# Zone division

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A friend and I are making a rogue-lite retro procedural game. As in many procedural rogue-lite games, it will have rooms to complete but also the notion of zones. The difference between a zone and a room is that a zone is open air whilst a room is not. Rooms are connected mainly by corridors while zones are mostly naturally connected / separated by rivers and mountains.

Because we want levels with zones to be generated, we need to tame the beast that is procedural generation. How can we generate each zone itself and also clearly divide them? Until now, I had only been using the Java noise library called Joise, which is the Java community port of JTippetts' Accidental Noise Library. I needed the zone data to be generated with basis function modules, i.e. Perlin noise, but in contrast I needed a more structured approach for the zone division. Joise library does have a cell noise module that is a Worley noise. It looks like this depending on its 4 parameters (1, 0, 0, 0) :

Using math modules, I was able to morph that noise into something that looks like a Voronoi diagram. Here's what a Voronoi diagram should look like (never mind the colors, the important parts are the cell edges and the cell centers) :

A more aesthetic version :

The Worley noise that I had morphed into a Voronoi-like diagram did not include the cell centers, did not include metadata about the edges and was not enough deterministic in a sense that sometimes, the edges would around 60 pixels large. I then searched for a Java Voronoi library and found this one called Voronoi-Java. With this, I was able to generate simple Voronoi diagrams :

Relaxed : 1 iteration

Relaxed : 2 iterations

The relaxation concept is actually the Lloyd's algorithm fortunately included within the library.

Now how can I make that diagram respect my level generation mechanics? Well, if we can limit an approximated number of cells within a certain resolution, that would be a good start. The biggest problem here, is that the relaxation reduces the number of cells within a restricted resolution (contrary to the global resolution) and so we need to keep that in mind.

To do that, I define a constant for the total number of sites / cells. Here's my code :

private Voronoi createVoronoiDiagram(int resolution) {
Random random = new Random();
Stream<Point> gen = Stream.generate(() -> new Point(random.nextDouble() * resolution, random.nextDouble() * resolution));
return new Voronoi(gen.limit(VORONOI_SITE_COUNT).collect(Collectors.toList())).relax().relax().relax();
}

A brief pseudo-code of the algorithm would be the following :

1. Create the Voronoi diagram
2. Find the centermost zone
3. Selects X number of zones while there are zones that respect the selection criteria
4. Draw the border map
5. Draw the smoothed border map

The selection criteria is applied for each edge that is connected only to one selected zone. Here's the selection criteria :

• Is connected to a closed zone, i.e. that all its edges form a polygon
• Does have two vertices
• Is inclusively in the resolution's boundaries

Here's the result of a drawn border map!

In this graph, I have a restricted number of cells that follow multiple criteria and I know each edge and each cell center point.

To draw the smoothed border map, the following actions must be taken : emit colors from already drawn pixels and then apply a gaussian blur. Personally, I use the JH Labs Java Image Filters library for the gaussian blur.

With color emission only :

With color emission and a gaussian blur :

You may ask yourself why have we created a smoothed border map? There's a simple reason for this, which is that we want the borders to be gradual instead of abrupt. Let's say we want rivers or streams between zones. This gradual border will allow us to progressively increase the depth of the river and making it look more natural in contrast with the adjacent zones.

All that's left is to flood each selected cell and apply that to a zone map.

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I am here to gather your opinion, remarks, ideas or any constructive criticism you may have about what I am going to present. Don’t be shy!

A bit of background:

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What is my latest idea?

I started to study more in-depth the Utility theory as described by Dave Marks (I read his book and watched his GDC AI lectures as well). I liked the idea. I like that I can start on something relatively simple and add more considerations as things progress to handle more and more situations. While my work began as something very close to utility theory, it evolved a bit afterward. Here is what I plan on doing to compute a unit’s best course of action:

A – Score every of its move (each move is a pair [skill, target]).

B – Chose the move according to a selection strategy (highest score, weighted random, random amongst the top scores… lots of different selection algorithm can be used there).

So far, easy, right? Let’s dig deeper into our first phase of scoring (A), which is the hard part. For all the damage or healing skills:

Step 1: The final scoring of the move [skill,target] will be function of the a “Survival” scoring for the player team and for the enemy team. An example of this relationship could be: Adding all the survival scores of each unit in Team A and divide the result by the addition of all the survival scores for each unit in team B.

Step 2: The survival score of each unit will be its Health after the move we are evaluating, divided by the total damage per turn that we estimate other units can deal to her (minus the total heal it ca receive). [This a step where we can process damage and heal over time as well]

Step 3: This damage per turn estimation will be, initially, the sum for every unit in battle of the damage or heal per second it can deal to that unit. For example: If I’m alone vs 2 bad guy that can deal 1 dmg/turn and if I can deal 1 heal/turn, the damage per turn estimation against me will be 2-1 = 1. [This is not optimal since we are counting the damage of each unit once per enemy unit but it’s a start]

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The tricky part comes from buffs and debuffs. If we use the above algorithm, (de)buffs that changes the damage or healing someone does or receive will be evaluated correctly as it will change the damage or heal per second output of units and it would affect the survival score and the final scoring. That is why I chose to include DPS and HPS computations for each unit for each move.

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o   A : After a cast of the buff skill I’m evaluating

o   B : Without the cast of the buff, just like if it was that unit’s turn to play

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No dumb decision / do not fall into obvious player’s traps
o   Not perfect but it should choose the best target whenever possible

Exploit obvious flaws of the opponent
o   Same as above

Act in coordination when appropriate with other units
o   This can be done simply by adding weight to some targets or computing moves for all units of a group before deciding which one to take (for example to take the best move vs a specific unit, on average)

Able to find who should be their focus in the player’s team (some notion of threat)
o   It will naturally focus the unit who is the easiest to kill and debuff or CC the ones that deal the more heal/damage. But, to better solve this, we will need to add other considerations to the AI scoring process, It should not be *too* hard

Find the best move to use and if there is some kind of combo possible, use it
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I’m quite happy with my initial tests. I’m not going to be coding it now. My goal was to reflect on the subject on paper and try to see if designing my AI would be a roadblock or not for my project. There are a few other area I want to design and take time to really think about before getting back to my project full time. I’d love to hear your toughs and feedbacks about my AI ideas. Do you see huge roadblocks I’m missing? Does it sound ok to you?

If you read that far…. thank you and I can"t wait to hear from you guys😊

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