Computing similarity between piecewise-linear functions
Document typeConference report
PublisherACM Press. Association for Computing Machinery
Rights accessOpen Access
We study the problem of computing the similarity between two piecewise-linear bivariate functions de ned over a common domain, where the surfaces they de ne in 3D|polyhedral terrains|can be transformed vertically by a linear transformation of the third coordinate (scaling and translation). We present a randomized algorithm that minimizes the maximum vertical distance between the graphs of the two functions, over all linear transformations of one of the terrains, in O(n4=3 polylog n) expected time, where n is the total number of vertices in the graphs of the two functions. We also study the computation of similarity between two univariate or bivariate functions by minimizing the area or volume between their graphs. For univariate functions we give a (1+")-approximation algorithm for minimizing the area that runs in O(n=p") time, for any xed " > 0. The (1 + ")- approximation algorithm for the bivariate version, where volume is minimized, runs in O(n="2) time, for any xed " > 0, provided the two functions are de ned over the same triangulation of their domain.
CitationAgarwal, P.K. [et al.]. Computing similarity between piecewise-linear functions. A: ACM Symposium on Computational Geometry. "2010 annual symposium on Computational geometry". Snowbird, Utah: ACM Press. Association for Computing Machinery, 2010, p. 375-383.