Visualization Interview Question:

What is Ellipse generating Algorithm in Visualization?

Submitted by: Muhammad

Algorithm
Step 1:Input radius rx, ry and ellipse center(Xc, Yc)and obtain the first
point on the circumference of a circle centered on the origin as
(X0, Y0) = (0, ry)
Step 2: Calculate the initial values of the decision parameter in region 1 as
P10 = ry
2 - rx
2 ry + 1/4 rx
2
Step 3: At each position starting at Xk position in region 1,starting at k = 0,
perform the following test:
If Pk < 0, the next point to plot is (Xk+1, Yk) and
P1k+1 = P1k+2 ry
2Xk+1 + ry
2
Otherwise the next point is (Xk+1, Yk-1) and
P1k+1 = P1k+2 ry
2Xk+1 - 2ry
2 Yk+1 + ry
2
Step 4: Calculate the initial values of the decision parameter in region 2 as
P20 = ry
2 (X0+1/2)2+ rx
2 (Y0 - 1)2- rx
2 ry
2
Step 5: At each position starting at Yk position in region 2,starting at k = 0,
perform the following test:
If Pk > 0, the next point to plot is (Xk, Yk-1) and
22
P2k+1 = P2k - 2 ry
2Yk+1 + rx
2
Otherwise the next point is (Xk+1, Yk-1) and
P2k+1 = P2k - 2 ry
2Yk+1 - 2rx
2 Yk+1 + rx
2
Step 6: Determine symmetry points in the other three octants
Step 7: Move each pixel position(X, Y) onto the circular path centred on
(Xc, Yc) and plot the coordinate values as
X = X + Xc Y = Y + Yc
Step 8: Repeat steps for region 1 until 2 ry
2X>=2 ry
2Y
Submitted by: Muhammad