Algorithm

The general algorithm [Geo91] is

1.

Define the boundary of the domain to be discretised.

2.

Initialise the front as a piecewise linear curve in conformity with the boundary.

3.

The edge to be deleted from the front is chosen based upon some criterion (generally smallest edge is chosen as it gives good quality meshes).

4.

For the edge to be deleted - 

(a)

Select the trial point position (trial point is the point lying inside the domain and making an equilateral triangle with the edge to be deleted).

(b)

Search for any already existing point within a certain proximity of the trial point. If any such point exists it becomes the trial point. Continue the search.

(c)

Determine whether the element formed with the new ideal point crosses any edges. If yes, select a new trial point from the front and try again (go to 4b).

5.

Add the new point, edges and triangles to the respective lists.

6.

Delete the base edge from the front and add the new edges.

7.

If the front is non-empty, go to 3.