Scan Line Polygon Fill

• Unmodified this deals with simple polygons.
• A closed line with self-intersecting segments causes a problem.
• 
• This figure creates a problem.
• We don't know what is "inside" and what is "outside" of this polygon
• There are two ways to deal with it
  Even-odd rule
  • Start with a count of 0.
  • Scan from left to right.
  • Count the lines as they are crossed.
  • If the number of lines crossed is even, the point is outside
  • If the count is odd, the point is inside.
  • We need to be careful at endpoints, but more on that later.
  • 
  • Winding number.
    • Count the number of times you cross a line going from right to left as a 1 (in my picture)
    • Count the number of times you cross a line going from left to right as a -1 (in my picture)
    • These tests can be done with cross or dot products.
    • 
    • This provides a different way to classify points and will cause the polygon to be filled differently
    • We can specify odd, inside, even outside or > 0 inside.
  • Scan line algorithm
    • In general identifies the same regions as the even-odd rule.
    • We scan between polygon boundaries where Δy = 0
    • 
    • The only problem occurs at vertexes
    • 
    • This can happen in other positions as well (sides)
    • No major problem, look at the edges connecting the vertex
      • If both segments are on the same side of the scan line, the vertex does not count.
      • If the segments are on opposite sides, the vertex counts as a line.
    • This is essentially a local max/min vs inflection point test.
      • And as we traverse the edges of the polygon we can record if for increasing/decreasing or not.
      • If we find it is a vertex that does/doesn't count.
      • When we find this, we can foreshorten the line.
      • 
    • We can also employ a modified version of Bressenham's to compute all rasterized versions of lines at once.
    • We will need to sort our vertexes, top to bottom then left to right.
    • 
  • Boundary Fill
    • Given a boundary color B
    • And a position x,y inside of the shape
    • And a fill color C.

    • BOUNDARY_FILL(B, x,y,C)
      
       if (B == pixel(x,y))
           return
       else
          pixel(x,y) = B
          BOUNDARY_FILL(B,x+1,y,C)
          BOUNDARY_FILL(B,x-1,y,C)
          BOUNDARY_FILL(B,x,y+1,C)
          BOUNDARY_FILL(B,x,y-1,C)
       return
      
      	 

    • This can "escape" if the border is not
    • FloodFill does the same, but only replaces all neighbor pixels of the same color.
  • With any of these, we can fill with a pattern too.