Scan conversion is the process of representing continuous graphics objects as discrete pixels. It involves converting geometric primitives like lines and circles, defined by parameters, into a set of pixels that make up the primitive in an image. This involves mapping real-valued coordinates to integer pixel coordinates. One approach is to take the floor of the x and y values, while another is to take the floor of x+0.5 and y+0.5 to center the coordinate system at the pixel grid.

1. Scan Conversion
The process of representing continuous
graphics object as a collection of discrete
pixels is called Scan Conversion.
For e.g a line is defined by its two end pts &
the line equation, where as a circle is
defined by its radius, center position &
circle equation.

2. It is the responsibility of graphics system or
the application program to convert each
primitive from its geometric definition into
a set of pixels that make up the primitive in
image space. This conversion task is
generally referred to as a scan conversion
or rasterization.
In case of line, it can be possible that any
pixel may have any floating value like
(2.7,5) which will not be considered by the
system.

3. Therefore, the process of making these
coordinate according to system’s
assumption i.e (3,5) to plot the pixel is scan
conversion.
Points to be remember:-
1.) All the objects should be drawn with
constant brightness.
2.) Object should be independent of length &
orientation.

4. Scan converting a Point:-
A mathematical point (x,y) where x & y are
real numbers within an image area, needs
to be scan-converted to a pixel at location
(x’,y’).
This may be done by making x’& y’ to be the
integer part of x & y.
x’= Floor(x) and y’= Floor(y)
Floor is a function that returns the largest
integer that is less than or equal to the
argument.

5. The origin is at lower left corner of the pixel
grid. All points that satisfy x’< x <x’+1 &
y’<y <y’+1are mapped to pixel (x’,y’).
For e.g P1(1.7,0.8) is represented by pixel
(1,0) P2(2.2,1.3) and P3(2.8,1.9) are both
represented by pixel (2,1).
2
1
0
0,0 0 1 2

6. Another approach is to scan convert (x,y) by
making x’ = Floor(x + 0.5) and y’ =
Floor(y+0.5). This essentially places the
origin of the coordinate system for (x,y) at
the center of pixel(0,0). All point that
satisfy x’-0.5<x<x’+0.5 & y’-
0.5<y<y’+0.5
are mapped to (x’,y’).This means that
points P1 and P2 are now both represented
by pixel (2,1) whereas point P3 is
represented by pixel (3,2).

7. 2 P3
P2
1
P1
0 0,0
0 1 2 3