**Ellipse**

**Drawing algorithm**

In
the case of

**ellipse**however symmetry is four rather than 8 way there are two methods of mathematically define**ellipse**.
1.

**Polynomial Method: -**with the use of second order polynomial we can define an**ellipse**as**(x-h)^2/a^2 + (y-k)^2/b^2 = 1**

Where (h,k) is the
center of

**ellipse**a is the length of major axis. b is the length of miner axis (x,y) are the coordinates.
When the polynomial method is used
define an

**ellipse**. The value of x is incremented from h to a for each step of x each value of y is found by evaluating the expirations
Y=b√1-((x-h)^2/a^2)+k

This method is very
efficient because the square of a and (x-h) must be found then floating point
division of (x-h)^2 by a^2 and floating point multiplication of the square root
of

1-((x-h)^2/a^2) by b must be perform.

2.

**Trigonometric Method: -**The following equation define an ellipse trigonometrically**x= acosÎ¸+h &**

y= bsinÎ¸+k

where x,y are the
current coordinates a & b is the length of major and minor axis
respectively and Î¸ is the current angle.

The value of Î¸ is
varied from 0 to Ï€/2.

The remaining points
are found by symmetric.

Also read this Midpoint ellipse theorem

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