Computational geometry with higher order primitives

Main partner: JKU. Cooperation partners: INRIA; UNICAN, NKUA

Recent progress in solvers for multivariate polynomial systems enables the use of higher order primitives for geometric computations. Compared with the traditional piecewise linear primitives, which are ubiquitous in computational geometry, higher geometric approximation order leads to a reduction of the number of geometric primitives that are needed to faithfully represent a given geometry. Moreover, certain geometric problems - such as medial axis computations - are not even well defined. On the other hand, the basic operations of geometric computing become more complicated, typically involving nonlinear systems of equations.

We aim at investigating this in a general framework and to apply it to the specific problem of 3D medial axis computation. Medial axis computation is regarded as one of the approaches to be explored to facilitate the merger of CAD and finite element representations by isogeometric representation and analysis.