This is effectively a "circle through three points". Either the circle solution or a "best-fit" solution.
Assuming that the 3 points are on the same line, you can convert the data so that the x-variable is distance and the y-variable is your z.
Your distances would be 0 (ie the start point), distance to sag point, distance to end point.
Your z values become y.
Solve for the equation and generate other points as needed.
The equation would be degenerate if the line was completely straight.
Assumptions:
This would work best if the sag point were in the middle of the span.
The length of cable relative to the distance between end points should be "uniform" so that the cable behaves in a similar fashion along its total length. (sloppy install with over or under tension will result in different deflections per unit length)
If there is significant elevation differences between the start and end points, the location of the sag point may shift significantly to the lower elevation end and the circle assumption would be void.
In those cases, you would have to consider a best-fit circle or ellipse through the points rather than a circle itself.
Best fit ellipses could be used, but "usually" at least 5 points are needed but code exists to handle situations like yours, but the effort is large.
There is little point in working on this with 3 dimensions given that the span should form a straight line with the sag point somewhere along the line. Translation and rotation to and from the initial coordinate system is covered by standard affine equations.
Final note. Before you begin on this venture, it would be useful to examine some of your transformed data to get an initial estimate of sag location and value relative to span length and span elevation difference.
... sort of retired...
