1. Fundamentals of Computer Graphics Part 6 Shading
prof.ing.Václav Skala, CSc.
University of West Bohemia
Plzeň, Czech Republic
©2002
Prepared with Angel,E.: Interactive Computer Graphics – A Top Down Approach with OpenGL, Addison Wesley, 2001

2. Shading – Light and Matter
Our perception depends on:
light directly – intensity, spectrum (color), position
material of objects that “reflects” or “transmit” light, roughness, color of the surface
Speed of computation – significant factor
Fundamentals of Computer Graphics

3. Shading – Light and Matter
Generally we do not need to compute all, but just those rays that contribute to the final image
Methods:
Global – ray tracing, radiosity – very slow
Local – constant, Gouraud, Phong etc. – relatively fast
Fundamentals of Computer Graphics

4. Shading – Light and Matter
Interaction between light and materials can be classified as
specular surfaces – ideal mirror
diffuse surfaces – reflected light is ideally reflected to all directions uniformly
translucent surfaces – allow some lights to penetrate the surface – refraction – glass, watter
optical properties – Snell’s law
Fundamentals of Computer Graphics

5. Shading – Light sources
Light source – an object with a surface
Each point (x,y,z) on the surface can emit light with characterization:
direction of emission (,)
intensity of energy emitted at each wavelength 
illumination function I(x,y,z,,,)
Basic light sources (sufficient for rendering the most simple scenes):
ambient lighting
point sources
spotlights
distance light
Fundamentals of Computer Graphics

6. Shading – Light sources
Light - an object with a surface
Each point (x,y,z) on the surface can emit light with characterization:
direction of emission (,)
intensity of energy emitted at each wavelength 
illumination function I(x,y,z,,,)
Usually I = [ Ir , Ig , Ib ]T
is handled as a scalar value
Basic light sources - sufficient for rendering the most simple scenes:
ambient lighting
point sources
spotlights
distance light
Fundamentals of Computer Graphics

7. Shading – Light sources
Ambient light Ia- uniform light in the space (room etc.)
Ideal point source – emits equally in all directions I(p0)
Light received at a point p
full shadow – umbra partial shadow – penumbra
for non-point sources (d is distance)
Fundamentals of Computer Graphics

8. Shading – Light sources
Spotlights – very narrow angles of emission, if  = 180° -> point source
distribution of light within the cone – usually cose() ; e determines how rapidly intensity drops off
cos() = sT l
s – vector that points from ps to a point s on a surface
l – vector of the light direction
Fundamentals of Computer Graphics

9. Shading – Distant light sources
we replace location of light sources with their directions
p0 = [ x , y , z , 0 ]T ( 0 is correct !)
Phong Reflection Model
I = Ia + Id + Is
disadvantages
linear model
superposition
Fundamentals of Computer Graphics

10. Ambient, Diffuse, Specular Reflections
Ambient reflection
0  ka  1
Ia = ka La global ambient term or light
Diffuse reflection
characterized by rough surfaces
perfectly diffuse surfaces – Lambertian surfaces
Fundamentals of Computer Graphics

11. Ambient, Diffuse, Specular Reflections
Lambert’s law:
diffuse reflection 0  kd  1
if the influence of the distance is considered
Fundamentals of Computer Graphics

12. Ambient, Diffuse, Specular Reflections
Specular Reflection: 0  ks  1
as  ideal specular reflection
  <100 , 500> metallic surfaces
Fundamentals of Computer Graphics

13. Fundamentals of Computer Graphics
Polygonal Shading
How to display surfaces with shading?
Flat (constant) shading
glShadeModel(GL_FLAT);
Mach bands
Fundamentals of Computer Graphics

14. Fundamentals of Computer Graphics
Polygonal Shading
Interpolative and Gouraud shading
Gouraud shading
glShadeModel(GL_SMOOTH);
normal in a vertex
average normal vector
intensity computation for a vertex
intensity & color interpolation for a scan-line
Fundamentals of Computer Graphics

15. Fundamentals of Computer Graphics
Polygonal Shading
Phong shading
normal in a vertex
interpolation of a normal
normal interpolation along the scan-line
intensity computation
Phong shading is almost always done off-line
Fundamentals of Computer Graphics

16. Light Sources in OpenGL
Study 6.6 – 6.9 on your own
Fundamentals of Computer Graphics

17. Global Rendering – Ray tracing
global versus local lightings models
Fundamentals of Computer Graphics

18. Global Rendering – Ray tracing
Algorithm complexity:
O(M2 N 2k)
M – resolution of a screen
N – number of objects
k – number of levels of the tree
Typical program:
POV Ray – available free
Fundamentals of Computer Graphics