Do you asking about some math to calculate angle between 2 vectors to check the arc? You mentioned about 3 points and i asume there is something like this:
[how do i see this
then you need to calculate angle or check dot product between 2 vectors and according to result you will be able to say if the arc is clockwise or counter-clockwise.
I'm not sure if this is such low level problem but if you need any other help with math-drawing feel free to ask. Stuff like this is kind of my hobby