- Improved the efficiency of the mesh data structure
(tetrahedron-based).
- Implemented a new edge flip algorithm that does recursive
combination of elementary flips.
- Improved the Bowyer-Watson point insertion algorithm for
robustness and efficiency.
- Implemented a new algorithm for boundary recovery (the -Y option).
- Implemented Shewchuk's CDT flip algorithm (the -p option).
- Implemented a new Delaunay refinement algorithm (the -q option)
for handling small input angles (sharp features).
- Fully supports isolated input segments and with segment markers (which do not attach to any facet).
- Many new options and parameters for improving mesh quality and mesh optimization.

- A new implementation of the Bowyer-Watson algorithm for Delaunay tetrahedralization. It is generally faster than the incrmental flip algorithm. From my tests, the flip algorithm usually constructs about twice (or more) as many intermediate tetrahedra as B-W algorithm. Now B-W algorithm is the default algorithm for Delaunay tetrahedralization.
- A new implementaton of the constrained Delaunay tetrahedralization algorithm (the -p option).
- A new implementation of the Steiner point removal algorithm (the -Y option).
- Improved the implementation of the constrained Delaunay refinement algorithm (the -q option).
- Add the minimum dihedral angle of tetrahedra as the tetrahedral shape quality parameter (set after -qq option). The minimum dihedral angle is made the major mesh quality measure now. Default it is 5 degree. One can increase it as larger as 18 degree. The radius-edge ratio (set after -q option) is still in use.

For an example, the string '-q1.4q10' sets both a radius-edge ratio (<= 1.4) and a minimum dihedral angle (>= 10 degree) as the tetrahedral shape quality measure. - Support the read and write of the legacy VTK file format which can be visualized by Paraview (see .vtk file format and -K option).

- Improved the constrained Delaunay mesh refinement algorithm. Slivers (very flat tetrahedra) are removed during the mesh refinement. For geometries having no input angle and dihedral angle smaller than 60 degrees, the boundary conforming Delaunay mesh property is guaranteed, hence the dual Voronoi diagram has no vertex lies outside the domain boundary - a desired property for finite volume partition.
- Mesh coarsening (deleting mesh points) is now possible. Two ways are implemented for doing mesh coarsening: (1) The user can specify the points wanted to be removed by using the "pointmarker" list (i.e., the last column in .node file), a '0' means "remove this point", otherwise "keep it"; or (2) The user can supply a mesh sizing function, let TetGen choose the point to remove, i.e., TetGen will remove a point if the mesh size at the point is too dense.
The new command line option for mesh coarsening is '-R'. It can be used either with '-p' (to coarse a CDT) or '-r' (to coarse a previously generated mesh). You can also use '-R' and '-q' together. TetGen will first perform mesh coarsening then do mesh refinement, hence the process must terminate and the mesh quality is improved.

- Implemented new mesh optimization and mesh smoothing functions which can be optionally performed to remove slivers and further improve mesh quality. High order edge flip operations (combination of several basic flips) (as suggested by Barry Joe [Joe, 1995]) are implemented. These operations help to remove the majority of slivers. The remaining slivers are then tried by mesh smoothing operations, which includes vertex moving and new vertex insertion.
- Improved the mesh boundary preserving (the '-Y' option) function. Most of the relocated interior points can be completely suppressed, remaining points are smoothed.
- New output of Voronoi diagrams. The Voronoi diagram is the geometric dual of the Delaunay triangulation. By using the '-v' option, the Voronoi diagram will be saved in files: .v.node, .v.edge, .v.face, and .v.cell.
- Many bugs are fixed including the '-o2' option.

- An adaptive mesh refinement algorithm has been implemented (for the '-q'
option). This algorithm extends Shewchuk's basic Delaunay refinement algorithm
in two ways: (1) no restriction on the input angle; (2) refines the mesh
according to a sizing function which may be automatcially derived from input
data or provided by user through a background mesh. A paper, "On Refinement of
Constrained Delaunay Tetrahedralizations", describes the algorithm will appear
in the proceeding of 15th international meshing roundtable, Birmingham AL,
September 2006.
- The '-Y' option (preserve the input boundary) has been
improved. Generally, more than 95% additional points can be completely removed,
the remaining points are relocated into the volume.
- Many bugs are fixed.

- Respect of the input boundary (the '-Y' switch). It is possible now to
preserve the input surface mesh unchanged in the result tetrahedral
mesh. A Steiner point removal algorithm based on Delaunay tetrahedralization
kernel and constrained flips is implemented.
- Shewchuk's Delaunay refinement algorithm has been improved. A new type of
Steiner point called "off-center" (suggested in paper Alper Üngör,
"Quality Triangulation Made Smaller", EWCG 2005) is used. This change
reduces the number of refinement points (up to 20%) and results in smaller
meshes. Consequently, the mesh speed is improved too.
- The constrained Delaunay tetrahedralization algorithm is improved. A
simple symbolic perturbation is used to remove the spherical degeneracies of
the point set which reduces the number of break points (thanks to Jonathan
Shewchuk).
- It is possible to let TetGen automatically assign the region attributes to
tetrahedra. When the '-AA' switch is used, in the output mesh, every
tetrahedron gets a non-zero attribute. Tetrahedra in the same region have the
same attribute.
- The '-z' switch has been activated. The ouput nodes can be
indexed from zero.
- Many bugs are fixed.
- Many typos in the user's manual are corrected (thanks to David Day).

- A new constrained Delaunay tetrahedralization algorithm has been
completely implemented. Now the CDT construction is rather fast and stable. A
paper, "Meshing Piecewise Linear Complexes by Constrained Delaunay
Tetrahedralizations", describes the algorithm has submitted to the 14th
international meshing roundtable held in Sandiego, September. Colleagues who
have the interest to read it are very welcome to contact me.
- In the -q switch. A new strategy for edge protecting has been used in
the Delaunay mesh refinement which saves a quite number of additional
points. It is a slighly modified version of our edge protecting algorithm (also
presented in the above paper). The quality mesh step is more stable than old
ones.
- In the -q switch. A sliver removal step is added after the Delaunay
refinement. It removes most of the survived slivers by flip operations and
inserting points.
- In the -q switch. More mesh refinement options are available. Besides the maximum volume constraint on tetrahedra, users now can set maximum area constraints on facets, maximum edge length constraint on segments.

Return to TetGen home page.

Hang Si