Page 43 - Computer Graphics

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Initial decision parameter

In region 1 the initial value of a decision parameter is obtained by giving

starting position = (0,ry).

2
2
2
i.e. p10=ry +1/4rx -rx ry
When we enter into a region 2 the initial position is taken as the last position
selected in region 1 and the initial decision parameter in region 2 is then:

2
2
2
2
2
2
p20=ry (x0+1/2) +rx (y0-1) -rx ry

Algorithm :

1. Take the input and ellipse centre and obtain the first point on an ellipse
cantered on the origin as a (x,y 0)= (0,r y).

2. Now calculate the initial decision parameter in region 1 as:
2
2
2
p10=ry +1/4rx -rx ry
3. At each xk position in region 1 perform the following task. If p1k<0 then
the next point along the ellipse centered on (0,0) is (xk+1,yk).
2
2
2
i.e. p1k+1=p1k+ ry xk+1+ry
Otherwise the next point along the circle is (x k+1,y k -1)
2
2
i.e. p1k+1=p1k+2ry xk+1 – 2rx yk+1+ry
2
4. Now, again calculate the initial value in region 2 using the last
2
2
2
2
point (x0,y0) calculated in a region 1 as : p20=ry (x0+1/2) +rx (y0-1) -
2
2
rx ry
5. At each yk position in region 2 starting at k =0 perform the following
task. If p2k<0 the next point along the ellipse centered on (0,0) is (xk , yk-
1)
2
2
i.e. p2k+1=p2k-2rx yk+1+rx
Otherwise the next point along the circle will be (xk+1,yk -1)
2
i.e. p2k+1 =p2k+2ry xk+1 -2rx yk+1+rx
2
2
6. Now determine the symmetric points in another three quadrants.
7. Plot the coordinate value as: x=x+xc , y=y+yc

2
2
8. Repeat the steps for region 1 until 2ry x>=2rx y.