Affiliation:
1. Universität Salzburg, FB Computerwissenschaften, A–5020 Salzburg, Austria
Abstract
We present an algorithm for approximating multiple closed polygons in a tangent-continuous manner with circular biarcs. The approximation curves are guaranteed to lie within a user-specified tolerance of the original input. If requested, our algorithm can also ensure that the input is within a user-specified tolerance of the approximation curves. These tolerances can be either symmetric, asymmetric, one-sided, or even one-sided and completely disconnected from the inputs. Our algorithm makes use of Voronoi diagrams to build disjoint and continuous tolerance bands for every polygon of the input. In a second step the approximation curves are fitted into the tolerance bands. Our algorithm has a worst-case complexity of O(n log n) for an n-vertex input. Extensive experiments with synthetic and real-world data sets show that our algorithm generates approximation curves with significantly fewer approximation primitives than previously proposed algorithms. This difference becomes more prominent the larger the tolerance threshold is or the more severe the noise in the input is. In particular, no heuristic is needed for smoothing noisy input prior to the actual approximation. Rather, our approximation algorithm can be used to smooth out noise in a reliable manner.
Publisher
World Scientific Pub Co Pte Lt
Subject
Applied Mathematics,Computational Mathematics,Computational Theory and Mathematics,Geometry and Topology,Theoretical Computer Science
Cited by
14 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献
1. Numerically robust computation of circular visibility;Computer Aided Geometric Design;2018-01
2. On the generation of spiral-like paths within planar shapes;Journal of Computational Design and Engineering;2017-11-24
3. Exploring Curved Schematization of Territorial Outlines;IEEE Transactions on Visualization and Computer Graphics;2015-08-01
4. Stenomaps: Shorthand for shapes;IEEE Transactions on Visualization and Computer Graphics;2014-12-31
5. Optimal arc spline approximation;Computer Aided Geometric Design;2014-06