Find all integer coordinates in a given radius

Question

Given a two-dimensional coordinate system how can I find all points with integer coordinates in a radius from a given point? I want the points as x-coordinate and y-coordina

Answer 1

You can make a small modification to the midpoint circle algorithm to get a filled circle.

First generate the coordinates:

data = new int[radius];
int f = 1 - radius, ddF_x = 1;
int ddF_y = -2 * radius;
int x = 0, y = radius;
while (x < y)
{
    if (f >= 0)
    {
        y--;
        ddF_y += 2; f += ddF_y;
    }
    x++;
    ddF_x += 2; f += ddF_x;
    data[radius - y] = x; data[radius - x] = y;
}

Then visit all the interior points:

int x0 = center.X;
int y0 = center.Y - Radius;
int y1 = center.Y + Radius - 1;

for (int y = 0; y < data.Length; y++)
{
    for (int x = -data[y]; x < data[y]; x++)
    {
        doSomething(x + x0, y + y0);
        doSomething(x + x0, y1 - y);
    }
}

That saves some work visiting points that won't be in the circle, but at the expense of a little pre-processing. It definitely won't help for smaller circles, and for bigger ones, well, I honestly don't know. You'd have to benchmark it.