1. GR2 Advanced Computer Graphics AGR
Lecture 14
Improving the Efficiency of Ray Tracing
Light Source Effects

2. Advantages and Disadvantages of Ray Tracing
Ray tracing is attractive because
shadows, reflections, refractions are easily incorporated
Ray tracing is expensive because
the cost of computing ray-object intersections is very high
This part of the lecture looks at efficiency issues in ray tracing

3. Ray Tracing - A Reminder
pixel positions
on view plane
camera
The intensity calculation
is now:
I = I local + k r * I reflected
+ k t * I transmitted
I reflected and I transmitted
are calculated recursively

4. Adaptive Tree Depth Control
Basic algorithm follows rays until they leave the scene (or hit diffuse surface) - in theory the tree depth can then be considerable
In practice, it is not usually necessary to trace rays to any great depth
As tree formed, a running product is kept of transmission and reflection coefficients
this product attenuates all intensities lower in tree
once product less than threshold, branch is stopped

5. Bounding Volumes Enclose groups of objects in a simple bounding volume
sphere or box
Test for intersection against bounding volume
if none, then ray does not intersect objects within
if intersection occurs, test against each object in turn
Idea can be extended to hierarchies of bounding volumes (usually boxes)

6. Spatial Subdivision
Idea: divide space into subregions, noting objects in each subregion
termed ‘spatial subdivision’ or ‘spatial coherence’
Calculation changes from:
for each object or bounding box, find ray intersection to
as ray proceeds through space, are there any objects in the current subregion?
if yes, calculate intersections; if not, move on
find next subregion entered by the ray

7. How do we Subdivide Space
One idea is octree partitioning
We illustrate in 2D - known as quadtree
First divide space into
four regions
Count number of objects
in each region
If a region contains an object,
subdivide again
Continue to a specified level
of subdivision

8. Octree A tree structure emerges, with the nodes at the leaves of
the tree containing (hopefully) a small number of objects,
or empty.
This is quadtree - in 3D
we subdivide cube into
8 each time, getting an
octree

9. Ray Tracing through Octree
We trace ray from subregion to subregion, only doing
intersection tests for the small number of objects in the
subregion.
Find region corresponding
to start point. Test ray for
intersections with any objects.
If none, find next region - by
calculating intersection with
region boundaries. Advance
a short way into next region -
say to (x,y,z)
Find region which includes
(x,y,z) and continue.

10. Finding Region Containing (x,y,z)
We use octree itself to locate region. Starting at top, a
simple test determines in which of eight (4 for quadtree)
regions the point (x,y,z) lies. Proceed down tree until
leaf node reached.

11. Binary Space Partitioning
An alternative to octrees is just to split into two at each step
separating plane typically chosen to divide space into regions of equal complexity
Known as Binary Space Partitioning, or BSP, trees

12. Octrees versus BSP trees
good for scenes where density of objects varies widely
possible to have small objects in large regions
stepping from region to region slow because trees tend to be unbalanced
BSP trees:
depth of tree smaller because tree balanced
memory costs lower
void areas smaller

13. Ray Tracing Software
Persistence Of Vision Ray Tracer (POV-RAY) is public domain ray tracing software
Download from:

14. More Teapots! The POVRAY version

15. POVLAB modeller

16. Lecture 14 Part 2 Light Source Effects

17. Light Source Sequence of Images
The following sequence of images were created by Alan Watt of University of Sheffield
They illustrate effects of different light sources in a scene

18. Ambient Light Only

19. Camera Light Source
Light source at
camera only.
Note no shadows.

20. Distant Light Source
Light rays parallel
to each other
Note shadows

21. Point Light Source Point light source close to object,
in same direction
as distant source
in previous picture.
Note shadows are
different.

22. Spotlight Spotlight in same position as previous point light.
Cone angle is
30 deg.
Note cone of
influence of the
light, and the
hard shadow.

23. Spotlight - Soft Shadows
Softer shadow
obtained by having
a gradual drop-off
of intensity at edge of
cone (here over last
5 deg)

24. Effect of Distance - No Attenuation
Here there is no
attenuation of light
over distance

25. Effect of Distance - Attenuation
Intensity is attenuated
by 1/distance

26. Effect of Distance - Attenuation
Here the
attenuation factor
is 1/(distance)2

27. Fog Intensity of fog increases linearly with depth. How is this
achieved?