Lecture 4

scheduled: Saturday, Jan 22, 2005

We discussed:

1. Problems with CSG

• Redundancy - A considerale part of a huge tree may result in a null-space.
• The operations at each level is much. The cost of CLASSFY increases considerable with the increase in the CSG-Tree size.
• Allowing very simple primitives poses restriction to the users.
• There is no provision to preserve the precomputed boundary-info (this computation is costly.
  

2. B-rep. Topological information is represented separately from the location/geometric information. In topological representation, we have one structure binding the other in a hierarchy. Say for instance, a solid/space is bounded by surfaces, a surface is bounded by edges and so on. Classification methods can be used to convert a CSG to B-rep.

3. The parameteric representation of a ray (say, emerging from the point (20,20,20) and passing through (-10,20,30)) helps in solving the 'classify' against a solid (say, {(x, y, z) | (x-3)^2 + (y-8)^2 <= 9, 0 <= z <= 12}). We saw, how do we decide the topological placement of the point w.r.t. the solid.

4. What are

• 2-manifold surfaces; nice and non-nice-objects
  
• orientability of a surface.
• Compactness of a solid.
  

5. An example of how a CGS operation can lead to a non-nice objects.

6. Home work!