Making the first Halberd game: Measuring foothills

In my last post, we did some simple calculations to estimate the amount of walking and combat to put into the game. Now, I'm going to use that data to do some real testing and level-building. But first, let's do a little more math.

Right now, Halberd's ability to resize maps is rather clunky. To make up for that fact, I want to get an idea of how big any given map should be before I make it. We can do this because we have the final length of the path the player has to follow: 250 tiles.

When in Manhattan...

The player won't have free movement in-game. Instead they'll be locked to the tile grid, with only north/south/east/west and diagonals available to them. Since position is locked, They're probably not going to take diagonals too often. So, we can get an estimate of our length using Manhattan Distance.

Unlike direct distance, Manhattan distance is just the sum of the distance on each axis. For instance, let's say your friend lived in a house 10 blocks north and 20 blocks west of you. With the Pythagorean Theorem, you could determine the distance "as the crow flies" to be ~17.3 blocks. But for the Manhattan Distance, you can just add the numbers together and get a distance of 30 blocks (the distance you're likely to walk to get there).

This can also work in reverse. Given a final length, we can subtract numbers from it to form a path, then add the segments on each axis together to get the dimensions of the map. It's hard to explain, so let me show you instead. Let's say we wanted to make a path that was 10 tiles in length. There are many ways to do this:

Even without drawing a box around these paths, we can still get their bounds by following them. Take the green one, for instance. It goes 5 units up, 4 to the right, then one more up:

Up 

• 5
• 1

Right

• 4

If we add all of the numbers together, we predictably end up with 10. However, we can also add them in their respective groups to get 6 up and 4 across. Taking the first corner into account, that gives us a 5x6 area for this path.

So why are we doing this?

Let's get back to the spreadsheets. We already have a predetermined length, so we can get either of two things by picking the other:

1. Map dimensions from the number/frequency of turns (as seen above)
2. Ratio of up/down to left/right paths from a ratio of map dimensions.

For now though, we'll put this work aside. We can't make this decision before making some others first.

What is Area 1?

If we want to decide what our new path should look like, it would benefit greatly to know what the area should be like terrain-wise. I already know the answer, and so do you if you read the title of this post. However, I think the process is more useful than the solution.

Because Halberd is as limited as it is right now, a lot of my design decisions are derived from those limits. When I discussed narrative earlier, I brought up the transition from known/safe to the unknown, and used woods and plains as examples. In retrospect, I'm not fond of either solution:

Plains are generally very open and exploratory affairs. This can be great if exploration is the goal, but in a limited game with few mechanics on offer an open field isn't really that interesting. They also tend to be pretty sparse, which isn't a good first impression for a game that will mostly live or die on its environments.

Woods are fairly ideal in general. A forest offers a lot of opportunities for interesting environmental details, and trees are good for creating paths (and hiding little passages for keen eyes to find). However, such a solution won't work too well in Halberd's current state: With no layers in maps, we can't make tiles overlap anything. Not each other, and certainly not the player! As a result, an environment full of trees would be a nightmare scenario.

Clearly, I needed something else. I chose the foothills of a mountain for a few reasons:

• On their own, the foothills of a mountain aren't as imposing or dangerous as the peaks. They also tend to have more greenery which helps lighten the atmosphere a bit.
• Mountains seem to get used a lot as a symbol for a challenge or ordeal. So, starting in some foothills implies that the real danger is up ahead. To me, this fits well with the progression established earlier.
• Mountain trails and the like are pretty restrictive. This presents the opportunity to add more interesting or complex scenery bits (translation: trees) where the player can't possibly reach and/or clip into them. Tile overlaps can be faked if you don't need tons of them, so it works for this situation.

Of course this isn't the only possible option, just the one I've chosen. Now that we know what the map will offer in terms of terrain, we can use this to get a general idea of the map's size. Since we're building a mountain trail, it stands to reason that we want our player to head up. This is especially true since making sloped tiles that work properly isn't yet possible in Halberd. However, most gentle trails have a lot of winding to them. If you look at any local mountains you'll probably see a long and circuitous 'easy trail' and a few more direct 'hard trails'. Since we want the first area to feel pretty non-threatening, I think it makes sense to have a winding path.

Whoops, more math!

Since the two ideas that I just outlined contradict each other, I think I'd like to see a fairly even map ratio. Unfortunately, getting the dimensions and path lengths will be difficult because the path winds back on itself. So, we need some more complicated calculations.

Lets say that we want a path that crosses the width of the map twice, like so:

Let's also assume that we know the path length (since in our real path, we'll know that too). In this case, we'll go with 100. Given that, the target map ratio (1:1) and the number of crosses, how do we determine the size of the map?

Since we have the width-height ratio, we can also determine the horizontal movement to vertical movement ratio by multiplying by the number of crosses. Better still, we can use this number with the total length to get the amount of horizontal/vertical movement and the width/height of the total map!

Let's try with a real example now. I want my 250-tile path to fit a map with a 2:3 ratio. So, I plug that information into this handy spreadsheet I just made:

Just like magic, I now have map dimensions! The 'pad' entries at the bottom represent the map dimensions with enough extra space to prevent the edges from scrolling onscreen. With this, everything is now in place to (finally) begin working on the map!

As a side-note: I think I'm starting to like spreadsheets a little too much. I suppose that's a fine quality for an RPG engine-builder, but still.....