5. Deformable reference frames

5.1 General

In the previous paragraphs, we considered curves and surfaces inscribed in a Cartesian space; this point of view is logical since all practical realization is carried out with the help of machines or screens using Cartesian or, possibly, cylindrical or spherical reference frames.

Sometimes, however, it can be advantageous to take this concept a step further and work first in a parametric frame of reference, before finally returning to a Cartesian frame of reference, which is necessary for plotting and machining.

We will limit ourselves here to three practical cases:

• drawing a curve on a parametric tile ;

• drawing a tile on a parametric tile ;...