Approximation of the medial axis of polygonal regions in R²

Martin Schmidt, Leibniz Universität Hannover, Studienarbeit
06/2007

Polygonal regions in the euclidean plane are often represented by a
large number of edgepoints. Consequently their Medial Axis Transforms
contain an extreme high number of local medial branches. The
computational demands of a meshing of the region based upon such a
medial axis can be very costly and of poor quality. Furthermore a
consecutive finite element method simulation can be downgraded.

The aim of this junior thesis is to approximate the medial axis of a
given complex polygonal region in the plane. The basic idea is to delete
unimportant local medial branches and to merge pairwise connected branches.

The results of the implementation are demonstrated on the real problem of a two-dimensional representation of certain tooth bridges by its medial axis. Topological problems appearing after the approximation will be discussed.

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Kontakt: Philipp Blanke