Termination Criteria for Subdivision Multivariate Solvers

Kdy? 16.9.2010 14:50 - 15:35
Kde? ZČU / FAV / KMA / UL610 (učebna)

Michael Bartoň: Termination Criteria for Subdivision Multivariate Solvers

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 B´ezier/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 underconstrained 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.

l freeform (typically NURBs) curves and surfaces, exploiting intrinsic and/or

geometric properties, on one side, and the algebraic structure of the shape, on the other.  Other methods are specific and employ special properties of the problem in hand, such as the case in offset computation.


In this talk, I will survey these results and provide a birds view of the current state-of-the-art on the self-intersections problems.

Evropská unie, ESF, MŠMT, OP Vzdělávání pro konkurenceschopnost, ZČU


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