We address the problem of continuously transforming or morphing one simple polyline into another so that every point p of the initial polyline moves to a point q of the final polyline using the geodesic shortest path from p to q. We optimize the width of the morphing, that is, the longest geodesic path between p and q. We present a linear-time algorithm for finding a morphing with width guaranteed to be at most 1.618 times the minimum width of a morphing. This improves the previous algorithm [9] by a factor of logn. We also develop a linear-time algorithm for computing a medial axis separator.
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