Non-monotonic interpolation methods

Question

I'm currently trying to interpolate curves through multiple dimensions (which just involves using interpolation methods on each dimension individually), and I'm a bit confused about the PCHIP (piecewise cubic hermite interpolation polynomial). Does the PCHIP only apply to monotonic data? The data I am interested in is necessarily non-monotonic, so I used a Catmull-Rom spline, but the PCHIP seems to fit my data better, but the off the shelf implementation of the PCHIP im using only works for strictly increasing/decreasing data. I would like to have written my own PCHIP interpolation algorithm (in java), but I cant seem to find the underlying algorithm anywhere on the web. I guess my questions are

1) Does the PCHIP apply to non-monotonic data?

2) If not, are there any other interpolation methods, which pass through the control points, that I could use?

3) Does anyone know of where I can find the algorithm behind the PCHIP?

Answer 1

I don't know PCHIP as an established term, but to me the name suggests any use of a cubic hermite polynomial for interpolation, i.e. a more general term which includes Catmull-Rom among others. The main distinguishing fact from common spline interpolation seems to be the explicitely computed tangents. Both might work for your situation, as both will pass through the defining points and neither will enforce monotonicity. Wikipedia has some descriptions and some references for you if these are the concepts you have in mind. If not, you should be more specific about the context in which you read about this term, as that context might provide a more specific definition.