Hi, so I'm trying to figure out a world generation algorithm for my game in Unity but I am having a hard time deciding how to implement it.

So few days ago, I stumbled on an old thread in this site which they achieve exactly what I am trying to do. They generate some circles and then use Perlin noise to mess with radius (or at least that's what I understood so far), resulting in irregular continents.

I tried using "if (x-x0)^2 + (y-y0)^2 <= r^2 then" but the thing is, I don't get the same result

According to that thread, their way of drawing a circle is using function that has a theta, but I can't find a way of doing that.
So my question is: How Can I get an array of points that make up a circle (NOT CIRCUMFERENCE) so that I can get the same results as the image bellow?

The reason I don't ask in that thread its because its already too old and is locked.

Thanks for your post, my problem is that using a parametric function, I just have the points surrounding the center, not actually the filled circle.

You do know that there are other potentially easier ways to create continents, right? Such as height maps or incremental flood fill..

Looking at those images, I'm guessing they are using very close points, possibly with variations in the theta as well as the radius. If you are interested in this for mathematical reasons or whatever, then by all means, but if you just want nice continents, there are probably easier ways.

I tried to take the challenge to make my own implementation, knowing nothing about the subject at all. It looks nothing like the images you showed. Then I noticed that they are using Perlin noise, and I was just using a simple random generator... Basically using the method AvengerDr suggested, drawing a circle with various displacements, deformations. (Basically drawing a jagged oval rather than a jagged circle.)

Edit: Looking at the picture you posted, it looks like they are not only using Perlin noise, but using spherical coordinates too. (Mapping to a sphere.)

On the other hand, looking at the picture from the answer in the thread that you posted a link to, the initial shapes looks very much like what I get with my attempt.

Picture prom the post:

Code (quick and dirty...)

- (void)drawRect:(NSRect)dirtyRect {

    [[NSColor blackColor] set];
    [NSBezierPath fillRect:dirtyRect];
    
    [[NSColor whiteColor] set];

    double centerX = [self bounds].size.width / 2.0f;
    double centerY = [self bounds].size.height / 2.0f;
    
    double x = 0.0f;
    double y = 0.0f;
    
    double radius = 100.0f;
    
    double delta = 0.05f;

    double randomValue = 0.0f;
    
    randomValue = (double)arc4random_uniform(10000) / 10000.0f;
    double scaleX = (randomValue + 0.1f);
    
    randomValue = (double)arc4random_uniform(10000) / 10000.0f;
    double scaleY = (randomValue + 0.1f);

    randomValue = (double)arc4random_uniform(10000) / 10000.0f;
    double clampToValue = randomValue * 200.0f;

    NSBezierPath *circle = [NSBezierPath bezierPath];
    BOOL isFirst = YES;
    double deviationRadius = 0.0f;

    for (double theta = 0.0f; theta < 2 * M_PI; theta += delta) {
        randomValue = ((double)arc4random_uniform(10000) / 10000.0f) - 0.5f;

        deviationRadius += randomValue * 100.0f;
        
        if ((clampToValue - (radius - deviationRadius)) < 0.0f) {
            deviationRadius += clampToValue;
        }
        
        x = sin(theta) * (radius + deviationRadius) * scaleX + centerX;
        y = cos(theta) * (radius + deviationRadius) * scaleY + centerY;

        if (isFirst) {
            [circle moveToPoint:NSMakePoint(x, y)];
            isFirst = NO;
        }
        else {
            [circle lineToPoint:NSMakePoint(x, y)];
        }
        
    }

    [circle closePath];
    [circle fill];
//    [circle stroke];
}