NURB curves
and surfaces are the industry standard for geometry description
in CAD/CAM or Computer Graphics.
NURBS
are piecewise rational; they are the logical
extension of Bspline or Bezier entitities.
While those
have their roots in affine
geometry, NURBS cannot be understood without paying attention to
their foundations
in projective geometry  this constitutes the first part of the
book.
After these
foundations have been laid, rational conics and Bezier curves are
introduced;
rational Bspline curves (NURBS) follow. As a further extension,
the surfaces corresponding
to these curves are also introduced. Applications include Pythagorean
Hodograph curves
and developable surfaces.
