Using Rational Numbers and Parallel Computing to Efficiently Avoid Round-off Errors on Map Simplification

This paper presentsEPLSimp, an algorithm for map generalization that avoids the creation of topological inconsistencies.EPLSimpis based on Visvalingam-Whyatt's (VW) algorithm on which least "important" points are removed first. Unlike VW's algorithm, when a point is deleted a verification is performed in order to check if this deletion would create topological inconsisten- cies. This was done by using arbitrary precision rational numbers to completely avoid errors caused by floating-point arithmetic.EPLSimpwas carefully imple- mented to be efficient, although using rational numbers adds an overhead to the computation. This efficiency was achieved by using a uniform grid for indexing the geometric data and parallel computing to speedup the process.

[1]  Tommy Färnqvist.  Number Theory Meets Cache Locality – Efficient Implementation of a Small Prime FFT for the GNU Multiple Precision Arithmetic Library , 2005 .

[2]  Urs Ramer,et al.  An iterative procedure for the polygonal approximation of plane curves , 1972, Comput. Graph. Image Process..

[3]  John D. Hobby,et al.  Practical segment intersection with finite precision output , 1999, Comput. Geom..

[4]  GoldbergDavid,et al.  "What Every Computer Scientist Should Know About Floating-Point Arithmetic" , 1991, ACM Comput. Surv..

[5]  A. Saalfeld.  Topologically Consistent Line Simplification with the Douglas-Peucker Algorithm , 1999 .

[6]  Thomas K. Peucker,et al.  2. Algorithms for the Reduction of the Number of Points Required to Represent a Digitized Line or its Caricature , 2011 .

[7]  John Hershberger.  Stable snap rounding , 2013, Comput. Geom..

[8]  J. D. Whyatt,et al.  Line generalisation by repeated elimination of points , 1993 .

[9]  Wenli Li,et al.  An Efficient and Topologically Correct Map Generalization Heuristic , 2015, ICEIS.

[10]  Bin Jiang,et al.  Scaling of Geographic Space as a Universal Rule for Map Generalization , 2011, 1102.1561.

[11]  Chee-Keng Yap,et al.  Recent progress in exact geometric computation , 2005, J. Log. Algebraic Methods Program..

[12]  Kurt Mehlhorn,et al.  Classroom Examples of Robustness Problems in Geometric Computations , 2004, ESA.

[13]  Mark de Berg,et al.  An intersection-sensitive algorithm for snap rounding , 2007, Comput. Geom..

[14]  David H. Douglas,et al.  ALGORITHMS FOR THE REDUCTION OF THE NUMBER OF POINTS REQUIRED TO REPRESENT A DIGITIZED LINE OR ITS CARICATURE , 1973 .