There are several techniques for texture mapping 3D surfaces depending on the surface type (NURBS, polygons, subdivision surfaces). Some techniques involve preparing the surfaces for texture mapping. For example, when texture mapping polygonal and subdivision surface types you need to understand how textures are applied using UV texture coordinates.
UV texture coordinates, or UVs as they are more commonly called, are two-dimensional coordinates that reside with the vertex component information for a 3D surface. UVs control the placement of a texture map on a 3D model by correlating the pixel position of the 2D texture map to the vertex positions on the model, so that the texture gets positioned (mapped) correctly.
For NURBS surfaces which have an inherent rectangular topology, the UV texture coordinates are implicit. That is, the UVs reside in the same location as the control vertices, so have a natural correlation to a rectangular shaped texture map.
In this lesson you’ll learn the basic principles of UVs by applying (mapping) an existing image (texture) to a simple polygonal model and creating and modifying the UV texture coordinates so that the texture map appears correctly on the surface.