Subquadratic Medial-axis Approximation in Ir

We present an algorithm that approximates the medial axis of a smooth surface in IR which is given by a sufficiently dense point sample. The resulting, non-discrete approximation is shown to converge to the medial axis as the sampling density approaches infinity. While all previous algorithms guaranteeing convergence have a running time quadratic in the size n of the point sample, we achieve a running time of at most O ( n log n ) . While there is no subquadratic upper bound on the output complexity of previous algorithms for non-discrete medial axis approximation, the output of our algorithm is guaranteed to be of linear size.