CS488 - Introduction to Computer Graphics - Lecture 23

Ray Tracing

Distribution Ray Tracing

What's wrong with

Beam tracing
Super sampling
Stochastic sampling

It doesn't try explicitly to put the work into the places that make the most difference.

Trying to do so we should get heuristics like

If <xxx> is important, then put extra rays into <yyy>.

Here are a few such heuristics

Distribute carefully over

Reflection directions <==>
- you want better highlights.
- Put extra rays in the highlight
- How?
  - Ray-trace a coarse image
  - find the pixels/rays that contribute to the highlight
  - Send extra rays between and near them
Area lights <==>
- you want soft shadows
- Put extra rays at the edges of the shadows
- How?
  - Ray-trace coarsely with a point light source
  - determine pixels/rays that are near the edges of shadows
  - Send extra rays doing a more complex lighting calculation near shadow edges
- How would you get them?
Time <==>
- you want motion blur.
- Concentrate on the objects that are moving
- How?
  - Ray-trace coarsely for different times
  - Determine pixels/rays that change between the images
  - Cast extra rays there for even more times
  - Average
Anti-aliasing
- You want better anti-aliasing
- Put extra rays where more than one primitive contributes to an object
- How?
  - Ray trace coarsely
  - Run an edge detector to find pixels/rays on edges
  - Cast extra rays for those pixels and their neighbours.

These techniques are hard!

Not to cast the extra rays
But to find out where extra rays are needed.

Modelling

Constructive Solid Geometry (CSG)

Geometric primitives can make other geometric primitives by

union
intersection
subtraction

This is like sculpting.

The result of doing CSG modelling is a complex Boolean expression to be evaluated.

Idea. Do it not on the volumes of objects but on the rays.
Then work out the Boolean expression

E.g. Cylinder, A, with stretched cube, B, subtracted unioned with a small sphere, C.

(A - B ) \union C

On the ray

    Bin    Ain     Cin     Bout     Cout     Aout
_____________________________________________________
A
           ____________________________________
B
    _________________________
A-B
                             __________________
C
                    ___________________
(A-B) \union C
                    ___________________________

build the expression tree
for each CSG primitive
   find entry and exit intersections
   recursively evaluate the expression tree

Texture Mapping

Basic

Start with a 2D image: pixellated or procedural
Map 2D image onto primitive using a 2D affine transformation
- Simple if the surface of the primitive is flat
- otherwise, ...
Backwards map intersection point with ray into the image to get the surface properties

Normal Mapping, aka Bump Mapping

Start with a difference surface, defined with respect to the surface
Calculate the normals to the difference surface and map them onto the surface of the primitive
Use the mapped surface models for lighting
No occlusion, shadows are wrong, silhouettes are wrong, nobody notices!

Solid Textures

Solution to mapping texture onto curved surfaces
- or objects like wood or marble where we see differently oriented surfaces
Usually procedural