6.2 Initial Point Generation

Many different styles to generate an initial mesh point distribution can be conceived. Corresponding algorithms are more easy to design, because of the lack of restrictions applied to the point set.

• The octree-type generation can be extended to use special point templates for each octree leaf instead of using corner points exclusively. The edges of the octree leafs as shown in Fig. 6.2 can be bisected, or more complex patterns similar to crystal lattices can be utilized.
• An advancing front technique to place the mesh points can produce boundary-fitted meshes.
• Random point distributions to fit inhomogeneous density requirements can be additionally smoothened.

Note that the generation of a Steiner point distribution as described in Section 5.6 does not require an initial point set and is based on a boundary mesh. A detailed investigation of finite octree point generation can be found in [192]. A test example of the finite octree and the resulting mesh is shown in Fig. 6.2 and Fig. 6.3.

Figure 6.2: Finite octree point generation.

Figure 6.3: Mesh for the octree point distribution, 25253 tetrahedra.