# How to draw a directed arc?

How to draw a directed arc with an initial point $$(x_i,y_i)$$, a terminal point $$(x_t,y_t)$$, and another given, intermediate point $$(x_m,y_m)$$ on the arc (say in the middle of the arc)? For instance, we may have $$(x_i,y_i)=(0,0)$$, $$(x_t,y_t)=(2,0)$$, and $$(x_m,y_m)=(1,1/3)$$.

I have noticed the nice answers to a related problem. However, with my very limited proficiency in Mathematica, I do not see a good way to modify those answers to get what I need here. I can certainly draw an arc -- but how to attach an arrow to it nicely?

• The documentation for Arrow gives examples of how to use Bezier curves to describe the path of an arrow, or a list of points. I expect you could create a function to draw a directed arc based on one or other of those. No Mathematica on this machine or I might have experimented a wee bit myself. Jan 14, 2022 at 14:49
• @HighPerformanceMark : Thank you very much for your hint. Jan 14, 2022 at 14:57
• pts = {{0, 0}, {2, 0}, {1, 1/3}}; and Graphics[Arrow[BezierCurve[pts]]].
– Syed
Jan 14, 2022 at 14:58
• @Syed : Thank you very much. Can you post this as an answer, so that I could accept it? Jan 14, 2022 at 15:04
• It is directly from the docs. If you make the question more interesting, then I would be happy to try to solve it and post an answer.
– Syed
Jan 14, 2022 at 15:07

Graphics[{Arrowheads[.06],Arrow[BezierCurve[{{0,0},{1,1},{2,0}}]]}]

• But this is not a circle arc. Compare with pts = {{0, 0}, {1, 1/3}, {2, 0}}; Graphics[{Circumsphere[pts], Point[pts], Red, {Arrowheads[.06], Arrow[BezierCurve[{{0, 0}, {1, 1}, {2, 0}}]]}}] Jan 14, 2022 at 15:08