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I am move this model by curve.
I want to realize slide my model by this curve.
In each step I have last position and current.
How to ROTATE my model for making the imitations of the repetition of the curvature:
There are several posts about rotating nodes to line them up with a vector, and that is exactly what you are trying to do. You want to align the axis (looks like the X axis in your drawing, but you might actually want the Z) to line up with the vector lastPos - curPos.
for some exact results you would need yur curve to be defined by some function.
But I would simply store old position in last frame, calculate future position in next frame, than find out angle from current position to old and future one, add it together then cut it by 2 and you end up with something very close of what you need.