Polygonal chain approximation: a query based approach
Computational Geometry: Theory and Applications
Optimal simplification of polygonal chains for subpixel-accurate rendering
Computational Geometry: Theory and Applications
Stabbing balls and simplifying proteins
International Journal of Bioinformatics Research and Applications
Generating parametric models of tubes from laser scans
Computer-Aided Design
Fast and simple approach for polygon schematization
ICCSA'12 Proceedings of the 12th international conference on Computational Science and Its Applications - Volume Part I
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In this paper we give bounds on the complexity of some algorithms for approximating 2-D and 3-D polygonal paths with the infinite beam measure of error. While the time/space complexities of the algorithms known for other error measures are well understood, path approximation with infinite beam measure seems to be harder due to the complexity of some geometric structures that arise in the known approaches. Our results answer some open problems left in previous work. We also present a more careful analysis of the time complexity of the general iterative algorithm for infinite beam measure and show that it could perform much better in practice than in the worst case. We then propose a new approach for path approximation that consists of a breadth first traversal of the path approximation graph, without constructing the graph. This approach can be applied to any error criterion in any constant dimension. The running time of the new algorithm depends on the size of the output: if the optimal approximating path has m vertices, the algorithm performs F(m) iterations rather than n–1 in the previous approaches, where F(m) \le n–1 is the number of vertices of the path approximation graph that can be reached with at most m–2 edges. This is the first output sensitive path approximation algorithm.