Refining continents

I've done more tinkering to my continents. With the inland-sea-removing function reinstated, I'm getting world maps like these:

A new element in these maps is rotation. I found that some continents were coming out rather square-shaped. I did a lot of tinkering with the way in which they're generated and couldn't reliably fix this. But it occurred to me that the visual annoyance of this could be greatly reduced if I simply rotated each continent by a random amount before placing it. I think it helps - if you look at the western-most continent in that last map, it's actually quite square, but because it's been rotated, it looks OK.

Now rotating a 2D shape around a given point is not very complicated. First, I make a copy of the continent into a backup array. Then I blank the continent. Then I go through it pixel by pixel. For each pixel, I apply the formula:

newx=x*cos(angle)-y*sin(angle)

newy=y*cos(angle)+x*sin(angle)

Then we simply take the value of {newx,newy} in the backup array (which contains a copy of the original continent) and paste that into {x,y} in the continent array.

(It's slightly more complicated, because if, like me, you want it to rotate around the centre rather than around the coordinates' point of origin, you have to add and subtract the coordinates of the centre at key points, but I'll ignore that for simplicity's sake.)

Now another thought occurred to me once I'd got this working. Suppose, before plugging x and y into the above formulae, I add an offset to them. And suppose that this offset varies! That's not difficult to do. All I need to do is create yet another diamond-square fractal. Then, as I go over the continent applying the above formulae, I add an offset to x and y before plugging them into the formulae, and the size of that offset varies depending on the value of the fractal that corresponds to that point. Might this produce interesting results?

Yes! It gives us crinklier coastlines! Lots of little peninsulas and islands. We don't want to over-use this effect though, as in real life continents don't have that kind of coastline all over. So some more judicious tinkering gives us maps like these:

With an effect like this, a little goes a long way. It's hard to get the balance right, but I think these are looking pretty decent.

Now we need to do something about mountains. With the original continent method, I put down mountain ranges and created the continents around them. We're not doing that with these. We could just put down mountain ranges at random across the continents, but it would be nice to do it a bit more realistically. That means ranges in two main kinds of places: where continents overlap (like the Himalayas), and along the edges of continents (like the Andes).

The Himalaya-type mountains are fairly straightforward. We just need to identify the points where continents overlap, and then send chains of mountain ranges meandering across them:

Sometimes a larger continent is drawn entirely covering a smaller one, triggering a mountain range where one wouldn't quite expect it, but this can make for quite nice effects (this one's zoomed in a bit:

That looks to me like it could easily be a fault line between three continental plates!

Now for Andes-style mountains. Ideally, we'd be able to run a mountain range along the edge of a continent, but this would be really tricky to do. Luckily, there's nothing stopping us tinkering with the shapes of the continents at this stage. So we can choose two points at opposite sides of the continent, and then run a chain of mountains from one to the other. We'll make land under and around the mountains, and we'll also delete all other land to one side of that new land. That way, we'll effectively create a new coastline near these mountains.

Needless to say, all of that proves easier said than done, but it generates some nice results:

As always, we don't want to over-use the effect, so it's only applied to some continents.

Now we can combine both of these mountain-making methods, and also bring back a host of other effects that we had before: smaller mountain ranges scattered over the land (with some noise applied to land elevation in general), chains of islands in the sea, and most crucially, removing land by applying a fractal to the whole map. For this last move, we'll do it much more judiciously than before. Only a few, fairly small areas on the map should see significant change.

All of this gets us global maps like these:

The mountains all look much the same height with this visualisation, so the ones at continent boundaries get a bit swamped out in these images, but they're considerably more prominent on the elevation maps and should become more so when the climates are added back in.

Yes, because as you can see, I've turned off the climate simulation for the moment. This is of course partly for the sake of speed while tinkering with the global terrain generation. But it's also because increasing the map size has also shown up issues with the climate routines, so some serious amendments to those are next on the agenda.