Looking at these from the front, observe the gaps between the tubes (fibers).

The gaps are largest when the "surface" faces the camera. As the surface curves away, the tubes appear closer together, decreasing the gaps.

On the far left and right, the tubes actually overlap and there are no gaps in those areas.

Now when seen from a normal distance, the fibers in a cloth are so tiny we can't even see them individually, the way we see these tubes. But the same thing is happening. The gaps between the fibers let us see what is behind. The size of the gaps, relative to the size of the tubes, changes as the surface angles away, until the point at which there are no gaps at all, and the cloth becomes opaque.

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Renderosity forum reply notifications are wonky. If I read a follow-up in a thread, but I don't myself reply, then notifications no longer happen AT ALL on that thread. So if I seem to be ignoring a question, that's why. (Updated September 23, 2019)