I am trying to draw a circle in discrete space (actual image pixel space). I have the center (x,y) and radius r of a circle that I am supposed to draw. The manner in which I draw this circle is the following:
Starting from the center position (x,y), I have a for loop over angles $\theta \in \{0,2\pi\}$. Lets say the angle is incremented by $\Delta\theta$ in every iteration. In each iteration, I calculate an x-deviation and a y-deviation based on, $\Delta x = r cos(\theta)\\ \Delta y = r sin(\theta).$ The point on the circumference of the circle is then calculated as $x' = \text{round}(x + \Delta x)\\ y'= \text{round}(y + \Delta y).$
This gives a location $(x', y')$ in discrete space at which I can color a pixel. How do I determine for a given radius, what is the minimum number of discrete "pixels" I will have along the circumference.
In other words, lets say if I have a radius of 10, then how many unique discrete points would I have along the boundary of the circle? Is this problem well defined? I know there is a pitfall here of what consists of a discrete circumference. I consider every connected pixel to be a circumference point.