Stipple dash length for diagonal line

I need to the know, with reasonably accuracy, the end position and length of an inital dash
specified through glLineStipple for a diagonal line of varying width.

Lets say the stipple pattern is 0x7777 == 0111011101110111
then when the line is horizontal or vertical it’s easy. It’ll be lineWidth*3 pixels after
the start of the line, say.
But when the line is orientated (i.e diagonal)?

[Hearn&Baker states that a diagonal dash is a factor of sqrt(2) greater orientated than
when it is horizontal, but I’m not sure if this hold for thick lines.
Anybody come across this?]

It varies depending on the renderer .