Texture coordinates

Last two days I was trying to figure out what are texture coordinates. It's name sounds pretty obvious, but in real code it was confusing for me what exactly are texture coordinates and texture buffer, and how they should be properly defined.

I have found a nice picture, that have everything to understand once and for all what they are.

According to OpenGL documentation each texture must have like 2Nx2N for better memory allocation and computation. Each object's vertex should be “bound” to some point on the texture so that when the texture is applied to the object, the graphics card will know how to “wrap” an object with a texture. To do it properly, the corresponding position of each vertex on a 2d texture should be defined. This is called texture coordinates, and they should be defined as [0;1] numbers.

For example, if we have a 3x3 square mesh, that consists from 9 vertices with any dimensions in 3d (lets say 10 by 10), the scheme of defining texture coordinates (and texture buffer lately) should be like this (texture coordinates are always 2d and in range of [0;1] for each vertex):

Black text represent 3d vertex coordinates, and red text - 2d texture coordinates.