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Timeline for Function describing two circles

Current License: CC BY-SA 4.0

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Mar 2, 2022 at 22:38 comment added Googlebot Because I look for a general function to describe it. I can think of two ways to do so, (i) with PDF similar to head equation, or (ii) by Fourier series. But there should be a simpler way, as the key is where the $c_1 - c_2 < r_1+r_2$.
Mar 2, 2022 at 21:57 comment added Ethan Bolker Why should there be a rule? You might remove one degree of freedom by requiring the tangent lines at the intermediate control points be reflections of each other across a vertical axis.
Mar 2, 2022 at 21:55 history edited Ethan Bolker CC BY-SA 4.0
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Mar 2, 2022 at 21:05 comment added Googlebot I thought of a cubic spline, as I used one to draw the red line. The point is that I could not find a general rule for the place of control points. I can visually find a rule, but what is the mathematical rule for the changes in the coordinates of the control points changing the black line into the blue line?
Mar 2, 2022 at 21:00 history answered Ethan Bolker CC BY-SA 4.0