CG Modeling 2: NURBS - An Introduction to Computer Graphics for Artists - page 245

Fig. 14.4 Each of these columns of shapes are genus 0 , 1 , 2 , and 3 , respectively. The genus of any
object is the number of completely enclosed holes

• Texture coordinates 1

• Normals (they can be reversed, but that is all)

Texture coordinates and normals (apart from reversal) are not editable because
these properties are embedded in the surface itself. Because a NURBS surface, or
patch , is always made between four connected edges, the edges may be mapped to
the four sides of UV space where “U” is the horizontal direction and “V” is vertical.
This allows a patch to have texture coordinates always mapped to it without regard
for the actual shape of the object. This can be advantageous when working with
convoluted shapes such as a knotted rope, as mentioned in Sect. 10.5.2 .

14.1.5 Surfaces and Curves

Surfaces are defi ned by curves and curves can be extracted from surfaces. Because
of this quality, switching from curves to surfaces and back again is easily done. For
an experienced artist, this can save a great deal of time.

14.2 Curves

Unlike polygons, with curves, less is almost always smoother (Fig. 14.5 ). Curves
allow you to “draw” in 3D, to create a simplifi ed yet totally accurate 3D image of
your object, and then build it into a renderable or manufacturable object based on

1 Some applications allow editing of NURBS UVs, with restrictions.