This is a course on the theoretical underpinnings of 3D Graphics in computing, suitable for students with a suitable grounding in technical computing.

1. RAY-TRACING AND
RADIOSITY
Michael Heron

2. INTRODUCTION
 Thus far our discussion of 3D graphics has
concentrated mainly of real-time rendering.
 In today’s lecture, we will discuss the two main
techniques for non real-time rendering.
 Raytracing
 Radiosity

3. REFLECTION MODELS
 Local reflection model
 Imagine lights and objects are floating in dark space
 Considers only direct illumination
 Global reflection model
 Indirect light considered
 Light is reflected multiple times
 Much more computationally expensive.
 Outside the reach of most real-time applications.
 For now…

4. LOCAL VERSUS GLOBAL
Direct
illumination
only
Local model
Light source
Global model
Direct and
indirect
illumination

5. GLOBAL ILLUMINATION
 In theory, for this we:
 Trace rays from each light source to each point
visible from that light source
 Trace reflections and refractions from this point to
other surfaces
 Continue until:
 We reach the viewport, or
 We exit the scene entirely
 Approximations still used
 Can’t trace all rays of light from a light source.

6. RAY-TRACING
 Ray tracing is the process of tracing the
path of light through pixels in an image.
Capable of producing high degrees of realism.
 Still not quite photorealistic, but not far off.
High computational cost
 Best used for scenes and animations that can be pre-
rendered.
 Incorporates many aspects of physics
Light reflection
Light refraction
Light scattering

7. RAY-TRACING
 Rays send away from the camera rather
than to it
Most rays of light emitted from a source would
not hit the viewing plane.
 Comparable method called photon mapping exists.
 Many orders of magnitude more expensive to calculate.
 Provides advantages:
Reflections and shadows realistically produced
 And disadvantages:
Expensive to calculate each scene
Still an approximation

8. RAY-TRACING
Rays sent backwards
from the camera.
Much less
computationally
expensive than the
alternative.
http://www.codinghorror.com/blog/archives/001073.html

9. LIGHT INTERACTIONS
 Remember our different kinds of light
interactions.
Perfect Specular
Imperfect Specular
Diffuse
 Must be able to combine light interactions
in a ray-tracing model.
Specular to Diffuse
Diffuse to Specular
And so on

10. TRANSMISSION OF LIGHT
 Indirect transmission of light occurs in several
ways
 Reflection
 Transparent refractions
 Translucent diffusion
 Transparency should refract light
 It looks unrealistic otherwise.
 Translucency transmits light in multiple new
directions.

11. RAY-TRACING
 For each pixel, we calculate the ray from the
centre of the viewport through that pixel.
 Find the intersection of that ray with the nearest
object.
 Determine the pixel colour based o surface
properties, orientation, and light intensities
 This may in itself have a component from reflected or
refracted light rays
 If the surface is reflective or transparent,
generate a new ray.
 Trace that onwards.
 Repeat for all pixels.
 If no intersection, pixel colour is background
colour.

12. RAY-TRACING
 Secondary rays may be used for diffuse reflection.
 Generate multiple new rays and trace them on.
 Depends on the kind of reflection needed.
 Each secondary ray is followed until it hits another
object, light source, or background.
 Recursion is used to permit this relationship to
extend to predefined limits.

13. RAY-TRACING RESULTS

14. EFFICIENCY
 Expense of computation based on number
of calculations required.
Consider a 1000x1000 resolution.
 On a scene with 1000 objects.
 With a single light source.
 Consider primary illumination first
 How about secondary rays?
 Further orders of illumination?
 How about a second light source?
 Or a third?
 Various optimisation schemes exist.

15. RADIOSITY
 Radiosity is based on a model of radiative
heat transfer.
Assumes conservation of light energy in a
closed environment.
 Energy emitted or reflected by every
surface accounted for by:
Absorption
Reflection
Refraction
Fluorescence

16. RADIOSITY
 All surfaces are broken up into patches
and elements.
Patches can emit or send light
 They send light to other parts of the model.
Elements can absorb light
 They receive light from other parts of the model.
 Number of patches relates to
computational intensity.
 Each element is associated with a patch.
Indeed, a patch may have many elements

17. RADIOSITY
 Radiosity works through a system of progressive
refinement
 Start with the patch which has most energy to ‘shoot’
 Each of the elements receive the energy appropriately, and
add to the energy of their own patches.
 Repeat with the patch which now has the most unspent
energy.
 Repeat until all patches are empty, or some minimal bound is
reached.

18. RADIOSITY
Every polygon
gets treated as a
patch (a light
source)
Every patch is
associated with a
number of
elements,
http://www.cs.princeton.edu/courses/archive/fall00/cs426/lectures/ra
diosity/radiosity.pdf

19. PATCHES
 Patches may be present in higher resolution than
surfaces.
 One surface may be broken up into many patches.
 Subdivision algorithms used to further refine
patch mapping over surfaces.
 Can be done blindly
 Or intelligently
 Focus at areas of high contrast in light levels.

20. RADIOSITY – A FIRST APPROACH
 Imagine a simple room
 Four walls
 A Ceiling
 A Floor
 No light source
 Radiosity makes each of the surfaces in the scene a light
source.
 Some of these surfaces may have no energy to spend to begin
with.
 Imagine the roof as a giant light source.
 Like in a supermarket
 Each surface stores:
 How brightly lit it is
 How much surplus energy it has to spend.
 We must calculate the interaction of energy to surface of
all surfaces in the scene.
 Can be calculated in many ways. Most usual is by geometric
distance.
 The resulting number is the form factor.

21. RADIOSITY
Radiosity creates a scene of soft
diffuse light. Represents the
interaction of surfaces well, but
cannot suitably deal with specular
reflection.
http://www.cs.dartmouth.edu/~spl/
Academic/ComputerGraphics/Fall2
004/outline.html

22. GLOBAL REFLECTION MODELS
 Ray Tracing
 Simulates perfect specular reflections
 Good for shiny objects reflecting in each other.
 Ray-traced images tend to have lots of shiny objects
with perfect reflections.
 Is viewport dependant.
 Change the viewport and you need to rerender.
 Radiosity
 Simulates the interactions of diffuse light
 Good for matte surfaces
 Images rendered using radiosity tend to be softly lit
rooms without shiny objects.
 Is viewport independent.
 Change the viewport and the radiosity image remains the
same.

23. GLOBAL REFLECTION MODELS
 Best results obtained by combining the two into a
two-pass method.
 Radiosity used to build a model of diffuse
illumination across a scene.
 Raytracing used to build a viewport dependant
illumination of the scene.
 Combination of two has representation of specular
and diffuse radiation.
 Permits soft and hard lighting in a single scene.

24. TWO PASS - RAYTRACING

25. TWO PASS - RADIOSITY

26. TWO PASS - COMBINED

27. SUMMARY
 Non real-time rendering works through two
primary methods.
 Ray-tracing
 Map the path of light from a viewport to objects.
 Radiosity
 Light interactions modelled as energy interactions between
patches.
 Best results obtained by combining both
approaches into a two-pass algorithm.