Assuming you have the center of each segment and its width and height, you can do this:
-Set imageMode to CENTER: https://processing.org/reference/imageMode_.html
- Load your rectangular texture in a PImage object
- Use translate/rotate. Translate is used to set the center of the sketch at the center of the line segment. You do a rotate and then you draw the image
- Use push/pop. Push/pop allows to set and reset your sketch coordinate system. This comes handy when you are ready to set your next segment
In your code above, the translate/rotate and push/pop would be inside the for loop. You will need to have a PImage array that you can get the textures from while interacting with each line segment.
By the way, iamgeMode CENTER is just a recommendation. You can use any image mode you want but I find that CENTER works better in these situations.
Kf