CGA is a creation and manipulation of image or picture with the help of computer.

1. UNIT – 2
LINE, CIRCLE AND POLYGON

2. INTRODUCTION
 The screen of computer is divided into
number of row and columns.
 The intersection of row and column is called
as pixel. Pixel is a smallest addressable point
that can be displayed on screen.
 To draw a line on screen firstly we have to
determine which pixels are to be switched
ON.
 Thus, the process of determining appropriate
pixel for representing picture is called as
Rasterization.

3. GENERAL CRITERIAS
 Lines should appear straight.
 Lines should start and end accurately.
 Lines should have constant density along
their length.
 Lines density should be independent of line
length and angle.
 Lines should be drawn rapidly.

4. LINE DRAWING ALGORITHM
 Straight line drawing algorithms are based on
incremental methods.
 In incremental method line starts with a
starting point, then some fix incremental
value is added to current point to get next
point on line and same is continued till end
of line.
 Following are the two main algorithm’s used
to draw a straight line.
1. DDA algorithm.
2. Bresenham’s algorithm

5. DDA ALGORITHM
 Read end point of line i.e.(x1, y1) and (x2, y2).
 ∆x=abs(x2-x1) and ∆y=abs(y2-y1)
 If dx>=dy then len=dx
else
len=dy
end if
 dx=(x2-x1)/len
dy=(y2-y1)/len
 X=x1+0.5*sign(dx)
y=y1+0.5*sign(dy)
 i=1
while(i<=len)
{
x=x+dx
y=y+dy
i=i+1
}
 stop

6.  Merits:-
 It is simple algorithm.
 It is faster method.

 Demerits:-
 Floating point arithmetic in DDA algorithm is
time consuming.
 Accumulation of round-off error in successive
additions of floating point increment can cause
the calculated pixel positions to draft away
from the true line path for long line segments.

7. EXAMPLE:
1. Consider a line from (0,0) to (5,6). Use
simple DDA algorithm to rasterize this line.
2. Consider a line from (0,0) to (-5,-5). Use
simple DDA algorithm to rasterize this line.

8. BRESENHAM’S ALGORITHM
 Read end point of line i.e.(x1, y1) and (x2, y2).
 ∆x=abs(x2-x1) and ∆y=abs(y2-y1)
 Initialize starting point of linei.e. x=x1
y=y1
 Plot (x, y) i.e plot first point.
 Obtain initial value of decision parameter PK as
PK =2∆y-∆x
 If PK <0
{ x=x+1
y=y
PK = PK +2∆y }
If PK >=0
{ x=x+1
y=y+1
PK = PK +2∆y-2∆x }
plot(x,y)
 Repeat step (6) ∆x times.
 stop

9. EXAMPLE
 Consider a line from (6,6) to (12,9). Use
simple Bresenham’s algorithm to rasterize
this line.

10. CIRCLE GENERATING
ALGORITHM
y axis y=x
x axis
y=-x

11.  Following are the main algorithm’s used to
draw a circle.
1. DDA algorithm.
2. Bresenham’s algorithm.
3. Mid-point algorithm.

12. DDA CIRCLE GENERATING ALGORITHM.
 Algorithm:-
1. Read radius of circle(r) and calculate value
of e(epsilon).
2. x=0 y=r
3. x1=x y1=y
4. While((y1-y)<e||(x-x1)>e)
{
x1=x1+e.y1
y1=y1-e.x1
}
5. stop

13. BRESENHAM’S CIRCLE
GENERATING ALGORITHM.
 Algorithm:-
1. Read radius of circle(r)
2. Calculate initial decision variable Pi.
3. x=0 and y=r
4. if(pi<0) { x=x+1 pi=pi+4x+6 }
elseif(pi>=0) { x=x+1 y=y-1
pi=pi+4(x-y)+610 }
5. Plot pixels in all octants
6. stop

14. MID-POINT CIRCLE GENERATING
ALGORITHM.
 Algorithm:-
1. Read radius of circle(r).
2. Obtain 1st
point on circle boundary as (x0,y0) = (0,r)
3. Calculate initial decision variable P0=1-r.
4. if(pi<0) { xi=xi+1
yi=yi pi+1=pi+2(xi+1)+1 }
elseif(pi>=0) { xi=xi+1
yi=yi-1 pi+1=pi+2(xi+1)+1-2yi+1
}

15. 5. Plot pixels in all octants
Plot(x,y)
Plot(y,x)
Plot(-y,x)
Plot(-x,y)
Plot(-x,-y)
Plot(-y,-x)
Plot(y,-x)
Plot(x,-y)
6. stop

16. THANK YOU