Computation of medial axis and offset curves of curved boundaries in planar domain

In this paper, we begin our research from the generating theory of the medial axis. The normal equidistant mapping relationships between two boundaries and its medial axis have been proposed based on the moving Frenet frames and Cesaro's approach of the differential geometry. Two pairs of adjoint curves have been formed and the geometrical model of the medial axis transform of the planar domains with curved boundaries has been established. The relations of position mapping, scale transform and differential invariants between the curved boundaries and the medial axis have been investigated. Based on this model, a tracing algorithm for the computation of the medial axis has been generated. In order to get the accurate medial axis and branch points, a Two_Tangent_Points_Circle algorithm and a Three_Tangent_Points_Circle algorithm have been generated, which use the results of the tracing algorithm as the initial values to make the iterative process effective. These algorithms can be used for the computation of the medial axis effectively and accurately. Based on the medial axis transform and the envelope theory, the trimmed offset curves of curved boundaries have been investigated. Several numerical examples are given at the end of the paper.

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