Lattice method reduces the dimensionality of surface
intersections by computing intersections of a number of iso-parametric
curves of one surface with the other surface followed by connection of
the resulting discrete intersection points to form different solution
branches [352]. For intersections of parametric patches,
the method reduces to the solution of a large number of independent
systems of nonlinear equations. The reduction of problem
dimensionality in lattice methods involves an initial choice of grid
resolution, which, in turn, may lead the method to miss important
features of the solution, such as small loops and isolated points
which reflect near tangency or tangency of intersecting surfaces, and
to provide incorrect connectivity. Appropriate methods for the
solution of the resulting nonlinear equations in the present context
are identified in Chap. 4.
