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Defining a circle using Polar Co-ordinates :

The second method of defining a circle makes use of polar coordinates as shown in fig:

            x=r cos θ             y = r sin θ
Where θ=current angle
r = circle radius
x = x coordinate
y = y coordinate

By this method, θ is stepped from 0 to Defining a circle using Polar Co-ordinates & each value of x & y is calculated.

Defining a circle using Polar Co-ordinates

Algorithm:

Step1: Set the initial variables:

            r = circle radius
            (h, k) = coordinates of the circle center
                i = step size
            θ_end=Defining a circle using Polar Co-ordinates
            θ=0

Step2: If θ>θendthen stop.

Step3: Compute

            x = r * cos θ            y=r*sin?θ

Step4: Plot the eight points, found by symmetry i.e., the center (h, k), at the current (x, y) coordinates.

Plot (x + h, y +k)             Plot (-x + h, -y + k)
Plot (y + h, x + k)             Plot (-y + h, -x + k)
Plot (-y + h, x + k)             Plot (y + h, -x + k)
Plot (-x + h, y + k)             Plot (x + h, -y + k)

Step5: Increment θ=θ+i

Step6: Go to step (ii).

Program to draw a circle using Polar Coordinates:

Output:

Defining a circle using Polar Co-ordinates




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