5.7.1 Rational polynomial parametric curve/implicit algebraic surface intersection (Case E3)

The intersection problem is defined as:

Let us consider an implicit algebraic surface of total degree

We substitute , and of degree into the implicit equation and multiply by leading to

of degree in . We then find its real roots in , as described in Sect. 5.6.1.

Alternatively, the problem can be formulated as a nonlinear polynomial system of four equations in four unknowns ( , , , ) and solved using the IPP algorithm.