How to put lines exactly onto a surface?

 From:  sosodef
6171.7 
Thank you Michael, Deform -> Flow worked perfectly for me !

But another problem occurs...

i need to sweep a circle over "projected" lines... If I do so, the ends look, messy, because the sweep goes over the edge of the yellow lines ...!

If i choose the option pointy start or pointy end it looks almost like how it shoud do, but in this case.. the start/end gets smaller, which shouldn´t do !

Can you help me out once again, please ?

Thank you !
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