Area Filling Algorithm used in computer graphics

Area fill algorithm
Bhanu Dwivedi
MRIIRS

Types of area fill algorithm
▪Scan line polygon fill
algorithm
▪Boundary fill algorithm
▪Flood fill algorithm

Scan-line polygon-filling algorithm
▪ The horizontal scanning of the polygon from its lowermost to its topmost vertex,
▪ Identifying which edges intersect the scan-line, and finally drawing the interior
horizontal lines with the specified fill color process.

4
Boundary Fill Algorithm
• Another approach to area filling is to start at a
point inside a region and paint the interior outward
toward the boundary.
• If the boundary is specified in a single color, the fill
algorithm processed outward pixel by pixel until the
boundary color is encountered.
• A boundary-fill procedure accepts as input the
coordinate of the interior point (x, y), a fill color,
and a boundary color.

5
The following steps illustrate the idea of the
recursive boundary-fill algorithm:
1. Start from an interior point.
2. If the current pixel is not already filled and if it is
not an edge point, then set the pixel with the fill
color, and store its neighboring pixels (4 or 8-
connected) in the stack for processing. Store only
neighboring pixel that is not already filled and is not
an edge point.
3. Select the next pixel from the stack, and continue
with step 2.

6
Order of Pixels
The order of pixels that should be added to stack
using 4-connected is above, below, left, and right.
For 8-connected is above, below, left, right, above-
left, above-right, below-left, and below-right.

7
Start Position
4-connected (Example)

8
3
2
1
1
2 3

9
1 4
2
4
2
1

10
1
2
2
1

11
5 1
5
1

12
1
1

13

14
Start Position

15
4 1 5
2 3
5
4
3
2
1

16
6
4 1
2 3
6
4
3
2
1

17
7 8
4 1
2 3
8
7
4
3
2
1

18
11 9 12
7 10
4 1
2 3
12
11
10
9
7
4
3
2
1

19
11 9
7 10
4 1
2 3
11
10
9
7
4
3
2
1

20
9
7 10
4 1
2 3
10
9
7
4
3
2
1

21
9
7
4 1
2 3
9
7
4
3
2
1

22
7
4 1
2 3
7
4
3
2
1

23
4 1
2 3
4
3
2
1

24
1
2 3
3
2
1

25
1
2 2
1

26
1
1

27

28
Flood Fill Algorithm
Sometimes we want to fill in (recolor) an area that is
not defined within a single color boundary.
We paint such areas by replacing a specified interior
color instead of searching for a boundary color
value.
This approach is called a flood-fill algorithm.

void floodFill4 (int x, int y, int fill, int oldColor)
{
if (getPixel(x,y) == oldColor) {
setColor(fill);
setPixel(x,y);
floodFill4 (x+1, y, fill, oldColor);
floodFill4 (x−1, y, fill, oldColor);
floodFill4(x, y+1, fill, oldColor);
floodFill4(x, y−1, fill, oldColor);
}
}

▪ Viewing is the mechanism to view the selected part of picture on an output device.
▪ Basic terms
 Window :- A world-coordinate area selected for
display.
defines what is to be viewed
 Viewport:- An area on a display device to which
a window is mapped.
defines where it is to be displayed
 Viewing transformation :- The mapping of a
part of a world-coordinate scene to device
coordinates.

2 Dimensional Viewing transformation Pipeline

Modeling Co-ordinates
World Co-ordinates
Viewing Co-ordinates
Normalized Viewing Co-ordinates
Device Co-ordinates
Construct World Co-ordinate Scene using
Modeling Co-ordinate Transformation
Construct World Co-ordinates to Viewing
Co-ordinates
Map Viewing Co-ordinates to Normalized
Viewing Co-ordinates using Window
Viewport Specification
Map Normalized Viewport to Device
Co-ordinates

Viewing Effects
▪ Zooming effects
• Successively mapping different-sized windows on a fixed-sized viewports.
▪ Panning effects
• Moving a fixed-sized window across the various objects in a scene.
▪ Device independent
• Viewports are typically defined within the unit square (normalized coordinates)
35

Viewing Coordinate Reference Frame
▪ The reference frame for specifying the world-
coordinate window.
• Viewing-coordinate origin: P0 = (x0, y0)
• View up vector V: Define the viewing yv direction
36

Window-to-Viewport
Coordinate Transformation
37

▪ To maintain the same relative placement in the
viewport as in the window we require following:-
xv –xvmin xw - xwmin
xvmax –xvmin xwmax - xwmin
yv –yvmin yw - ywmin
yvmax –yvmin ywmax – ywmin
▪ Solving these expressions for the viewport position
(xv,yv), we have
xv = xvmin + (xw- xwmin)Sx
yv = yvmin + (yw- ywmin)Sy

▪ Where scaling factors Sx and Sy are used to converts the
window area into the viewport area.
Sx = xvmax – xvmin
xwmax – xwmin
Sy = yvmax – yvmin
ywmax – ywmin
(i) Perform Scaling using a fixed point position of
(xwmin, ywmin) that scales the window area to the size
of the viewport.
(ii) Translate the scaled window area to the position of the
viewport.

Area Filling Algorithm used in computer graphics

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