The CSpline function presented in a previous post fits a series of cubic polynomial curves to a specified series of points, returning the Y values for listed intermediate X values. I was recently asked if this could be reversed to find the X value for a specified Y value. Since CSpline can also return the coefficients defining each of the cubic curves it turns out that this is fairly simple. The procedure is:

- Use CSpline to find the coefficients defining each segment of the spline, that is find the value of a, b, c, and d in Y = aX^3 + bX^2 + cX + d.
- For each Y value:
- For each segment
- Solve the applicable cubic equation for the specified Y value
- Check if any solutions lie within the X range of the current segment
- If a solution is found add, it to the results array and go to the next Y
- If all solutions are outside the segment X range go to the next segment

- If no solution is found for any segment return a message to the results array and go to the next Y

- Assign the results array to the function return value.

The new version of CSpline.xls, including the new function, SolveSplineA, can be downloaded from: CSpline2.zip

Some screenshots of examples are shown below:

Solvespline input and output (click for full size view)

Example 1

Examples 2 and 3

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