## Friday, June 14, 2019

Circle generation algorithm

A circle is a symmetrical figure with 8 symmetrical figure with 8 symmetrical region with the 8 different point. Which are plot on a same plane surface 8 way symmetric is used by reflecting each point around each 45 degree axis.

Where,
P1 = (x,y)
P2 = (y,x)
P3 = (-y,x)
P4 = (-x,y)
P5 = (-x,-y)
P6 = (-y,-x)
P7 = (y,-x)
P8 = (x,-y)
There are two standard method od methodically defining a circle centered at the origin.

1.First methodology defines a circle with the second order polynomial equation.

r^2 = x^2+y^2
r = √x^2+y^2
where x = x-coordinate
y = y-coordinate
the second method of defining a circle with may use of trigonometric function

sin θ = y / r
sin θ = x / r
x = r cos θ
y = r sin θ
where,
θ= correct angle
r = radius of the circle
x = x-coordinate ,
y = y-coordinate.

By this method θ is stepped θ to π/4 and each value of x and y is calculated by the trigonometric function.
However computation of sinθ and cosθ is more time consuming then the calculation required by the first method.