I made a terrible MSPaint illustration below to try and communicate what I'm looking to achieve. I have two circles of radius 0.4 located at (0,0) and (1,0), respectively. I am using TikZ.
I am trying to draw a smooth and symmetric arc (hand-approximated in red) subject to the following constraints:
- The end-points are tangent to each circle and are located on the outer edge of the circle. The end-points are defined on each circle by the same 45deg polar angle(albeit, in opposite facing directions).
- The mid-point is located at (0.5, 0.2) with a flat tangent.
It may be true that defining an arc according to the above requires additional constraints; if a symmetric pair of control points can also be included so I might play with the concavity that would also be ideal.
Eventually I will want to put the same curve on the underside of the two circles as well, and fill with color the area in between.