How to draw a repeating texture along a line/polygon path?

Question

Graphic arts

That's what I mean. Moreover, the pattern should not start over from each top, it should continue. It is also noticeable how the dotted line works.

As far as I understand, it is impossible to bind a texture of arbitrary height directly to a line, because the line width is limited. To do this, triangulate each segment of the line and apply a texture to the polygons.
I solved the issue with triangulation in this way:

Drawing the resulting array of points through

GL_TRIANGLE_STRIP

- I get a line of arbitrary width. It remains only to apply the texture in the right way. But with the texture coordinates, I'm completely confused.
No matter how I tried, but even on the example of one segment it does not work. the texture is smudged and broken.