Implementation

The above algorithm requires the implementation of both the Delaunay triangulation and the AFM. These have been done as described in the previous chapters. The algorithm can now be described as -

• The domain/boundary is read (only one level of holes are allowed for need of continuum) and converted to a PLC if not already so.
• Initial Delaunay triangulation is done using these boundary points and the triangles are stored in a TRI structure [Nan95].
• The node density of each boundary point is now computed using the above information and stored. This is simply the mean of all the edges in the triangulation meeting at that point.
• Now, the AFM proceeds and the function for determining the new insertion point is modified as follows -

  1.

  A first approximation to the insertion point (called trial point) is made in the same way as described earlier for the conventional AFM.

  2.

  Using this point, the background triangle containing the point is found using a simple search algorithm.

  3.

  Upon finding this background triangle, the barycentric coordinates ($\alpha$, $\beta$ and $\gamma$) of the trial point w.r.t. the triangle is computed. These are simply the ratios of the area of the three triangles formed by the trial point and the background triangle to the area of the background triangle.

  4.

  The already computed node densities of the nodes of the background triangle (L₁, L₂ and L₃) are now recalled.

  5.

  The new length of the trial point from the edge of the front is now recomputed based on a suitable function of the above 6 parameters $\alpha$, $\beta$, $\gamma$, L₁, L₂ and L₃.

  6.

  Having got a new trial point, iteration starts again from 2, till the next point obtained by the procedure is the same as the previous point or within a certain tolerance band of the previous point.

• Having got the final insertion point, the AFM proceeds till the triangulation is completed.

Also, apart from the above mentioned 6 parameters, the gradation function is implemented to accept two additional parameters x and y which specify the location of the current trial point.