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Put sin on segment in 3d

i need to put a sin function, or any other function on start of segment in 3d space. Something like that:

Example

But in 3d space, help me pls, i spent about 4 days for solving it, but did not get result

There are 2 points in space at arbitrary positions. I need a sinusoid between these two arbitrary points.

3d segment example

An example of the final result

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Answer

Generate point set in OXY plane and apply affine transformation to make OX axis coincide with desired vector, also you need to define one normal vector to get sin plane unambiguously.

Math for affine matrix calculation (here simpler because we can choose unit-length vectors)

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