Re: Loop antenna
It sounds like you are trying to plot the radiation pattern in polar coordinates. Most calculus texts have sections describing various plotting techniques. The two most commonly used are cartesian (x y plots) and polar (r, Θ)
What you probably want is plot with each point defined by a vector (in the x-y plane) whose origin is at the coordinate axis and the direction is an angle, counter-clockwise from the x-axis. The vector length is the gain. Be careful about letting the length "reflect" through the origin for small values as this will produce a strange looking plot. You will probably want to plot amplitude (gain) using a dB scale. I usually truncate the amplitude at whatever value corresponds to the center of the plot to avoid having the plot pass through the center. Stopping at the center does not look weird the way it would if you allowed it to go through the origin and beyond. Plotting in cartesian coordinates avoids this issue, but then you want a polar plot.
The other warning is pay attention to the angular units (radians or degrees) when you prepare your plot.