Reference: https://www.physicsforums.com/forums/differenti

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I have a line of so many units long and in a location and angle relative to a bounding domain. If the domain is shifted along a vector form bottom left to top right, how long of a distance along the vector of the line will it be until the line is in the same position again.

The X and Y shift vector could be anything, but will always be a positive move.
The Offset of the line has to be in the direction of the line from its origin and moving at the angle between 0 and [tex]\pi[/tex]

**Please note that I have an iterative programmatic solution to solve by replicating the box and checking to see if the lines correspond, but I am just seeing if there may be a formulaic way to just get it or something better than "try and check"

This is what the definition looks like:

angle.PNG (68.59 KiB) Viewed 876 times

This is what a 4x4 sample of the final pattern would look like, but it would vary.

patternpreveiw.PNG (24.52 KiB) Viewed 876 times

**Another note that for "clean" lines in a shift or better angle (45, 30, 60 etc) I easily find this just using this:
COS((180/[tex]\pi[/tex])*(angle-90))*ShiftX

Any pointers or idea I would greatly appreciate, honestly even if there isn't an easy way I will just keep trying and checking.