1. Agenda Polygon Terminology Types of polygons Inside Test
Polygon Filling Algorithms
Scan-Line Polygon Fill Algorithm
Flood-Fill Algorithm

2. A Polygon Vertex = point in space (2D or 3D)
Polygon = ordered list of vertices
Each vertex connected with the next in the list
Last is connected with the first
May contain self-intersections
Simple polygon – no self-intersections
These are of most interest in CG

3. Polygons in graphics
The main geometric object used for interactive graphics.
Different types of Polygons
Simple Convex
Simple Concave
Non-simple : self-intersecting
Self-intersecting
Convex
Concave

4. Polygon Representation and Entering

5. Inside Test Why ? Want to fill in (color) only pixels inside a polygon
What is “inside” of a polygon ?
Methods
Even –odd method
Winding no. method

6. Even –odd method Case:2 Case :1
Count number of intersections with polygon edges
If N is odd, point is inside
If N is even, point is outside P Q
Odd P Q P
even Q P Q

7. Winding no. Method Every side has given a no. called winding no.
Total of this winding no. is called net winding.
If net winding is zero then point is outside otherwise it is inside. +1 -1

8. Polygon Filling Seed Fill Approaches
2 algorithms: Boundary Fill and Flood Fill
works at the pixel level
suitable for interactive painting apllications
Scanline Fill Approaches
works at the polygon level
better performance

9. Seed Fill Algorithms: Connectedness
4-connected region: From a given pixel, the region that you can get to by a series of 4 way moves (N, S, E and W)
8-connected region: From a given pixel, the region that you can get to by a series of 8 way moves (N, S, E, W, NE, NW, SE, and SW)
4-connected
8-connected

10. Boundary Fill Algorithm
Boundary-defined region
Start at a point inside a region
Paint the interior outward to the edge
The edge must be specified in a single color
Fill the 4-connected or 8-connected region
4-connected fill is faster, but can have problems:

11. Boundary Fill Algorithm (cont.)
void BoundaryFill(int x, int y, newcolor, edgecolor) {
int current;
current = ReadPixel(x, y);
if(current != edgecolor && current != newcolor)
putpixel(x,y, newcolor);
BoundaryFill(x+1, y, newcolor, edgecolor);
BoundaryFill(x-1, y, newcolor, edgecolor);
BoundaryFill(x, y+1, newcolor, edgecolor);
BoundaryFill(x, y-1, newcolor, edgecolor); }

12. Flood Fill Algorithm Interior-defined region
Used when an area defined with multiple color boundaries
Start at a point inside a region
Replace a specified interior color (old color) with fill color
Fill the 4-connected or 8-connected region until all interior points being replaced

13. Flood Fill Algorithm (cont.)
void FloodFill(int x, int y, newcolor, oldColor) {
if(ReadPixel(x, y) == oldColor)
putpixel(x,y, newcolor);
FloodFill(x+1, y, newcolor, oldColor);
FloodFill(x-1, y, newcolor, oldColor);
FloodFill(x, y+1, newcolor, oldColor);
FloodFill(x, y-1, newcolor, oldColor); }

14. Problems with Seed Fill Algorithm
Recursive seed-fill algorithm may not fill regions correctly if some interior pixels are already displayed in the fill color.
This occurs because the algorithm checks next pixels both for boundary color and for fill color.
Encountering a pixel with the fill color can cause a recursive branch to terminate, leaving other interior pixels unfilled.
This procedure requires considerable stacking of neighboring points, more efficient methods are generally employed.

15. Scan line polygon Filling
Interior Pixel Convention
Pixels that lie in the interior of a polygon belong to that polygon, and can be filled.
Pixels that have centers that fall outside the polygon, are said to be exterior and should not be drawn and filled.
Basic Scan Line Algorithm
For each scan line:
1. Find the intersections of the scan line with all edges of the polygon.
2. Sort the intersections by increasing x-coordinates
3. Fill in all pixels between pairs of intersections.

16. Basic Scan-Fill Algorithm
For scan line number 8 the sorted list of x-coordinates is (2,4,9,13) (b and c are initially no integers)
Therefore fill pixels with x- coordinates 2-4 and 9-13.

17. What happens at edge end-point?
Intersection points along the scan lines that intersect polygon vertices.
Scan line y’ has odd intersection points and intersects four polygon edges
Scan line y has even intersection points and intersects five polygon edges

18. What happens at edge end-point?
Edge endpoint is duplicated.
In other words, when a scan line intersects an edge endpoint, it intersects two edges.
Two cases:
Case A: edges are on opposite side of the scan line
Case B: edges are on the same side of current scan line
In Case A, we should consider this as only ONE edge intersection
In Case B, we should consider this as TWO edge intersections
Scan-line
Scan-line
Case A
Case B

19. Spacial Handling (cont.)
Case 1
Intersection points: (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.

20. Spacial Handling (cont.)
Case 2
However, in this case we count p1 once (p0,p1,p2,p3),

21. What happens at edge end-point?
For Scan line y’ (1,2,2,3)
For Scan line y (1,2,3,4)

22. Coherence
Coherence: pixels that are nearby each other tend to share common attributes (color, illumination, normal vectors, texture, etc.).
Types of Coherence
Span coherence: Pixels in the same scan line tend to be similar.
Scan-line coherence: Pixels in adjacent scan line tend to be similar.
Edge coherence means that most of the edges that intersect scan line i also intersect scan line i+1.
(In order to calculate intersections between scan lines and edges, we must avoid the brute-force technique of testing each polygon edge for intersection with each new scan line – it is inefficient and slow.)

23. Edge Coherence Problem: Calculating intersections is slow.
Solution: Incremental computation / coherence
Computing the intersections between scan lines and edges can be costly
Use a method similar to the midpoint line drawing algorithm
y = mx + b, x = (y – b) / m
At y = s, xs = (s – b ) / m
At y = s + 1, xs+1 = (s+1 - b) / m = xs + 1 / m
Incremental calculation: xs+1 = xs + 1 / m

24. Active Edge Table
A table of edges that are currently used to fill the polygon
Scan lines are processed in increasing Y order.
Polygon edges are sorted according to their minimum Y.
When the current scan line reaches the lower endpoint of an edge it becomes active.
When the current scan line moves above the upper endpoint, the edge becomes inactive.

25. Active Edge Table Active edges are sorted according to increasing X.
Filling in pixels between left most edge intersection and stops at the second.
Restarts at the third intersection and stops at the fourth.