If you don't care too much about how exact any particular curve is you could ignore the semircle and try some formulas that work in on an x and y grid of size 180.
You may want to look at some of the drawing programs for Processing to get an idea of the kinds of images you can create. Your servo version will only have a resolution of 180 steps and it will have some distortion because the servo moves in an arc, but Processing could be a help in seeing how images can be created using mathematical formula