  A concurrent binary tree (CBT) is a GPU-friendly data-structure suitable for
the generation of bisection based terrain tessellations, i.e., adaptive
triangulations over square domains. In this paper, we expand the benefits of
this data-structure in two respects. First, we show how to bring bisection
based tessellations to arbitrary polygon meshes rather than just squares. Our
approach consists of mapping a triangular subdivision primitive, which we refer
to as a bisector, to each halfedge of the input mesh. These bisectors can then
be subdivided adaptively to produce conforming triangulations solely based on
halfedge operators. Second, we alleviate a limitation that restricted the
triangulations to low subdivision levels. We do so by using the CBT as a memory
pool manager rather than an implicit encoding of the triangulation as done
originally. By using a CBT in this way, we concurrently allocate and/or release
bisectors during adaptive subdivision using shared GPU memory. We demonstrate
the benefits of our improvements by rendering planetary scale geometry out of
very coarse meshes. Performance-wise, our triangulation method evaluates in
less than 0.2ms on console-level hardware.
