CGAL
AABB_tree: Circle_2/Iso_rectangle_2 intersection with inclusion
Issue Details
The AABB_tree with 2D primitives uses its own do_intersect_circle_iso_rectangle_2 which considers inclusion as intersection while the corresponding function in Intersection_2 does not. The AABB_tree with 3D primitives also uses a static filter for some optimization which would also be helpful in the 2D variant.
https://github.com/CGAL/cgal/pull/8891 created the internal do_intersect_circle_iso_rectangle_2 in AABB_traits_2, which provides correct closest_point results.
Differences between 2D and 3D: A Segment_2 inside a Circle_2 is considered as intersection. All other contained objects are not considered intersections. Only a Bbox_3 or Iso_cuboid_3 contained in a Sphere_3 are considered as intersection. A Segment_3 is not.
Is inclusion intersection? in 2D:
| Triangle_2 | Iso_rectangle_2 | Circle_2 | Point_2 | Segment_2 | |
|---|---|---|---|---|---|
| Triangle_2 | 1 | 1 | 1 | 1 | 1 |
| Iso_rectangle_2 | 1 | 1 | 1 | 1 | 1 |
| Circle_2 | (1) | 1 |
Intersections are symmetric, i.e., do_intersect(a, b) = do_intersect(b, a). Triangle_2 inside Circle_2 do not intersect, but Circle_2 inside Triangle_2 does intersect.
3D:
| Tetrahedron_3 | Iso_cuboid_3 | Sphere_3 | Point_3 | Segment_3 | Triangle_3 | |
|---|---|---|---|---|---|---|
| Tetrahedron_3 | 1 | 1 | 1 | 1 | 1 | 1 |
| Iso_cuboid_3 | 1 | 1 | 1 | 1 | 1 | 1 |
| Sphere_3 | 1 |
In case we opt for "inside" semantics, do we then also have to take into account orientation?
