cgal/Kinetic_shape_reconstruction/todo.md

• Use the exact tag in the Delaunay triangulation.
• After converting exact to inexact, we may have equal points in the bbox faces. We should fix that. Can we?
• Can we accelerate initializer when using exact kernel?

QUESTIONS:

1. The first step: we compute N full line arrangements. That gives an intersection graph. But to get it, we need to intersect 3D planes. Right?
2. How do they handle cases with multiple coplanar polygons?
3. Can we avoid kinetic completely? What if we use labeling instead?
4. What is the exact stop criteria for k intersections? When two polygons intersect at the very beginning, does it count as an intersection? How to count it when we meet an iedge or an ivertex? Can we squeeze through the whole or not?
5. It looks like for open case, we never insert new polygons. Or better, do we need open case at all? Maybe it should be reassigned into closing case! Because, in the original paper, they do not have such a case.
6. Graph-cut based surface extraction does not guarantee a 2-manifold. What if we simply stop when we meet a roof polygon or another wall polygon? In this case, we do not guarantee convex polyhedra but who cares?
7. Do we use the trick from the paper when inserting only the first three events (corresponding to the three closest lines) of an active vertex in the queue instead of all possible events?

ANSWERS:

1. Do we need to intersect all 3D planes in order to find N full line arrangements?

• Yes.

2. How do you handle cases with multiple coplanar polygons?

• Merge polygons, which are at the same cell.

3. Can we avoid kinetic completely?

• Probably yes, but there is a problem of how to find the correct criteria that guarantees the volume convexity. But we can use the trick with tagging pfaces at least for all initial polygons.

4. Do you have any guarantee on the number of final volumes? Is this number optimal for each k?

• No, it is super difficult.

5. When two polygons intersect at the very beginning, does it count as an intersection? Can we squeeze through the whole or not?

• Both are ok.