Solving (piecewise) polynomial systems of equations is a crucial problem in
many fields such as computer-aided design, manufacturing, robotics, kinematics
and many others. A robust and efficient solution is in strong demand.

Subdivision-based multivariate constraint solvers typically employ the convex
hull and subdivision/domain clipping properties of the Bezier/B-spline
representation to detect all regions that may contain a feasible solution.
Termination criteria for this subdivision/domain clipping approach are
necessary so that, for example, no two roots reside in the same sub-domain
(root isolation).

Such a criteria for well-constrained systems, consisting of n
equations in n unknowns, as well as for under-constrained systems,
consisting of n equations in (n+1) unknowns, will be introduced.
Several possible applications of the subdivision-based solver,
namely computing 3D trisector curves, surface-surface intersection
problem or kinematic simulations in 3D will also be discussed.