Algorithms for Path Simplification, Ph.D. Dissertation Sharif University of Technology ; Ghodsi, Mohammad (Supervisor)
Abstract
In this thesis, we present different algorithms for path simplification. We first study this problem under area measures. We present an approximation algorithm for sum-area measure and an optimal algorithm for diff-area measure. Both of these algorithms can be applied on general paths. Moreover, we study the homotopic path simplification. We present a general framework for path simplification which work for desired error measure. We first present a strongly homotopic simplification algorithm for x-monotone paths. Also, we study the strongly homotopic simplification for general paths. We present a geometric tree data structure and present an algorithm based on this data structure....
Cataloging briefAlgorithms for Path Simplification, Ph.D. Dissertation Sharif University of Technology ; Ghodsi, Mohammad (Supervisor)
Abstract
In this thesis, we present different algorithms for path simplification. We first study this problem under area measures. We present an approximation algorithm for sum-area measure and an optimal algorithm for diff-area measure. Both of these algorithms can be applied on general paths. Moreover, we study the homotopic path simplification. We present a general framework for path simplification which work for desired error measure. We first present a strongly homotopic simplification algorithm for x-monotone paths. Also, we study the strongly homotopic simplification for general paths. We present a geometric tree data structure and present an algorithm based on this data structure....
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