Calculating delaunay triangulation with two diagonal lines using ArcGIS Desktop?

Question

How do I obtain a line output similar to a delaunay triangulation but with two diagonal lines, from a point layer containing a regular-spaced point grid using ArcGIS Desktop?

The current result is this:

As you can see, this solution only creates a single diagonal line. I've also tried Thiessen polygons, but it merely creates a square grid encompassing each point. I also tried 'Tesselate' after creating a square layers from my points, but it provides an identical solution to the delaunay polygons (a single diagonal line). The aim is to later use this output as a dummy road network (the single diagonal line produces sub-optimal routes currently).

Answer 1

I believe this would work for ArcGIS Desktop:

1. Use the “Create Fishnet” tool, setting the output to “polygons”.
2. Convert fishnet polygons to lines.
3. Split lines at vertices.
4. Identify split-line midpoints.
5. Create Thiessen polygons from midpoints.
6. Convert Theissen polygons to lines.
7. Merge lines from step 2 and step 6 if you want as shown below. Or just use the diagonals from step 6.