1. SI23 Introduction to Computer Graphics
Lecture 14 – Polygon Shading Techniques

2. Reflection Models
We have seen how the reflected intensity at a point may be calculated
A reminder of the Phong reflection model...

3. Phong Reflection Model
light
source N R
eye L  V 
surface
I() = Ka()Ia() + ( Kd()( L . N ) + Ks( R . V )n ) I*() / dist
dist = distance attenuation factor
In practice, we evaluate IRED, IGREEN, IBLUE for red, green, blue intensities:
IRED= KaREDIaRED + ( KdRED( L . N ) + Ks( R . V )n ) I*RED/dist

4. Phong Reflection Model
Remember calculation depends on:
surface normal at a point
light source intensity and position
material properties
viewer position
L.N and R.V constant if L, V taken to be far away

5. Viewing Polygons
We have also seen how a 3D polygon can be projected to screen space via a sequence of transformations
This lecture looks
at how we shade
the polygon, using
our reflection model

6. Constant (or Flat) Shading
light
viewer
Calculate normal (how?)
Assume L.N and R.V constant (light & viewer at infinity)
Calculate IRED, IGREEN, IBLUE using Phong reflection model
Project vertices to viewplane
Use scan line conversion to fill polygon N

7. 2D Graphics - Filling a Polygon
Scan line methods used to fill 2D polygons with a constant colour
find ymin, ymax of vertices
from ymin to ymax do:
find intersection with polygon edges
fill in pixels between intersections using specified colour
See lecture 6 for details of algorithm with edge tables etc
See also
Hearn&Baker, Ch 3

8. Polygonal Models
Recall that we use polygonal models to approximate curved surfaces
Constant shading will emphasise this approximation because
each facet will be constant shaded, with sudden change from
facet to facet

9. Flat Shading

10. Gouraud Shading
Gouraud shading attempts to smooth out the shading across the polygon facets
Begin by calculating the normal at each vertex N

11. Gouraud Shading N
A feasible way to do this is by averaging the normals from surrounding facets
Then apply the reflection model to calculate intensities at each vertex

12. Gouraud Shading
We use linear interpolation to calculate intensity at edge intersection P
IPRED = (1-)IP1RED + IP2RED
where P divides P1P2 in the ratio 1-
Similarly for Q P4 P2 P1 P3 P Q
1- 

13. Gouraud Shading
Then we do further linear interpolation to calculate colour of pixels on scanline PQ P2 P1 P3 P Q

14. Gouraud Shading

15. Henri Gouraud
Henri Gouraud is another pioneering figure in computer graphics

16. Gouraud Shading Limitations - Specular Highlights
Gouraud shading gives intensities within a polygon which are a weighted average of the intensities at vertices
a specular highlight at a vertex tends to be smoothed out over a larger area than it should cover
a specular highlight in the middle of a polygon will never be shown

17. Gouraud Shading Limitations - Mach Bands
The rate of change of pixel intensity is even across any polygon, but changes as boundaries are crossed
This ‘discontinuity’ is accentuated by the human visual system, so that we see either light or dark lines at the polygon edges - known as Mach banding

18. Phong Shading N
Phong shading has a similar first step, in that vertex normals are calculated - typically as average of normals of surrounding faces

19. Phong Shading
However rather than calculate intensity at vertices and then interpolate intensities as we do in Gouraud shading ...
In Phong shading we interpolate normals at each pixel ... P4 P2 P1 P3 P Q N2 N1 N

20. Phong Shading
... and apply the reflection model at each pixel to calculate the intensity - IRED, IGREEN, IBLUE P4 P2 P1 P3 P Q N2 N1 N

21. Phong Shading

22. Phong versus Gouraud Shading
A major advantage of Phong shading over Gouraud is that specular highlights tend to be much more accurate
vertex highlight is much sharper
a highlight can occur within a polygon
Also Mach banding greatly reduced
The cost is a substantial increase in processing time because reflection model applied per pixel
But there are limitations to both Gouraud and Phong

23. Gouraud versus Phong

24. Interpolated Shading Limitations - Perspective Effects
Anomalies occur because interpolation is carried out in screen space, after the perspective transformation
Suppose P2 much more distant than P1. P is midway in screen space so gets 50 : 50 intensity (Gouraud) or normal (Phong)
... but in world coordinates it is much nearer P1 than P2 P3 P2 Q P P1 P4

25. Interpolated Shading Limitations - Averaging Normals
Averaging the normals of adjacent faces usually works reasonably well
But beware corrugated surfaces where the averaging unduly smooths out the surface

26. Wall Lights

27. Wall Lights with Fewer Polygons

28. Final Note on Normals
If a sharp polygon boundary is required, we calculate two vertex normals for each side of the joint
NLEFT
NRIGHT

29. Simple Shading - Without Taking Account of Normals

30. Constant or Flat Shading - Each Polygon has Constant Shade

31. Gouraud Shading

32. Phong Shading

33. Phong Shading with Curved Surfaces

34. Better Illumination Model

35. Further Study Hearn and Baker, section 14-5
Think about the relative computational costs of flat, Gouraud and Phong

36. Acknowledgements Thanks again to Alan Watt for the images
The following sequence is the famous Shutterbug from Foley et al