Efficient querying of triangles within a radius of a point

[Alan-Leo-Wong]

Hi, everyone!

I have a requirement: given a triangle mesh $M$ (which may be unoriented, non-manifold, or a soup), as well as an arbitrary 3D point $p$ and a radius $r$, I want to query all triangles on $M$ whose distance from point $p$ is less than or equal to $r$, and return the results sorted in ascending order of distance from point $p$ to these triangles.

My current idea is to use CGAL to construct an AABB Tree for $M$, then construct a sphere centered at point $p$ with radius $r$, and finally use the AABB's function all_intersected_primitives() to find all intersecting triangles. However, this does not guarantee that the results are sorted by distance, and may exhibit performance issues especially with a large number of queries.

Are there any other better and faster alternatives?