The extension to surfaces of the various curves and splines covered the previous chapter is mercifully straightforward. In the first section of this chapter the lofted, translated and Coons surfaces are based on Bézier curves, but could equally be based on the B-spline or NURBS definitions from Chapter 3. To get started with these surfaces try the Matlab scripts figure4_1.m, figure4_2.m and figure4_3.m from the Aircraft Geometry Toolbox.
The chapter then goes on to consider surfaces created from grids of control points which, although more awkward to define, yield enhanced local control. We then show how to use free-form deformation, which manipulates geometry by attaching it to Bézier curves, which are defined by a grid of control points. Here we also include implementations in OpenNURBS/Rhino-Python.
