QUALITY LOCAL REFINEMENT OF TETRAHEDRAL MESHES BASED ON BISECTION

We present a three-dimensional (3-D) local refinement algorithm for te trahedral meshes based on a bisection procedure. The quality of refine d meshes is guaranteed in terms of a tetrahedron shape measure eta. Sp ecifically, it is proved that the algorithm creates a finite number, w hich only depends on the number of tetrahedra in the initial mesh, of classes of similar tetrahedra in all refined tetrahedra. Furthermore, if T is a tetrahedron in the original mesh, and T-i(n) is any refined tetrahedron of T, then eta(T-i(n)) greater than or equal to c eta(T), where c is a positive constant independent of T and the number of refi nements. It is also proved that for any interior face in the final mes h, the absolute value of the difference of the bisection levels of the two adjacent tetrahedra incident on the face is less than or equal to 2, which indicates that local refinements on tetrahedra can be smooth ly extended to their neighbors. The expected time complexity of the al gorithm is O(N), where N is the number of refined tetrahedra in a refi ned mesh. Implementation details and experimental results are provided .