Page 72 - DCAP313_LAB_ON_COMPUTER_GRAPHICS

Lab on Computer Graphics

Notes Output
Enter the Radius Value: (Rx, Ry) =10, 30
Enter the xcenter and ycenter Values: =300,150

In 1970 Danny Cohen presented at the “Computer Graphics 1970” conference
in England a linear algorithm for drawing ellipses and circles.

5.2 Midpoint Ellipse Algorithm

Midpoint ellipse algorithm is a technique for drawing ellipses in computer graphics. This
method is customized from Bresenham’s algorithm. The advantage of this modified method is
that single calculation operations are required in the program loops. This leads to simple and
fast execution in all processors.
Let us consider one quarter of an ellipse. The curve is divided into two regions. In region I, the
slope on the curve is greater than –1 while in region II less than –1.
y
Region I
b
dy/dx =–1

Region II
a x

m =–1

Consider the general equation of an ellipse,
b x + a y – a b = 0
2 2
2 2
2 2
In region I (dy/dx > –1),
x is always incremented in each step, i.e. x k + 1 = x k + 1.
y k+1 = y k if E is selected, or y k+1 = y k – 1 if SE is selected.
In order to make decision between S and SE, a prediction (x k + 1, y k –½) is set at the middle
between the two candidate pixels. A prediction function Pk can be defined as follows:

Region I
P k = f(x k + 1, y k – ½)
= b (x k + 1) + a (y k – ½) – a b
2 2
2
2
2
2
66 LOVELY PROFESSIONAL UNIVERSITY