The intersection problem between a procedural parametric curve and an
implicit algebraic surface is defined as:
(5.74)
This leads to four nonlinear equations in four
unknowns
,
. We could use Newton's method initiated
by a linear approximation of
, which can be
intersected more easily with
using the method of
Case E3 (see Sect. 5.7.1). However, no
robustness guarantees exist in general.