Computation of medial axis and offset curves of curved boundaries in planar domains based on the Cesaro's approach

In this paper, we begin our research from the generating theory of the medial axis. The normal equidistant mapping relationships between the two boundaries and the 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. This algorithm overcomes the topological singularity of the polygon approximation algorithms by using exact curved boundaries, and doesn't need iteration. So, it 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.