1. Illumination Model
고려대학교 컴퓨터 그래픽스 연구실

2. Shading Compute the radiance for each object
Figure out which pixels to fill
Determine a color for each filled pixel

3. Illumination Components
Emission at light sources
Scattering at surfaces
Wireframe
Without Illumination
With Illumination

4. Light Source Model Simple mathematical models Point light
Directional light
Spot light

5. Point Light Source Omni-directional point source, ex) bulb
Intensity (I)
Position (px, py, pz)

6. Directional Light Source
Point light source at infinity, ex) sun
Intensity (I)
Direction (dx,dy,dz)

7. Spot Light Source Point light source with direction, ex) Luxo
Intensity (I),
Position (px, py, pz)
Direction (dx, dy, dz)

8. Light Intensity Function
IE: emitted intensity for light sources
KA, KD, Ks
Ambient / diffuse / specular reflection coefficient
IAL: ambient light intensity
N: unit normal vector L
Unit direction vector to the point light source from a position on the surface
IL: the intensity of the point light source
V: unit viewing direction vector
R: specular reflection vector

9. Reflectance Model Simple analytic model Diffuse reflection
Specular reflection
Emission
Ambient

10. Diffuse Reflection Surface reflects equally in all directions
With equal intensity

11. Diffuse Reflection How much light is reflected? N L
Depends on angle of incident light
dL = dA cos  = N  L
Maximum at the head-on light ( = 0) N L

12. Specular Reflection Strongest reflection near the mirror angle
Examples: mirrors, metals

13. Specular Reflection How much light is reflected? Depends on
Angle of incident light
Angle to viewer

14. Ks: Specular Reflectance Factor
Specular Reflection
Phong model
{cos(a)}n = (VR)n
n: exponent
Ks: Specular Reflectance Factor

15. Effects of Exponent
Ambient
Exponent(n)

16. Emission Light emitting directly from surfaces ex) light source

17. Ambient Term
Compensated reflection of indirect illumination

18. Reflectance Model Simple analytic model Diffuse reflection
Specular reflection
Emission
Ambient

19. Reflectance Model Simple analytic model Diffuse reflection
Specular reflection
Emission
Ambient
Affected by the position of the light source
Not affected by the position of the light source

20. Ambient and Diffuse
Ambient
Diffuse

21. Surface Illumination Calculation
Single light source

22. Surface Illumination Calculation
Multiple light sources
Not Affected

23. Shadows Which light sources are blocked
Cast ray towards each light source Li
Si = 0 if ray is blocked, Si = 1 otherwise
Shadow Term

24. Transparency Alpha value Back to front
How much light can be transmitted?
Back to front

25. Polygon Shading Spatial coherence
Illumination calculations for pixels covered by the same primitive

26. Flat Shading Constant-intensity shading OK for polyhedral objects
Not so good for ones with smooth surfaces

27. Flat Shading Process One illumination calculation per polygon
Assign all pixels inside each polygon the same color
Polygon Normal Vector

28. <Gouraud Shading>
Intensity-interpolation scheme
Produces smoothly shaded polygonal mesh
Piecewise linear approximation
To capture subtle lighting effects
Needs fine mesh  Phong shading solves it
<Flat Shading>
<Gouraud Shading>

29. Mesh with Shared Normals at Vertices
Gouraud Shading
Polygonal mesh with the vertex normal vectors
Smooth shading over adjacent polygons
Curved surfaces
Illumination highlights
Soft shadows
Mesh with Shared Normals at Vertices

30. Gouraud Shading Process (1/2)
One lighting calculation per vertex
Assign pixels inside polygon
By interpolating colors computed at vertices N1
Viewer L1
Light V1 N2 N3
Polygon
Vertex Normal Vector

31. Gouraud Shading Process (2/2)
Bilinearly interpolate colors at vertices
Down and across scan lines I1 I I2 I3

32. Vertex Normal Vector Average of the surface normals
For each polygon sharing that vertex N2 N1 N3 N4

33. Phong Shading Normal-vector interpolation shading
Subtle illumination effects in polygon interiors

34. Phong Shading Process (1/2)
One lighting calculation per pixel
Approximate surface normals for inside points N1
Viewer L1
Light V1 N2 N3
Polygon

35. Phong Shading Process (2/2)
Bilinearly interpolate surface normals at vertices
Down and across scan lines N1 N α β γ N2 N3

36. Various Shading Results
<Wireframe>
<Flat>
<Gouraud>
<Phong>

37. Ray Casting & Tracing
Independent lighting calculation for every pixel

38. Ray Casting & Tracing

39. Ray Casting Find surface intersection point Visible surface detection
Ray from eye to the screen pixel
No reflection or refraction
Direct illumination
Visible surface detection
Shadow calculation

40. Ray Tracing Recursive ray casting
Inter-object light reflection effects
Global (mutual) illumination
For global reflection and transmission
Highly realistic quality vs. computation time
Overview
Bounce (reflect) or refract the ray
Collecting its intensity
At each reflection point

41. Ray Tracing Example
<Reflection and refraction ray paths through a scene for a screen pixel>

42. <Ray Tracing Tree>
Left branch: reflection
Right branch: transmission (refraction)
Terminate when
Reaches the defined maximum depth
Strikes the light sources
Accumulate the intensity
From the bottom to top
<Ray Tracing Tree>

43. Summary Polygon shading Ray casting Ray tracing Radiosity Flat shading
Gouraud shading
Phong shading
Ray casting
Ray tracing
Recursive ray casting
Inter-object reflection (global illumination)
Highly realistic quality vs. computation time
Radiosity
Supported by OpenGL

44. For Implementation

45. Intensity Calculation
For general object, IE = 0
IAL ≠ IE
Intensity calculation for RGB channel (IR, IG, IB)
KAR, KDR, KSR, KAG, KDG, KSG, KAB, KDB, KSB

46. Shading Function Example
IE = 0, KA = 0.2, KD = 0.4, KS = 0.1, IAL = 0.3, I0 = 0.8, n = 32 N1 N2 N3

47. Scan-line Shading Example2
1.5 2 1 N2 1 1 N3 P2 P3

48. Flat Shading Example N1 P1 N N2 N3 P2 P3

49. Gouraud Shading Example
I4=(I1*1+I2*2)/3 2
I5=(I1*1+I3*1.5)/2.5
1.5 2 1 N2 1
I=(I4*1+I5*2)/3 1 N3 P2 P3 I3 I2

50. 2 1.5 2 1 1 N=(N4*1+N5*2)/3 1 Phong Shading Example N1 P1 N2 N3 P2 P3