Efficient Computation of A Simplified Medial Axis

Abstract

The computation and application of the medial axis have been limited because of its instability and algebraic complexity. In this paper, we use a simplification of the medial axis, the θ-SMA, that is parameterized by a separation angle formed by the vectors connecting a point on the medial axis to the closest points on the boundary. We formally characterize the degree of simplification of the θ-SMA as a function of θ. We present a fast algorithm to compute an approximation of the θ-SMA. It relies on computation of the distance field and its gradient using graphics hardware. The complexity of the algorithm varies based on resolution of the volume discretization and is a linear function of the input size. We have applied this algorithm to approximate the SMA of complex models composed of tens or hundreds of thousands of triangles. On a 2-GHz PC, its running time varies from a few seconds, for a model consisting of hundreds of triangles, to minutes for highly complex models.