How can i divide intervals into n sub-intervals of equal distance in order to interpolate by using spline?

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Hy everyone,
My goal is to interpolate, by using spline, the six points reported in Figure 1.
However i was wondering if it was possible to divide, each interval (for example the interval between the point 1 and point 2) in n equidistant sub-intervals by creating other points and after interpolate to obtain Fig 2.
I dont know if it is possible creating the sub-intervals before performing the spline interpolation or after the interpolation.
Any help would be appreciated
Thank You
Lorenzo
FIG. 1
FIG. 2
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Image Analyst
Image Analyst 2020-12-10
See attached demo.

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