Circle is defined as a set of points that are all at a given distance r from a center position (Xc,Yc).

**Circle Generating algorithm
Properties of the Circle**

Circle is
defined as a set of points that are all at a given distance r from a center
position (Xc,Yc). This distance relationship is expressed by the Pythagorean
theorem in Cartesian coordinates as

(X-Xc)^{2}
+(Y-Yc)^{2}=r^{2}

Bresenham’s
line algorithm for raster display is adapted to circle generation by setting up
the decision parameters for finding the closest pixel for each sampling step.

A method
for direct distances comparison is to test the halfway position between two
pixels, to determine if this midpoint is inside or outside the circle boundary.
This method is more easy . For an integer circle radius, the midpoint approach
generates the same pixel position.

**Midpoint Circle Algorithm**

1.Input
radius r and circle center (xc,yc) and obtain the first point on the
circumference of a circle centered on the origin as

(x0,y0)=(0,r)

2.Calculate the initial value of the decision parameter as P0=5/4 –r

3 At each
xk position, starting at k=0,perform the following test:

if
Pk<0 , then next point along the circle centered on (0,0) is (xk+1,yk) and

Pk+1=Pk+2xk+1
+1

otherwise
the next point along the circle is (xk+1,yk-1) and

Pk+1=Pk +
2xk+1 +1 – 2yk+1

where
2xk+1 =2xk + 2, 2yk+1=2yk-2

4.
Determine the symmetry points in the other seven octants

5.Move
each calculated position(x,y) onto the circular path centered on (xc,yc) and
plot the coordinate values x=x+xc,y=y+yc

6.Repeat
steps 3 to 5 until x > = y

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Computer Graphics and Multimedia : Circle Generating algorithm Properties of the Circle |

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