Hi Guosheng,
The bisection is coded following Arnold + Mukherjee
www-users.math.umn.edu/~arnold/papers/bistetima.pdf
When one tetrahedral element is marked for refinement, it will be bisected 3 times to obtain half the mesh-size.
Also un-marked elements get refined to form the conforming closure.
I also wonder why parent nodes are newly generated vertices on the current level, on tetrahedral meshes.
Can you provide an example ?
Joachim