumination) Global illumination
Emission at light sources
Scattering at surfaces
Global illumination
Shadows
Refractions
Inter-object reflections

6. Modeling Light Sources…
Describes the intensity of energy,
Leaving a light source,
Arriving at location (x, y, z),
From direction (q, f),
With wavelength l

7. Empirical Models Ideally measure Irradiant energy for “all” situations
Too much storage
Difficult in practice

8. OpenGL Light Source Models
Simple mathematical models:
Point light
Directional light
Spot light

9. Point Light Source Models omni-directional point source
Intensity (I0),
Position (px, py, pz),
Factors (ca, la, qa) for attenuation with distance (d)

10. Directional Light Source
Models point light source at infinity
Intensity (I0),
Direction (dx, dy, dz)

11. Spot Light Source (2/2) Models point light source with direction
intensity (I0),
position (px, py, pz),
direction (dx, dy, dz)
Factors (ca, la, qa) for attenuation with distance
falloff (sd), and cutoff (sc)

12. Light Falling on a Surface
Move surface away from light
Inverse square law:
Tilt surface away from light
Cosine law:

13. Overview Direct Illumination (=Local illumination) Global illumination
Emission at light sources
Scattering at surfaces
Global illumination
Shadows
Refractions
Inter-object reflections

14. Modeling Surface Reflectance
BRDF (θi, φi, θo, φo, λ)…
Bidirectional Reflectance Distribution Function
describes the amount of incident energy,
arriving from direction (θi, φi), ... (쎄타, 파이)
leaving in direction (θo, φo), ...
with wavelength l (람다)

15. Empirical Models
Ideally measure BRDF for “all” combinations of angles : θi, φi, θo, φo
Difficult in practice
Too much storage

16. Parametric Models
Approximate BRDF with simple parametric function that is fast to compute.
Phong [75]
Blinn-Phong [77]
Cook-Torrance [81]
He et al. [91]
Ward [92]
Lafortune et al. [97]
Ashikhmin et al. [00]
etc.

17. OpenGL Reflectance Model
Simple analytic model:
Diffuse reflection +
Specular reflection +
Emission +
“Ambient”

18. Diffuse Reflection Assume surface reflects equally in all directions
Example: chalk, clay

19. Diffuse Reflection How much light is reflected?
Depends on angle of incident light

20. Diffuse Reflection
Lambertian model
Cosine law (dot product)

21. Specular Reflection Reflection is strongest near mirror angle
Examples: mirrors, metals

22. Specular Reflection How much light is seen? Depend on:
Angle of incident light
Angle to viewer

23. Specular Reflection Phong Model
cos (a)n : This is a physically-motivated hack!

24. Emission
Represent light eminating directly from polygon

25. Ambient Term Represents reflection of all indirect illumination
This is a total hack
Avoid complexity of global illumination

26. OpenGL Reflectance Model
Simple analytic model:
Diffuse reflection +
Specular reflection +
Emission +
“Ambient”

27. OpenGL Reflectance Model
Sum diffuse, specular, emission, and ambient

28. Surface Illumination Calculation
Single light source:

29. Surface Illumination Calculation
Multiple light sources:

30. Example

31. Overview Direct Illumination (=Local illumination) Global illumination
Emission at light sources
Scattering at surfaces
Global illumination
Shadows
Refractions
Inter-object reflections
Global Illumination

32. Shadows Shadow term tells if light sources are blocked
Cast ray towards each light source Li
Si = 0 if ray is blocked, Si = 1 otherwise

33. Ray Casting Trace primary rays from camera
Direct illumination from unblocked light only

34. Recursive Ray Tracing Also trace secondary rays from hit surfaces
Global illumination from mirror reflection and transparency

35. Mirror reflections Trace secondary rays in mirror direction
Evaluate radiance along secondary ray and include it into illumination model

36. Transparency Trace secondary rays in direction of refraction
Evaluate radiance along secondary ray and include it into illumination model

37. Transparency Transparency coefficient is fraction transmitted
KT = 1 for translucent object, KT = 0 for opaque
0 < KT <1 for object that is semi-translucent

38. Refractive Transparency
For thin surfaces, can ignore change in direction
Assume light travels straight through surface 에타

39. Refractive Transparency
For solid objects, apply Snell’s law:

40. Refractive Index (굴절률) in Maya
⊙ Vacuum: 1.00
⊙ Air:
⊙ Acetone: 1.36
⊙ Alcohol: 1.329
⊙ Amorphous Selenium: 2.92
⊙ Calspar 1: 1.16
⊙ Calspar 2: 1.486
⊙ Carbon Disulfide(탄소 황화물): 1.63
⊙ Chromium Oxide(크롬 산화물): 2.705
⊙ Copper Oxide(구리 산화물): 2.705
⊙ Crown Glass(크라운 창 유리): 1.52
⊙ Crystal: 2.00
⊙ Diamond: 2.471
⊙ Emerald: 1.57
⊙ Ethyl Alcohol(에틸 알콜): 1.36
⊙ Flourite: 1.434
⊙ Fused Quartz(석영, 수정): 1.46
⊙ Heaviest Flint Glass(렌즈, 프리즘 등 광학용 고급유리): 1.89
⊙ Heavy Flint Glass: 1.65
⊙ Glass: 1.5
⊙ Ice: 1.309
⊙ lodine Crystal: 3.34
⊙ Lapis Lazuli(청금석): 1.61
⊙ Light Flint Glass: 1.575
⊙ Liquid Carbon Dioxide: 1.2
⊙ Polystyrene(폴리스티렌): 1.55
⊙ Quartz 1(석영): 1.644
⊙ Quartz 2: 1.535
⊙ Ruby: 1.77
⊙ Sapphire: 1.77
⊙ Sodium Chloride1(소금): 1.544
⊙ Sodium Chloride2(소금): 1.644
⊙ Sugar Solution 30%(30% 설탕물): 1.38
⊙ Sugar Solution 80%(80% 설탕물): 1.49
⊙ Topaz(황옥): 1.61
⊙ Water_섭씨 20도에서의 물: 1.333
⊙ Zinc Crown Glass: 1.517

41. Recursive Ray Tracing
Ray Tree represents illumination computation

42. Recursive Ray Tracing GetColor call RayTrace recursively
Image RayTrace(Camera camera, Scene scene, int width, int height) {
Image image = new Image(width, height);
for (int i; i< width; i++)
for (int j=0; j<height; j++) {
Ray ray=ConstructRayThroughPixel(camera, i, j);
Intersection hit = FIndIntersection(ray, scene);
Image[i][j]=GetColor(scene, ray, hit); }
return image;

43. Recursive Ray Tracing GetColor is called recursively
Color GetColor(Scene scene, Ray ray) {
Intersection hit = FindIntersection(ray, scene);
Ray specular_ray = SpecularRay(ray, hit);
Ray refractive_ray = RefractiveRay(ray, hit);
Color color = Phong(scene, ray, hit) +
Ks * GetColor(scene, specular_ray, hit) +
Kt * GetColor(scene, refractive_ray, hit);
return color; }

44. Summary Ray casting (direct illumination)
Usually use simple analytic approximations for light source emission and surface reflectance
Recursive ray tracing (global illumination)
Incorporate shadows, mirror reflections, and pure refractions
All of this is an approximation
So that it is practical to compute

45. Illumination Terminology
Radiant power [flux] (F)
Rate at which light energy is transmitted (in Watts)
Radiant Intensity (I)
Power radiated onto a unit solid angle in direction (in Watts/sr)
Ex) energy distribution of a light source (inverse square law)
Radiance (L)
Radiant intensity per unit projected area (in Watts/m2/sr)
Ex) light carried by a single ray (no inverse square law)
Irradiance (E)
Incident flux density on a locally planar area (in Watts/m2)
Ex) light hitting a surface at a point
Radiosity (B)
Exitant flux density on a locally planar area (in Watts/m2)