1. Lighting and Shading Wen-Chieh (Steve) Lin
Department of Computer Science
I-Chen Lin’ CG Slides, Doug James’ CG Slides,
Angel, Interactive Computer Graphics, Chap 6
Shirley, Fundamentals of Computer Graphics, Chap 9

2. Illumination and Shading
Is it a ball or a plate?
What color should I set for each pixel?
ILE5014 Computer Graphics 10F

3. Why Do We Need Shading?
Suppose we color a sphere model. We get something like
But we want
ILE5014 Computer Graphics 10F

4. Shading Why does the image of a real sphere look like
Light-material interactions cause each point to have a different color or shade
Need to consider
Light sources
Material properties
Location of the viewer
Surface orientation
ILE5014 Computer Graphics 10F

5. Factors that affect the “color” of a pixel
Light sources
Emittance spectrum (color)
Geometry (position and direction)
Directional attenuation
Objects’ surface properties
Reflectance spectrum (color)
Geometry (position, orientation, and micro-structure)
Absorption
ILE5014 Computer Graphics 10F

6. Light and Matter Light strikes A Some of reflected light strikes B
Some reflected
Some absorbed
Some of reflected light strikes B
Some of reflected light reflected back to A and B, and so on
Rendering equation describes this recursive process
ILE5014 Computer Graphics 10F

7. Rendering Equation
The infinite reflection and absorption of light can be described by the rendering equation
[outgoing] = [emitted] + [reflected] (+[transmitted])
Cannot be solved in general
Ray tracing is a special case for perfectly reflecting surfaces
Rendering equation is global and includes
Shadows
Multiple reflection from object to object
ILE5014 Computer Graphics 10F

8. Global Effects shadow transmission multiple reflection
translucent surface
ILE5014 Computer Graphics 10F

9. Local vs Global Illumination
Correct shading requires a global calculation
Incompatible with a pipeline model which shades each polygon independently (local rendering)
However, in computer graphics, especially real time graphics, we are happy if things “look right”
many techniques for approximating global effects exist
ILE5014 Computer Graphics 10F

10. Local Illumination Adequate for real-time graphics.
No inter-reflection, no refraction, no realistic shadow ….
ILE5014 Computer Graphics 10F

11. Light Sources General light sources are difficult to simulated
because we must integrate light coming from all points on the source
ILE5014 Computer Graphics 10F

12. Simple Light Sources Point light Directional light Spotlight
Model with position and color
Directional light
Distant source = infinite distance away (parallel)
Spotlight
a point light source with a small light cone radius
Ambient light
Same amount of light everywhere in scene
Can model contribution of many sources and reflecting surfaces
ILE5014 Computer Graphics 10F

13. Surface Types
The smoother a surface, the more reflected light is concentrated in the direction
A very rough surface scatters light in all directions
smooth surface
rough surface
ILE5014 Computer Graphics 10F

14. Phong Reflection (Lighting) Model
A simple model that can be computed rapidly
Has three components
Ambient
Diffuse
Specular
Uses four vectors
To source l
To viewer v
Normal n
Perfect reflector r
r = 2 (l · n ) n - l
ILE5014 Computer Graphics 10F

15. Ambient Light
The result of multiple interactions between (large) light sources and the objects in the environment.
Ia = kaLa
ambient light intensity
ILE5014 Computer Graphics 10F

16. Diffuse Reflection Light scatters equally in all directions
Reflected intensities vary with the direction of the light.
Lambertian Surface
Perfect diffuse reflector
Id = kd (l·n) Ld
ILE5014 Computer Graphics 10F

17. Specular Surfaces
Most surfaces are neither perfectly diffuse nor perfectly specular (ideal reflectors)
Incoming light reflects in concentrated directions close to the direction of a perfect reflection
specular
highlight
ILE5014 Computer Graphics 10F

18. Modeling Specular Relections
Phong model
Is = ks Ls (r·v)α
= ks Ls cosαΦ f
shininess coefficient
reflected
intensity
incoming intensity
absorption coefficient
ILE5014 Computer Graphics 10F

19. The Shininess Coefficient α
Values of α between 100 and 200 correspond to metals
Values between 5 and 10 give surfaces that look like plastic
ILE5014 Computer Graphics 10F

20. Distance Terms Account for attenuation
Original: Inversely proportional to the square of the distance d between light source and surface
Modified: add a factor of the form 1/(a + bd +cd2) to the diffuse and specular terms
The constant and linear terms soften the effect of the point source
ILE5014 Computer Graphics 10F

21. Adding up the Components
A primitive virtual world with lighting can be shaded by combining the three light components:
I = Iambient + Idiffuse + Ispecular
= kaLa + kd (l · n) Ld + ks Ls (v · r )α
diffuse
diffuse +
specular
diffuse +
ambient
ILE5014 Computer Graphics 10F

22. Coefficients 3 color channels and 3 surface types
9 coefficients for each point light source
Lra, Lrd, Lrs, Lga, Lgd, Lgs, Lba, Lbd, Lbs
Material properties
9 absorption coefficients
kra, krd, krs, kga, kgd, kgs, kba, kbd, kbs
Shininess coefficient α
ILE5014 Computer Graphics 10F

23. Modified Phong Model r = 2 (l · n ) n - l
Problem: In the specular component of Phong model, it requires the calculation of a new reflection vector and view vector for each vertex
Blinn suggested an approximation using the halfway vector that is more efficient
r = 2 (l · n ) n - l
ILE5014 Computer Graphics 10F

24. The Halfway Vector h is the normalized vector halfway between l and v
h = ( l + v )/ | l + v |
ILE5014 Computer Graphics 10F

25. Using the Halfway Angle
Replace (v · r )α by (n · h )b
b is chosen to match shininess
Note that halfway angle is half of angle between r and v if vectors are coplanar n β
Θ-β h l r θ θ Φ v
ILE5014 Computer Graphics 10F

26. Blinn lighting model
Resulting model is known as the modified Phong or Blinn lighting model
Specified in OpenGL standard and most real-time applications
ILE5014 Computer Graphics 10F

27. Example Teapots with different parameters.
ILE5014 Computer Graphics 10F

28. What’s next?
So far, we know how to compute the color at a point given lighting model, illumination model, and surface normals
The required computation can be huge if we compute for every point on a surface
Exploit efficiency by decomposing curved surfaces into many small flat polygons
ILE5014 Computer Graphics 10F

29. Polygonal Shading Curved surfaces are approximated by polygons
How do we shade?
Flat shading
Interpolative shading
Gouraud shading
Phong shading (not Phong reflection model)
Two questions:
How do we determine normals at vertices?
How do we calculate shading at interior points?
ILE5014 Computer Graphics 10F

30. Flat Shading: Normal: given explicitly before vertex
Shading constant across polygon
Single polygon: first vertex
Triangle strip: vertex n+2 for triangle n
glShadeModel(GL_FLAT);
glNormal3f(nx, ny, nz);
glVertex3f(x, y, z);
ILE5014 Computer Graphics 10F

31. Flat Shading Assessment
Inexpensive to compute
Appropriate for objects with flat faces
Less pleasant for smooth surfaces
ILE5014 Computer Graphics 10F

32. Flat Shading and Perception
Lateral inhibition: exaggerates perceived intensity
Mach bands: perceived “stripes” along edges
ILE5014 Computer Graphics 10F

33. ILE5014 Computer Graphics 10F

34. Interpolative Shading
Enable with glShadeModel(GL_SMOOTH);
Calculate color at each vertex
Interpolate color in interior
Compute during scan conversion (rasterization)
More expensive to calculate
ILE5014 Computer Graphics 10F

35. Gouraud Shading Special case of interpolative shading
How do we calculate vertex normals?
Gouraud: average all adjacent face normals
Requires knowledge
about which faces share
a vertex—adjacency info
ILE5014 Computer Graphics 10F

36. Gouraud Shading Algorithm
Find average normal at each vertex
Apply Phong reflection model at each vertex
Linearly interpolate vertex shades (colors) across each polygon
I1(x1, y1)
Ia(xa, ys)
Ib(xb, ys)
Is(xs, ys)
I2(x2, y2)
I4(x4, y4)
I3(x3, y3)
ILE5014 Computer Graphics 10F

37. Problem with Gouraud Shading
See the artifact of specular highlight on a rotating sphere
Highlight lies inside a polygon will not be apparent
Highlight occurs at vertex will be spread unnaturally across all neighboring polygons
if a highlight lies in the middle of a polygon, but does not spread to the polygon's vertex, it will not be apparent in a Gouraud rendering; conversely, if a highlight occurs at the vertex of a polygon, it will be rendered correctly at this vertex (as this is where the lighting model is applied), but will be spread unnaturally across all neighboring polygons via the interpolation method. The problem is easily spotted in a rendering which ought to have a specular highlight moving smoothly across the surface of a model as it rotates. Gouraud shading will instead produce a highlight continuously fading in and out across neighboring portions of the model, peaking in intensity when the intended specular highlight passes over a vertex of the model
ILE5014 Computer Graphics 10F

38. Phong Shading Interpolate normals rather than colors
Significantly more expensive
Not supported in OpenGL
Can be implemented using pixel shader
In Phong shading we linearly interpolate a normal vector across the surface of the triangle from the three given normals. The surface normal is interpolated and normalized at each pixel and then used in the Phong reflection model to obtain the final pixel color. Phong shading is more computationally expensive than Gouraud shading since the reflection model must be computed at each pixel instead of at each vertex.
In some modern hardware, variants of this algorithm are implemented using pixel or fragment shaders.
ILE5014 Computer Graphics 10F

39. Phong Shading Algorithm
Find vertex normals
Interpolate vertex normals across edges
Interpolate edge normals across each line
Compute shades at each pixels of a polygon
The most serious problem with Gouraud shading occurs when specular highlights are found in the middle of a large triangle. Since these specular highlights are absent from the triangle's vertices and Gouraud shading interpolates based on the vertex colors, the specular highlight will be missing from the triangle's interior. This problem is fixed by Phong shading.
ILE5014 Computer Graphics 10F

40. Polygonal Shading Summary
Gouraud shading
Set vertex normals
Calculate colors at vertices
Interpolate colors across polygon
Must calculate vertex normals!
Must normalize vertex normals to unit length!
ILE5014 Computer Graphics 10F

41. Problems with Interpolated Shading
Polygonal silhouette
Perspective distortion
Orientation dependence
Problems at shared vertices
Unrepresentative vertex normals
ILE5014 Computer Graphics 10F