1. CSE 470 Introduction to Computer Graphics Arizona State University
Lighting
CSE 470 Introduction to Computer Graphics
Arizona State University
Dianne Hansford

2. Lighting Overview Elements of a lighting model
The Phong illumination model
Application of the Phong model Shading methods: flat, Gouraud, Phong
OpenGL aspects

3. Perception of an object influenced by:
light sources: number, type, color
reflections
material properties: reflection & absorption of light
3D feel – depth perception
CG: approximate
real-world lighting with a model

4. CG Lighting Models Local Single interaction of light & objects
Phong illumination model
Global Multiple interaction of light & objects raytracing or radiosity

5. Elements of the Phong Model
Light Source Properties
ambient light
diffuse light
specular light
point source vs spotlight
positional vs directional

6. Light Source Properties
ambient light scattered, no detectable direction backlighting in a room
diffuse light directional, scatters once hits object, closest to the color of light
specular light directed and bounces off object in preferred direction plays a role in shininess

7. Elements of the Phong Model
Material (object) properties influences interaction with light
1. reflectance of light
a. ambient b. diffuse
c. specular d. translucent (opaque)
2. surface normals
3. emissive color

8. Material Properties
ambient reflectance amount of ambient light most visible where no direct light hits
diffuse reflectance degree of scattering of light on surface matte vs flat paint finish
specular reflectance degree of mirror-like quality

9. Light & Material Properties Examples
increasing diffuse
increasing ambient
increasing specular

10. Light & Material Properties
absorption/reflectance influence on color
Example:
red ball will reflect red light
absorb green and blue light
white light illuminating a red ball  red ball
green light illuminating a red ball  black ball

11. Notation: Light Properties
Model is computed independently for red, green, blue components
Light’s luminance represented by boldface vectors:
La := ambient
Ld := diffuse
Ls := specular
% of full intensity
r g b
Each vector takes form

12. Notation: Material Properties
Material’s properties represented by boldface vectors:
ka := ambient
kd := diffuse
ks := specular
% of reflection of light source’s corresponding property
r % g % b %
0 <= r,g,b % <= 1
Each vector takes form

13. Math of the Phong Model Primary geometry v p point on surface
l light – p vector
n normal to surface
r reflection vector
v viewpoint – p vector
theta angle of incidence
phi angle between v and r p
Recall: angle of incidence
equals angle of reflection
All vectors normalized

14. Phong Model in OGL vertex color = material emission‡
+ (global ambient light scaled by material ambient property)
+ (ambient, diffuse, specular of lights, attenuated by material properties, viewer location and light position)
‡ at vertex

15. Diffuse Intensity Calculation
Lambert’s
Law:
light reflected is proportional to the cosine of the angle (theta) between surface normal n and light vector l
theta is called the angle of incidence

16. Diffuse Intensity Calculation
Id := intensity of reflected diffuse light
Id = kd x Ld x cos(theta)
cos(theta) = l • n
angles 0 90°
Id = kd x Ld x (max{l • n, 0})
“x” is not cross product 3 separate scalar products
“• “ is dot product
Note: independent of viewer

17. Specular Intensity Calculation
Is := intensity of reflected specular light
Basic idea: Is = ks x Ls x cos^s(phi)
cos(phi) = v • r r = [2(l•n)]n - l
phi = 0°  full specular
|phi| > 90°  no specular
(never compute angle directly)
Focus of specular influenced by s
Note: depends on viewpoint

18. Specular Intensity Calculation
s: Phong constant or “shininess” coefficient
cos^s(phi)
s=0.1
spread
s=1
s=10
focus
- 90°
90°

19. Specular Intensity Calculation
Blinn-Torrence modification – simplification for faster computation
h = (l + v) / || l + v || “halfway” vector
cos(alpha) = h • n
alpha ~ ½ phi
so good approximation

20. Specular Intensity Calculation
Is = ks x Ls x [max{h • n, 0}]^s
if l • n < 0 then Is = 0
(no diffuse, no specular)

21. Attenuation Function For a positional light ...
d := distance of light source to vertex
ogl choices for functions
constant
linear
quadratic
f(d) = 1/a
f(d) = 1/(a + b*d)
f(d) = 1/(a + b*d + c*d^2)
inverse distance functions  diminish intensity d increases
for directional light, f(d) = 1

22. Spotlight Effect c Cone-shaped spotlight defined by: gamma c position
gamma “cut-off” angle
d direction d
sp := spotlight effect for a light source
defined by angle between -l and d :
cos(delta) = -l • d
if delta > gamma sp = 0
else sp = (max{-l • d, 0})^p
p influence similar to
Phong constant;
focus of intensity

23. Putting It All Together
Phong Model
I := intensity at a vertex
e := emission intensity at a vertex
Ma := ambient intensity for the entire model
I = e + (ka x Ma)
+ for each light { [f(d) * sp * (ka*La + Id + Is)] }
Remember: boldface indicates r,g,b values

24. Shading Methods Phong model  color of vertex
Shading methods  color of triangle
Methods:
Flat shading
Gouraud (smooth) shading
Phong‡ Shading
in ogl
Recall: triangle normal .vs.
averaged vertex normal
‡ confusing, but different from Phong illumination model

25. Flat Shading One normal per triangle
Simulates viewer and light source distant
then v, n, l same over triangle
 one shading calculation

26. Gouraud (smooth) Shading
One normal per vertex
Lighting calculation made at each vertex  I1, I2, I3
Lighting at any point p within triangle v1, v2, v3
I = b1*I1 + b2*I2 + b3* I3
where b1, b2, b3 are the
barycentric coordinates
of p wrt v1, v2, v3
p = b1*v1 + b2*v2 + b3*v3
(b1 + b2 + b3 = 1)

27. Phong Shading One normal per vertex ... however
a normal is calculated for each rendered point p in triangle
vertex normals n1, n2, n3
p = b1*v1 + b2*v2 + b3*v3
n = b1*n1 + b2*n2 + b3*n3
Calculate intensity at p wrt n

28. Resources
Many figures for these slides were taken from Pascal Vuytsteker’s website:
Delphi3d’s Phong for dummies

29. Material Properties

30. Material Properties