I am making some assumptions, here, about how you count pixels. Hopefully, these assumptions will be clear via the following examples.
I assume your radial lines go from the center of pixel (0,0) to the center of pixel (a,b).
- Example 1: (a,b) = (0,b). Answer = b+1.
- Example 2: (a,b) = (1,2). Answer = 4. The line passes through (0,0), (0,1), (1,1), and (1,2).
- Example 3: (a,b) = (2,2). Answer = 3. The line passes through (0,0), (1,1), and (2,2).
To summarize this counting method into a formula, we need to characterize the conditions under which the line passes through a pixel vertex (as in example 3) and not a pixel edge (as in examples 1 and 2). I can give you the reasoning behind my answer if you like. For now I give you the formula below.
function numPts = numPoints(a,b)
diagPixels = gcd(a+1,b+1) - 1;
numPts = a + b + 1 - diagPixels;
end
~Jonathan
