What is an simple way to compute the overlap between an image and a polygon?

Question

I have a closed non-self-intersecting polygon. Its vertices are saved in two vectors X, and Y. Finally the values of X and Y are bound between 0 and 22.

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Answer 1

Slight improvement

Firstly, to simplify your "partial solution" - what you're doing is just looking at the corners. If instead of considering the 22x22 grid of points, you could consider the 23x23 grid of corners (which will be offset from the smaller grid by (-0.5, -0.5). Once you have that, you can mark the points on the 22x22 grid that have at least one corner in the polygon.

Full solution:

However, what you're really looking for is whether the polygon intersects with the 1x1 box surrounding each pixel. This doesn't necessarily include any of the corners, but it does require that the polygon intersects one of the four sides of the box.

One way you could find the pixels where the polygon intersects with the containing box is with the following algorithm:

For each pair of adjacent points in the polygon, calling them pA and pB:
    Calculate rounded Y-values: Round(pA.y) and Round(pB.y)
    For each horizontal pixel edge between these two values:
        * Solve the simple linear equation to find out at what X-coordinate
          the line between pA and pB crosses this edge
        * Round the X-coordinate
        * Use the rounded X-coordinate to mark the pixels above and below
          where it crosses the edge
    Do a similar thing for the other axis

So, for example, say we're looking at pA = (1, 1) and pB = (2, 3).

• First, we calculated the rounded Y-values: 1 and 3.
• Then, we look at the pixel edges between these values: y = 1.5 and y = 2.5 (pixel edges are half-offset from pixels
• For each of these, we solve the linear equation to find where pA->pB intersects with our edges. This gives us: x = 1.25, y = 1.5, and x = 1.75, y = 2.5.
• For each of these intersections, we take the rounded X-value, and use it to mark the pixels either side of the edge.
  • x = 1.25 is rounded to 1 (for the edge y = 1.5). We therefore can mark the pixels at (1, 1) and (1, 2) as part of our set.
  • x = 1.75 is rounded to 2 (for the edge y = 2.5). We therefore can mark the pixels at (2, 2) and (2, 3).

So that's the horizontal edges taken care of. Next, let's look at the vertical ones:

• First we calculate the rounded X-values: 1 and 2
• Then, we look at the pixel edges. Here, there is only one: x = 1.5.
• For this edge, we find the where it meets the line pA->pB. This gives us x = 1.5, y = 2.
• For this intersection, we take the rounded Y-value, and use it to mark pixels either side of the edge:
  • y = 2 is rounded to 2. We therefore can mark the pixels at (1, 2) and (2, 2).

Done!

Well, sort of. This will give you the edges, but it won't fill in the body of the polygon. However, you can just combine these with your previous (red) results to get the complete set.