Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  consider the problem of continuously transforming or morphing one simple polyline into another polyline 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. The width of a morphing is defined as the longest geodesic path beten corresponding points of the polylines. The optimization problem is to compute a morphing that minimizes the width.  present a linear-time algorithm for finding a morphing with width guaranteed to be at most two times the minimum width of a morphing. This improves the previous algorithm10 by a factor of log n.  develop a linear-time algorithm for computing a medial axis separator.  also show that the approximation factor is less than two for κ-straight polylines.
['Sergey Bereg']
I am writing a research paper on a idea AN APPROXIMATE MORPHING BETWEEN POLYLINES
[{"from": "human", "value": "I am writing a research paper on a idea AN APPROXIMATE MORPHING BETWEEN POLYLINES"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  consider the problem of continuously transforming or morphing one simple polyline into another polyline 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. The width of a morphing is defined as the longest geodesic path beten corresponding points of the polylines. The optimization problem is to compute a morphing that minimizes the width.  present a linear-time algorithm for finding a morphing with width guaranteed to be at most two times the minimum width of a morphing. This improves the previous algorithm10 by a factor of log n.  develop a linear-time algorithm for computing a medial axis separator.  also show that the approximation factor is less than two for \u03ba-straight polylines."}]