1. Computer Graphics
Filling

2. Filling Polygons So we can figure out how to draw lines and circles
How do we go about drawing polygons?
We use an incremental algorithm known as the scan-line algorithm

3. Polygon Ordered set of vertices (points)
Usually counter-clockwise
Two consecutive vertices define an edge
Left side of edge is inside
Right side is outside
Last vertex implicitly connected to first
In 3D vertices are co-planar

4. Filling Polygons Three types of polygons
Simple convex 2. simple concave 3. non-simple
(self-intersection)
Convex polygons have the property that intersecting lines crossing it either one (crossing a corner), two (crossing an edge, going through the polygon and going out the other edge), or an infinite number of times (if the intersecting line lies on an edge).

5. Some Problems 1. Which pixels should be filled in?
2. Which happened to the top pixels? To the rightmost pixels?

6. Scan-Line Polygon Example
Polygon Vertices
Maxima / Minima
Edge Pixels
Scan Line Fill

7. Scan Line Algorithms
Create a list of vertex events (bucket sorted by y)

8. Scan-Line Polygon Fill Algorithm2 4 6 8 10
Scan Line 12 14 16

9. Scan-Line Polygon Fill Algorithm
The basic scan-line algorithm is as follows:
Find the intersections of the scan line with all edges of the polygon
Sort the intersections by increasing x coordinate
Fill in all pixels between pairs of intersections that lie interior to the polygon

10. Scanline Algorithms given vertices, fill in the pixels
arbitrary polygons
(non-simple, non-convex)
build edge table
for each scanline
obtain list of intersections, i.e., AEL
use parity test to determine in/out and fill in the pixels
triangles
split into two regions
fill in between edges

11. Scan-Line Polygon Fill Algorithm (cont…)

12. Examples:

13. Solutions:

14. Scan Line Algorithms
Create a list of the edges intersecting the first scanline
Sort this list by the edge’s x value on the first scanline
Call this the active edge list

15. Polygon Fill B C
Parity
0 = even
1 = odd
Parity 1 D A E F

16. Polygon Fill 2 B C
Parity
0 = even
1 = odd F D
Parity 1 1 A E

17. Edge Tables edge table (ET) active edge table (AET)
store edges sorted by y in linked list
at ymin, store ymax, xmin, slope
active edge table (AET)
active: currently used for computation
store active edges sorted by x
update each scanline, store ET values + current_x
for each scanline (from bottom to top)
do EAT bookkeeping
traverse EAT (from leftmost x to rightmost x)
draw pixels if parity odd

18. Scanline Rasterization Special Handling
Intersection is an edge end point, say: (p0, p1, p2) ??
(p0,p1,p1,p2), so we can still fill pairwise
In fact, if we compute the intersection of the scanline with edge e1 and e2 separately, we will get the intersection point p1 twice. Keep both of the p1.

19. Scanline Rasterization Special Handling
But what about this case: still (p0,p1,p1,p2)

20. Edge Table

21. Active Edge Table (AET)
A list of edges active for current scanline, sorted in increasing x
y = 9
y = 8

22. Edge Table Bookkeeping
setup: sorting in y
bucket sort, one bucket per pixel
add: simple check of ET[current_y]
delete edges if edge.ymax > current_y
main loop: sorting in x
for polygons that do not self-intersect, order of edges does not change between two scanlines
so insertion sort while adding new edges suffices

23. Parity (Odd-Even) Rule
Begin from a point outside the polygon, increasing the x value, counting the number of edges crossed so far, a pixel is inside the polygon if the number of edges crossed so far (parity) is odd, and outside if the number of edges crossed so far (parity) is even. This is known as the parity, or the odd-even, rule. It works for any kind of polygons.
Parity starting from even
even
odd
odd
even
odd
even
odd

24. Polygon Scan-conversion Algorithm
Construct the Edge Table (ET);
Active Edge Table (AET) = null;
for y = Ymin to Ymax
Merge-sort ET[y] into AET by x value
Fill between pairs of x in AET
for each edge in AET
if edge.ymax = y
remove edge from AET
else
edge.x = edge.x + dx/dy
sort AET by x value
end scan_fill

25. Rasterization Special Cases
-Edge Shortening Trick:
-Recall Odd-Parity Rule Problem:
-Implement “Count Once” case with edge shortening: A A B B B B B B ' ' C C
xA,yB’,1/mAB
xC,yB’,1/mCB

26. Scan Line Algorithms For each scanline:
Maintain active edge list (using vertex events)
Increment edge’s x-intercepts, sort by x-intercepts
Output spans between left and right edges
delete
insert
replace

27. Penetrating Polygons False edges and new polygons!
Compare z value & intersection when AET is calculated

28. Flood Fill
4-fill
Neighbor pixels are only up, down, left, or right from the current pixel
8-fill
Neighbor pixels are up, down, left, right, or diagonal

29. 4 vs 8 connected Define: 4-connected versus 8-connected,
its about the neighbors

30. 4 vs 8 connected  Fill Result: 4-connected versus 8-connected
“seed pixel”

31. Flood Fill Algorithm: Draw all edges into some buffer
Choose some “seed” position inside the area to be filled
As long as you can
“Flood out” from seed or colored pixels
4-Fill, 8-Fill

32. Flood Fill Algorithm Seed Position Edge “Color” Fill “Color”
void boundaryFill4(int x, int y, int fill, int boundary) {
int curr;
curr = getPixel(x, y);
if ((current != boundary) && (current != fill)) {
setColor(fill);
setPixel(x, y);
boundaryFill4(x+1, y, fill, boundary);
boundaryFill4(x-1, y, fill, boundary);
boundaryFill4(x, y+1, fill, boundary);
boundaryFill4(x, y-1, fill, boundary); }
Fill “Color”

33. Example
Let’s apply the rules to scan line 8 below. We fill in the pixels from point a, pixel (2, 8), to the first pixel to the left of point b, pixel (4, 8), and from the first pixel to the right of point c, pixel (9, 8), to one pixel to the left of point d, pixel (12, 8). For scan line 3, vertex A counts once because it is the ymin vertex of edge FA, but the ymax vertex of edge AB; this causes odd parity, so we draw the span from there to one pixel to the left of the intersection with edge CB.
odd
even a b c d A B C D E F

34. Four Elaborations (cont.)D E F G H I J A B C D F G H I J E

35. Halftoning
For 1-bit (B&W) displays, fill patterns with different fill densities can be used to vary the range of intensities of a polygon. The result is a tradeoff of resolution (addressability) for a greater range of intensities and is called halftoning. The pattern in this case should be designed to avoid being noticed.
These fill patterns are chosen to minimize banding.