# Formula for Graphing Circle based on Points

I'm a Software Engineer, not super awesome at Math; however, I definitely need some help on the Math side for some animation work I'm trying to accomplish, and I am clueless how to get there :)

For a basic idea of what I am trying to achieve, imagine a circle whose $0$ degree mark is $12$ o'clock and $180'$ is $6$ o'clock. I need to draw the outline starting at about $200$ degrees to about $160$ degrees.

The platform I am developing on, is limited to drawing lines, or a dot at point$(x, y)$. This animation must change position each frame, so I need to be able to re-apply the formula to the new $(x, y)$, the old ones, and draw it again. Is there a formula that would change $(x, y)$ each time I pass it that would graph a circle? I'm probably not explaining things that great, so I'll try to break it down as simply as I can, because I do not know what the word/terminology is for what I'm attempting to ask...

I need to say, computer, take point$(x, y)$, draw a dot. (NEW_FRAME) Now, take point$(x, y)$. draw a dot, and take point$(x_2, y_2)$, draw a dot. Over and over. I need a way to get $(x, y)$ to $(x_2, y_2)$, and then to $(x_3, y_3)$ until the outline of a circle would be created.

I apologize in advance for sounding like complete moron and using all of the wrong terminology. Thanks in advance for any advice!

In an x–y Cartesian coordinate system, the circle with centre coordinates (a, b) and radius r is the set of all points (x, y) such that $$\left(x - a \right)^2 + \left( y - b \right)^2=r^2.$$ (Source: Wikipedia) Use the equation to plot all points/lines on your table of x's and y's. This might help, you can take the image down .

If the center of the circle is at $(a,b)$ and the radius is $r$. Then this pseudo code would create the vertices of a dodecagon with vertices at $3$ o'clock, $4$ o'clock, $\dots$, $2$ o'clock.

$\quad \texttt{DTHETA = 2*PI()/12}$
$\quad \texttt{THETA = 0}$
$\quad \texttt{FOR N = 0, 11}$
$\qquad \texttt{X[N+1] = A + R*COS(THETA)}$
$\qquad \texttt{Y[N+1] = B + R*SIN(THETA)}$
$\qquad \texttt{THETA = THETA + DTHETA}$
$\quad \texttt{END FOR}$