Computational geometry: an introduction
Computational geometry: an introduction
Optimal shortest path queries in a simple polygon
Journal of Computer and System Sciences
Polygonal approximations that minimize the number of inflections
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
Simplifying a polygonal subdivision while keeping it simple
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
Approximation of Polygonal Curves with Minimum Number of Line Segments
ISAAC '92 Proceedings of the Third International Symposium on Algorithms and Computation
Number Theory Helps Line Detection in Digital Images
ISAAC '93 Proceedings of the 4th International Symposium on Algorithms and Computation
Computing the visibility graph of points within a polygon
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Optimal simplification of polygonal chain for rendering
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Streaming algorithms for line simplification
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
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We study the well-known problem of approximating a polygonal path P by a coarse one, whose vertices are a subset of the vertices of P. In this problem, for a given error, the goal is to find a path with the minimum number of vertices while preserving the homotopy in presence of a given set of extra points in the plane. We present a heuristic method for homotopy-preserving simplification under any desired measure for general paths. Our algorithm for finding homotopic shortcuts runs in O(mlog(n + m) + n log n log(nm) + k) time, where k is the number of homotopic shortcuts. Using this method, we obtain an O(n2 +mlog(n+m)+n log n log(nm)) time algorithm for simplification under the Hausdorff measure.