# Calculating delaunay triangulation with two diagonal lines using ArcGIS Desktop?

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).

• Exactly an X pattern. I can't select the diagonal lines only, as there is no attribute that indicates they are diagonal. And how do you mean to flip them? By means of affine transform? That's an idea, perhaps mirror (flip) the whole layer, then dissolve it with the regular diagonal – 15Step Feb 19 '19 at 10:10
• Select existing diagonals, export and rotate using gis.stackexchange.com/questions/201867/… if rectangles are squares. – FelixIP Feb 19 '19 at 20:11

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.
• This will create 4 half diagonals inside each square. Also the squares are rotated, fishnet making is tricky. – FelixIP Feb 19 '19 at 18:48
• Split line at vertices returns a line layer, where each record is a side of the square - how do you identify "split-line midpoints"? – 15Step Feb 22 '19 at 13:17
• Feature vertices to points with the “mid” option. – Jae Feb 22 '19 at 13:19
• Great solution Jae, thanks! @FelixIP, actually if I stop at Step 6 then it's only two diagonals per square, just like I wanted. – 15Step Feb 22 '19 at 13:31
• I tested it. Fantastic! +1 – FelixIP Feb 23 '19 at 3:32