Circle -DRAWING ALGORITHMS

Circle -DRAWING ALGORITHMS

The Polar method

Cos(th)=Delta(X)/r
Sin(th) =Delta(y)/r
Delta(x)=r*cos(th)
X-Xc=r*cos(th)
X=Xc-r*cos(th)
Delta(y)=r*sin(th)
Y-Yc=r*sin(th)
Y=Yc+r*sin(th)


The Cartesian method
(Y-Yc)2 + (X-Xc)¬2 =r2
(Y-Yc)2=r2 -(X-Xc)¬2
(Y-Yc) =Sqrt(r2 -(X-Xc)¬2 )
Y= Yc +Sqrt(r2 -(X-Xc)¬2)


The Polar method

We have
X=Xc+r*cos(th) …1
Y=Yc+r*sin(th) …2
Let Xc,Yc is (0,0) then the above Eq. as follow

X=r*cos(th) …3
Y=r*sin(th) …4

dx= -r*sin(th)*dth ...5
dy= r*cos(th)*dth …6
Replace Eq. 3 in Eq. 6 and 4 in 5

dx= -Y*dth …7
dy= x*dth ….8
then we can calculate any new point Xi+1 , Yi+1 depending on previous point Xi , Yi
Xi+1= Xi +dx ….9
Yi+1= Yi +dY …10
Xi+1= Xi –Yi*dth ….11
Yi+1=Yi+Xi+1*dth …12
Let dth=1/r























Circle DDA with symmetric

Let Xc,Yc is (0,0) we have

X=r*cos(th) …..13
Y=r*sin(th) …..14


dx= -r*sin(th)*dth ….15
dy= r*cos(th)*dth ….16

replace 13 in 16 and 14 in 15
dx= -Y*dth ….17
dy= X*dth …..18

we have
Xi+1= Xi +dx ….9
Yi+1= Yi +dY …10
then
Xi+1= Xi - Yi * dth ….19
Yi+1= Yi + Xi+1*dth …10