Interpolation

One way to implement n-dimensional interpolation is to use the fact that an n-dimensional interpolation can be expressed as a 1-dimensional interpolation of (n-1)-dimensional interpolations.

Therefore, we first can defined one dimensional interpolation functions as all higher dimensional interpolations can be expressed as multiple applications of these one dimensional functions.

• Linear Interpolation
• Cubic Interpolation

These interpolation functions have static attributes that tell you how many data-points they need to operate. As an input they take the Data struct with the dimension set to 1. This Data struct is an n-dimensional array (internally using std::array).

• Variadic template Data struct

One also needs to decide how to deal with the image boundaries. There are various ways to do this. Currently, only the following way is implemented.

• Constant boundary

Finally, two functions are defined that realise the nD interpolation. One is to extract the necessary data from a given image, the other one is to take a given position and interpolate that data.

• Extract
• Apply interpolation function