# Linear Interpolation for scattered 3-D data

I have a dataset of scattered 3-D points (non-regular) that carry some variable and am trying to interpolate that variable to a new point. I have currently implemented a couple of methods, but don't like the behavior of inverse distance and am getting overshoot issues with the polyharmonic spline RBF. Is there a method that would simply provide me with a linear interpolation? If possible, a detailed explanation/example of a matrix setup would be greatly appreciated.

For example (and for those familiar), the software Tecplot has an option for linear interpolation, but I can't find any documentation on its method.

• Does the standard linear regression model serve your purpose? – Adrian Keister Nov 28 '18 at 14:11
• To my knowledge a linear regression wouldn't guarantee that the fit would "pass through" or reproduce values at the known data points. I need them to maintain values at known points and vary linearly in space between them – Travis Nov 28 '18 at 17:07
• Try scipy.interpolate.griddata from the scipy library in Python. It's at least sure to be well-documented. – Adrian Keister Nov 28 '18 at 17:16
• Thanks for the tip. I'll look into this – Travis Nov 28 '18 at 17:30