Why is it possible to encounter a texture coordinate greater than 1 or less than 0

Question

I'm studying a text about texture mapping and in the preparing to draw session, I read:

Define the texture wrapping parameters. This will control what happens when a texture coordinate greater than 1.0 or less than 0.0 is encountered:

glTexParameteri( GL_TEXTURE_2D, GL_TEXTURE_WRAP_S,wrap);  
glTexParameteri( GL_TEXTURE_2D, GL_TEXTURE_WRAP_T,wrap);  

where wrap is:
GL_REPEAT : specifies that this pattern will repeat (i.e., wrap-around) if transformed texture coordinates less than 0.0 or greater than 1.0 are encountered.

GL_CLAMP : specifies that the pattern will “stick” to the value at 0.0 or 1.0.

But there's no explanation what is the reason of encountering such texture coordinates?
For example suppose that I have just drawen a rectangle and I want to apply an image as a texture on it, is it possible to encounter such coordinates?

Answer 1

Not all textures use texture coordinates that come from the mesh data. For example, with projective texturing, you transform the world into the space of the texture. Well, a lot of that world falls outside the [0, 1] range of the texture. Without some sort of clamping mode in place, you're going to get problems.

Answer 2

Precisely, to repeat a texture.

So, if you have a quad, and the texture coordinates go from 0 to 1, the texture will be drawn once. If the coordinates go from 0 to 2 and wrap is set to GL_REPEAT, then the texture will be drawn twice.

Try it and see it by yourself

Answer 3

Yes, you can encounter texture coordinates greater than 1.0 and smaller than 0.0.

This depends completely on the model, you loaded. Normally, for each vertex there is position, normal, and texture coordinate stored. In most mesh file formats, the texture coordinate is not restricted to any range.

This is used to repeat a texture. For example, to span a texture four time between a quad of vertices, the texture coordinates would be 0,0, 0,4, 4,0 and 4,4. Without texture wrapping, you would need additional vertices to split the surface into 4 times 4 sub surfaces with each the texture coordinates 0,0, 0,1, 1,0, 1,1. Fewer vertices results in better rendering performance.

Typically, it is not desired that the user notices the edges of a repeated texture. Therefore, repeated textures are tileable in most cases. Than means, the right edge fades seamlessly to the left one and the top edge to the bottom one. This way, the transition is smooth and hopefully not notices by the user.

A more advanced, but related topic is, to cleverly obscure the fact that the same texture was repeated multiple times. For example, blending repeated textures of different size, for example a wall texture and a dirt decal, is a common technique.