3D Interpolation with 2 dependent function values

Hey everybody,

I have calculated a set of 5-dimensional data which must be interpolated. The special thing is that 3 dimensions define the querry points, while the remaining two are functions values at each querry point.

You can think about that like following:

• A device is moved in x,y and z. Therefore, its position in space is defined by the first three dimensions of the data.
• To stabilize the related process, the device must be tilted with cartesian angles alpha and beta, which correspond to the device's actual position in space.
• It is possible to calculate the required tilts (alpha, beta) for some querry points (x,y,z).
• It's not possible to define the xyz-grid fine enough for the application. Therefore an interpolation must be done.
• Unfortunately, it seems like that the required tilts (alpha and beta) are dependent on each other, which means that two separate interpolations (x,y,z, alpha) and (x,y,z, beta) will not be successful.

Is there a way (in general) to conduct an interpolation for 3D querry points that provides multiple function values? If yes, how is this doable in Matlab?

Nice weekend to everybody!

Answer 1

[Torsten]

Unfortunately, it seems like that the required tilts (alpha and beta) are dependent on each other, which means that two separate interpolations (x,y,z, alpha) and (x,y,z, beta) will not be successful.

I don't see that it should matter for the interpolation that alpha and beta are dependent. If this dependency is reflected in the data points, it will also be reflected in the query points - also if you make separate interpolations.

[Alexander Graf]

Hey Torsten,

thanks for your fast reply! Seems that you are right :)

I've tried it with 2 separate interpolations & it seems to provide the correct results. My gut feeling was wrong ;)