Spiral through arbitrary points on the imaginary axis

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There are several points on the imaginary axis.

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Are there formulas that allow build a spiral that will pass through these points?

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You could use linear interpolation to construct a function $r(t)$ such that $r(0)=.2034$, $r(1)=.3533$, $r(2)=.5499$ and $r(3)=.9088$ and consider the spiral $s(t)=r(t)(-\sin(2\pi t),\cos(2\pi t))$

Here is an example with the first two points.