Jiri Kosinka: Medial Axis Transform Approximation via C^2 MPH Splines

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Jiri Kosinka: Medial Axis Transform Approximation via C^2 MPH Splines

Povzetek: We will briefly describe and analyze an algorithm for $C^2$ Hermite interpolation by Pythagoren hodograph curves of degree 9 in Minkowski space. We will show that for any data there exists a four-parameter system of interpolants and we will identify the one which preserves symmetry and planarity of the input data and which has the optimal approximation degree. The new algorithm is applied to an efficient approximation of the medial axis transform of a planar domain leading to rational parameterizations of the offsets of the domain boundaries with a high order of approximation. This is joint research with Zbynek Šir.