2. Rational curves, point interpolation and polynomial spline smoothing

2.1 Rational curves

Fiorot and Jeannin in introduced, in the 1990s, the control of curves and rational surfaces via the use of mass vectors composed of either weighted points or vectors. These mass vectors are the equivalents for the rational case of poles or control points for the polynomial case. The mathematical context of the polynomial is linear and affine, that of the rational is non-linear and projective. Projective geometry is the essential tool for this construction. Let's take the example of the circle. It can be expressed in the following parametric rational...