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How to increase warpPerspective Or warpAffine precision?

I would like to transform my images with rotation degree of 0.001 degree, and translate them with 0.0001 pixel in row or column. The problem with this library is that it cannot manage this kind of tiny transformation steps and the result is that the source and transformed images are identical with this tiny transformations!

Is there any way to increase this precision such that I could get correct and different images when I rotate them and translate them by 0.001 degree and 0.0001 pixels respectively ?

One approach is changing the interpolation mask size which is defined by "INTER_BITS" inside imgproc.hpp file and compiling opencv library from scratch, but it could only increase the precision only a little bit.