Tangent space is (when speaking of rendering) the space built up by the vertex normal and the vertex texture coordinates often called (u,v). This space is useful when dealing with textures with information in tangent space, for example a normal map.
The tangent space matrix can be separated in three vectors:
- The normal vector
- The tangent vector
- The bitangent vector
A detailed description of how to create the tangent vector from the u,v coordinates. (including source code)
http://www.terathon.com/code/tangent.html
More information about tangent Space (and an OpenGL implementation):
http://jerome.jouvie.free.fr/OpenGl/Lessons/Lesson8.php