One of the things that's bothered me about my Introduction to A* page and also my older A* pages is that I use grids everywhere. I fear that some of my readers will think that A* is only for grids or that it's best with grids. In my opinion it's worst when it is given grids, especially grids where every step has the same movement cost.
I decided the simplest thing I could do would be to change the grid map at the top of the page. That's the first impression a reader gets. Instead of showing non-grid maps halfway down the page, I should show a map that's not a grid. That way the reader immediately sees that we're not solving a grid problem. This was the first map on the page:
I took some graph paper and came up with a polygon version of this map. I hand-coded it and got the A* page to show it:
Although making the initial version of this map with pen and graph paper wasn't too bad, iterating was quite a pain. I decided to make a quick & dirty tool to edit the shapes. I wanted to edit the graph connectivity too but didn't want to spend more than an hour writing the tool, so I didn't implement that. I put the connectivity in manually.
The tool helped a lot! I made it output JSON, and then I copied-and-pasted that JSON into my A* page, where I wrote some code to turn that into the diagram. I spent a few hours on that map and also several others. The tool made it so much easier to edit maps that I ended up making more maps for the page.
After I had this new map up, the next step was to add a section to the page that described graphs. Although I have a link to another page that describes graphs, I think the input and output to an algorithm are too important to not explain on the main page.
I had implemented the A* diagrams with layers (see this); I was able to easily add new layers to show graph nodes and graph edges. With this I made a new diagram:
I wanted to demonstrate two things with pathfinding graphs:
Completely different game maps might have similar pathfinding graphs. I drew a game map based on StarRaven's cartography brushes that shared the same pathfinding map as the main example.
The same game map can be represented by different pathfinding graphs. I added two more pathfinding graphs for the same game map:
Comparing these, you can see how A* has to do a lot more work when the pathfinding graph is a grid than when the pathfinding graph is a navmesh or waypoint graph. If you're looking to optimize pathfinding on a grid, the first thing to try is to construct a non-grid pathfinding map.
With all of the new content on the page, I also wanted to simplify some of the other parts of the page. I decided that the contour maps were the least valuable concept, and removed most of the contour map diagrams. I think it's an interesting way of looking at things, but I was never quite happy with them, and they probably belong on an advanced level page, not on this introductory page.
While testing on iPhone and Android, I realized that I had never finished a touch version of the drag-and-drop maps. Until now, it didn't matter, because the diagrams were grid-based, and I had a touch version of the grid code. I had to fill in the non-grid touch event handlers. It doesn't work that well but it's good enough for now.